Describtion and Pratical Application of Electrical Components

DESCRIBTION AND PRATICAL APPLICATION OF ELECTRICAL COMPONENTS

NAME: AMAN VIKASH CHAND
ID NO. : 2011001207
GROUP: TDEEN 1A
TEACHER: MR. WILLIAM FONG
YEAR: 2011

|RESISTORS |
|Resistors(R) are a two-terminal passive electronic component which implements electrical resistance as a circuit element. They are purposely placed in electric |
|circuits to reduce voltage values and limit current flow. |
|Resistors are the most fundamental and commonly used of all the electronic components. |
|There are many different Types of Resistors available to the electronics constructor, from very small surface mount chip resistors up to large wirewound power |
|resistors. |
|The principal job of a resistor within an electrical or electronic circuit is to "resist" or to impede the flow of electrons through them by using the type of |
|material that they are composed from. |
|Resistors can also act as voltage droppers or voltage dividers within a circuit. |
|[pic] |
|A Typical Resistor |
|Resistors are "Passive Devices", that is they contain no source of power or amplification but only attenuate or reduce the voltage signal passing through them. |
|This attenuation results in electrical energy being lost in the form of heat as the resistor resists the flow of electrons through it. |
|Then a potential difference is required between the two terminals of a resistor for current to flow. This potential difference balances out the energy lost. |
|When used in DC circuits the potential difference, also known as a resistors voltage drop, is measured across the terminals as the circuit current flows through the |
|resistor. |
|“Most resistors are linear devices that produce a voltage drop across themselves when an electrical current flow through them because they obey Ohm's Law and |
|different values of resistance produces different values of current or voltage. This can be very useful in Electronic circuits by controlling or reducing either the |
|current flow or voltage produced across them.” |
|There are many thousands of different Types of Resistors and are produced in a variety of forms. |
|This is because of their particular characteristics and accuracy suit certain areas of application, such as High Stability, High Voltage, High Current etc, or are |
|used as general purpose resistors where their characteristics are less of a problem. |
|Some of the common characteristics associated with the humble resistor are; Temperature Coefficient, Voltage Coefficient, Noise, Frequency Response, Power as well as |
|Temperature Rating, Physical Size and Reliability. |
|“In all Electrical and Electronic circuit diagrams and schematics, the most commonly used symbol for a fixed value resistor is that of a "zig-zag" type line with the |
|value of its resistance given in Ohms, Ω. Resistors have fixed resistance values from less than one ohm, ( 10MΩ ) in |
|value. Fixed resistors have only one single value of resistance, for example 100Ω's but variable resistors (potentiometers) can provide an infinite number of |
|resistance values between zero and their maximum value.” |
| |
|Standard Resistor Symbols |
|[pic] |
|The symbol used in schematic and electrical drawings for a Resistor can either be a "zig-zag" type line or a rectangular box. |
| |
|All modern fixed value resistors can be classified into four broad groups; |
|Carbon Composition Resistor - Made of carbon dust or graphite paste, low wattage values |
|Film or Cermet Resistor - Made from conductive metal oxide paste, very low wattage values |
|Wire-wound Resistor - Metallic bodies for heatsink mounting, very high wattage ratings |
|Semiconductor Resistor - High frequency/precision surface mount thin film technology |
|Composition Type Resistors |
|Carbon Resistors are the most common type of Composition Resistors. |
|Carbon resistors are a cheap general purpose resistor used in electrical and electronic circuits. |
|Their resistive element is manufactured from a mixture of finely ground carbon dust or graphite (similar to pencil lead) and a non-conducting ceramic (clay) powder to|
|bind it all together. |
|[pic] |
|Carbon Resistor |
|“The ratio of carbon dust to ceramic (conductor to insulator) determines the overall resistive value of the mixture and the higher the ratio of carbon, the lower the |
|overall resistance. The mixture is moulded into a cylindrical shape with metal wires or leads are attached to each end to provide the electrical connection as shown, |
|before being coated with an outer insulating material and colour coded markings to denote its resistive value.” |
| |
| |
|Carbon Resistor |
|[pic] |
| |
|The Carbon Composite Resistor is a low to medium type power resistor. |
|Has a low inductance making them ideal for high frequency applications. |
|However, they can also suffer from noise and stability when hot. |
|“Carbon composite resistors are generally prefixed with a "CR" notation (e.g. CR10kΩ) and are available in E6 (±20% tolerance (accuracy), E12 ( ±10% tolerance) and |
|E24 ( ±5% tolerance) packages with power ratings from 0.125 or 1/4 of a Watt up to 2 Watts.” |
|Carbon composite resistors are very cheap to make and are therefore commonly used in electrical circuits. |
|But, due to their manufacturing process carbon type resistors have very large tolerances so for more precision and high value resistances, film type resistors are |
|used instead. |
|Film Type Resistors |
|“The generic term “Film Resistor” consists of Metal Film, Carbon Film and Metal Oxide Film resistor types, which are generally made by depositing pure metals, such as|
|nickel, or an oxide film, such as tin-oxide, onto an insulating ceramic rod or substrate.” |
|[pic] Film Resistor |
|The resistive value of the resistor is controlled by increasing the desired thickness of the deposited film giving them the names of either "thick-film resistors" or |
|"thin-film resistors". |
|Once deposited, a laser is used to cut a high precision spiral helix groove type pattern into this film. |
|The cutting of the film has the effect of increasing the conductive or resistive path, a bit like taking a long length of straight wire and forming it into a coil. |
| |
|“This method of manufacture allows for much closer tolerance resistors (1% or less) as compared to the simpler carbon composition types. The tolerance of a resistor |
|is the difference between the preferred value (i.e., 100 ohms) and its actual manufactured value i.e., 103.6 ohms, and is expressed as a percentage, for example 5%, |
|10% etc, and in our example the actual tolerance is 3.6%. Film type resistors also achieve a much higher maximum ohmic value compared to other types and values in |
|excess of 10MΩ (10 Million Ω´s) are available.” |
|Film Resistor |
|[pic] |
| |
|Metal Film Resistors have much better temperature stability than their carbon equivalents, lower noise and are generally better for high frequency or radio frequency |
|applications. |
|Metal Oxide Resistors have better high surge current capability with a much higher temperature rating than the equivalent metal film resistors. |
|“Another type of film resistor commonly known as a Thick Film Resistor is manufactured by depositing a much thicker conductive paste of Ceramic and Metal, called |
|Cermet, onto an alumina ceramic substrate.” |
|Cermet resistors have similar properties to metal film resistors and are generally used for making small surface mount chip type resistors, multi-resistor networks in|
|one package for pub’s and high frequency resistors. |
|They have good temperature stability, low noise, and good voltage ratings but low surge current properties. |
|“Metal Film Resistors are prefixed with a "MFR" notation (e.g. MFR100kΩ) and a CF for Carbon Film types. Metal film resistors are available in E24 (±5% & ±2% |
|tolerances), E96 (±1% tolerance) and E192 (±0.5%, ±0.25% & ±0.1% tolerances) packages with power ratings of 0.05 (1/20th) of a Watt up to 1/2 Watt. Generally speaking|
|Film resistors are precision low power components.” |
|Wirewound Type Resistors |
|Another type of resistor, called a Wirewound Resistor, is made by winding a thin metal alloy wire (Nichrome) or similar wire onto an insulating ceramic former in the |
|form of a spiral helix similar to the film resistor above. |
|“These types of resistors are generally only available in very low ohmic high precision values (from 0.01 to 100kΩ) due to the gauge of the wire and number of turns |
|possible on the former making them ideal for use in measuring circuits and Whetstone bridge type applications”. |
|They are also able to handle much higher electrical currents than other resistors of the same ohmic value with power ratings in excess of 300 Watts. |
|These high power resistors are moulded or pressed into an aluminum heat sink body with fins attached to increase their overall surface area to promote heat loss and |
|cooling. |
|These types of resistors are called "Chassis Mounted Resistors". |
|They are designed to be physically mounted onto heatsinks or metal plates to further dissipate the generated heat increasing their current carrying capabilities even |
|further. |
|[pic] |
|Wirewound Resistor |
|Another type of wirewound resistor is the Power Wirewound Resistor. |
|These are high temperature, high power non-inductive resistor types generally coated with a vitreous or glass epoxy enamel for use in resistance banks or DC |
|motor/servo control and dynamic braking applications. |
|They can even be used as space or cabinet heaters. |
|The non-inductive resistance wire is wound around a ceramic or porcelain tube covered with mica to prevent the alloy wires from moving when hot. |
|Wirewound resistors are available in a variety of resistance and power ratings with one main use of power wirewound resistor is in the electrical heating elements of |
|an electric fire which converts the electrical current flowing through it into heat with each element dissipating up to 1000 Watts, (1kW) of energy. |
|Because the wire is wound into a coil, it acts like an inductor causing them to have inductance as well as resistance and this affects the way the resistor behaves in|
|AC circuits by producing a phase shift at high frequencies especially in the larger size resistors. |
|“The length of the actual resistance path in the resistor and the leads contributes inductance in series with the "apparent" DC resistance resulting in an overall |
|impedance path Z. impedance (Z) is the combined effect of resistance (R) and inductance (X), measured in ohms and for a series AC circuit is given as, Z2 = R2 + X2.” |
|When used in AC circuits this inductance value changes with frequency (inductive reactance, XL = 2πƒL) and therefore, the overall value of the resistor changes. |
|Inductive reactance increases with frequency but is zero at DC (zero frequency). |
|Then, wirewound resistors must not be designed into AC or amplifier type circuits where the frequency across the resistor changes. However, special non-inductive |
|wirewound resistors are also available. |
| |
|Wirewound Resistor |
|[pic] |
| |
| |
|”Wirewound resistor types are prefixed with a "WH" or "W" notation (e.g. WH10Ω) and are available in the WH aluminium cladded package (±1%, ±2%, ±5% & ±10% tolerance)|
|or the W vitreous enamelled package (±1%, ±2% & ±5% tolerance) with power ratings from 1W to 300W or more.” |

http://www.electronics-tutorials.ws/resistor/res_1.html

Resistor Colour Code

Resistors are available in a range of different resistance values from fractions of an Ohm (Ω) to millions of Ohms. Therefore, resistors are manufactured in what are called "preferred values" with their resistance value printed onto their body in coloured ink.
[pic]
4 Coloured Bands • The resistance value, tolerance, and wattage rating are generally printed onto the body of the resistor as numbers or letters when the resistors body is big enough to read the print, such as large power resistors. • But when the resistor is small such as a 1/4W carbon or film type, these specifications must be shown in some other manner as the print would be too small to read. So to overcome this, small resistors use coloured painted bands to indicate both their resistive value and their tolerance with the physical size of the resistor indicating its wattage rating. • These coloured painted bands produce a system of identification generally known as a Resistors Colour Code.
An international and universally accepted resistor colour coding scheme was developed many years ago as a simple and quick way of identifying a resistors value no matter what its size or condition. It consists of a set of individual coloured rings or bands in spectral order representing each digit of the resistors value. • The resistors colour code is always read one band at a time starting from the left to the right, with the larger width tolerance band oriented to the right side indicating its tolerance. • By matching the colour of the first band with its associated number in the digit column of the colour chart below the first digit is identified and this represents the first digit of the resistance value. • Again, by matching the colour of the second band with its associated number in the digit column of the colour chart we get the second digit of the resistance value and so on as illustrated below:

The Standard Resistor Colour Code Chart.
|[pic] |

The Resistor Colour Code Table.
|Colour |Digit |Multiplier |Tolerance |
|Black |0 |1 | |
|Brown |1 |10 |± 1% |
|Red |2 |100 |± 2% |
|Orange |3 |1,000 | |
|Yellow |4 |10,000 | |
|Green |5 |100,000 |± 0.5% |
|Blue |6 |1,000,000 |± 0.25% |
|Violet |7 |10,000,000 |± 0.1% |
|Grey |8 | | |
|White |9 | | |
|Gold | |0.1 |± 5% |
|Silver | |0.01 |± 10% |
|None | | |± 20% |

Calculating Resistor Values
The Resistor Colour Code system is all well and good but we need to understand how to apply it in order to get the correct value of the resistor. The "left-hand" or the most significant coloured band is the band which is nearest to a connecting lead with the colour coded bands being read from left-to-right as follows; • Digit, Digit, Multiplier = Colour, Colour x 10 colour in Ohm's (Ω's)
The fourth and fifth bands are used to determine the percentage tolerance of the resistor. Resistor tolerance is a measure of the resistors variation from the specified resistive value and is a consequence of the manufacturing process and is expressed as a percentage of its "nominal" or preferred value. Typical resistor tolerances for film resistors range from 1% to 10% while carbon resistors have tolerances up to 20%. Resistors with tolerances lower than 2% are called precision resistors with the or lower tolerance resistors being more expensive. Most five band resistors are precision resistors with tolerances of either 1% or 2% while most of the four band resistors have tolerances of 5%, 10% and 20%. The colour code used to denote the tolerance rating of a resistor is given as; • Brown = 1%, Red = 2%, Gold = 5%, Silver = 10 %
If resistor has no fourth tolerance band then the default tolerance would be at 20%.
The British Standard (BS 1852) Code.
Generally on larger power resistors, the resistance value, tolerance, and even the power (wattage) rating are printed onto the actual body of the resistor instead of using the resistor colour code system. Because it is very easy to "misread" the position of a decimal point or comma especially when the component is dirty, an easier system for writing and printing the resistance values of the individual resistance was developed. This system conforms to the British Standard BS 1852 Standard and its replacement, BS EN 60062, coding method were the decimal point position is replaced by the suffix letters "K" for thousands or kilo-ohms, the letter "M" for millions or mega ohms both of which denotes the multiplier value with the letter "R" used where the multiplier is equal to, or less than one, with any number coming after these letters meaning it's equivalent to a decimal point.
The BS 1852 Letter Coding for Resistors.
|BS 1852 Codes for Resistor Values |
|0.47Ω = R47 or 0R47 |
|1.0Ω = 1R0 |
|4.7Ω = 4R7 |
|47Ω = 47R |
|470Ω = 470R or 0K47 |
|1.0KΩ = 1K0 |
|4.7KΩ = 4K7 |
|47KΩ = 47K |
|470KΩ = 470K or 0M47 |
|1MΩ = 1M0 |

Sometimes depending upon the manufacturer, after the written resistance value there is an additional letter which represents the resistors tolerance value such as 4k7 J and these suffix letters are given as.

Tolerance Letter Coding for Resistors.
|Tolerance Codes for Resistors (±) |
|B = 0.1% |
|C = 0.25% |
|D = 0.5% |
|F = 1% |
|G = 2% |
|J = 5% |
|K = 10% |
|M = 20% |

Also, when reading these written codes is careful not to confuse the resistance letter k for kilo-ohms with the tolerance letter K for 10% tolerance or the resistance letter M for mega ohms with the tolerance letter M for 20% tolerance.
Tolerances, E-series & Preferred Values. o Resistors come in a variety of sizes and resistance values but to have a resistor available of every possible resistance value, literally hundreds of thousands; if not millions of individual resistors would need to exist. Instead, resistors are manufactured in what are commonly known as Preferred values. o Instead of sequential values of resistance from 1Ω and upwards, certain values of resistors exist within certain tolerance limits. o The tolerance of a resistor is the maximum difference between its actual value and the required value and is generally expressed as a plus or minus percentage value. o “In most electrical or electronic circuits the large 20% tolerance of the resistor is generally not a problem, but when close tolerance resistors are specified for high accuracy circuits such as filters or oscillators etc, then the correct tolerance resistor needs to be used, as a 20% tolerance resistor cannot generally be used to replace 2% or even a 1% tolerance type.” o The five and six band resistor colour code is more commonly associated with the high precision 1% and 2% film types while the common garden variety 5% and 10% general purpose types tend to use the four band resistor colour code. o “Resistors come in a range of tolerances but the two most common are the E12 and the E24 series. The E12 series comes in twelve resistance values per decade, (A decade represents multiples of 10, i.e. 10, 100, 1000 etc). The E24 series comes in twenty four values per decade and the E96 series ninety six values per decade. “ o A very high precision E192 series is now available with tolerances as low as ±0.1% giving a massive 192 separate resistor values per decade.
Tolerance and E-series Table.
|E6 Series at 20% Tolerance - Resistors values in Ω's |
|1.0, 1.5, 2.2, 3.3, 4.7, 6.8 |
|E12 Series at 10% Tolerance - Resistors values in Ω's |
|1.0, 1.2, 1.5, 1.8, 2.2, 2.7, 3.3, 3.9, 4.7, 5.6, 6.8, 8.2 |
|E24 Series at 5% Tolerance - Resistors values in Ω's |
|1.0, 1.1, 1.2, 1.3, 1.5, 1.6, 1.8, 2.0, 2.2, 2.4, 2.7, 3.0, 3.3, 3.6, 3.9, 4.3, 4.7, 5.1, 5.6, 6.2, 6.8, 7.2, 8.2, 9.1 |
|E96 Series at 1% Tolerance - Resistors values in Ω's |
|1.00, 1.02, 1.05, 1.07, 1.10, 1.13, 1.15, 1.18, 1.21, 1.24, 1.27, 1.30, 1.33, 1.37, 1.40, 1.43, 1.47, 1.50, 1.54, 1.58, 1.62, |
|1.65, 1.69, 1.74, 1.78, 1.82, 1.87, 1.91, 1.96, 2.00, 2.05, 2.10, 2.15, 2.21, 2.26, 2.32, 2.37, 2.43, 2.49, 2.55, 2.61, 2.77, |
|2.74, 2.80, 2.87, 2.94, 3.01, 3.09, 3.16, 3.24, 3.32, 3.40, 3.48, 3.57, 3.65, 3.74, 3.83, 3.92, 4.02, 4.12, 4.22, 4.32, 4.42, |
|4.53, 4.64, 4.75, 4.87, 4.99, 5.11, 5.23, 5.36, 5.49, 5.62, 5.76, 5.90, 6.04, 6.19, 6.34, 6.49, 6.65, 6.81, 6.98, 7.15, 7.32, |
|7.50, 7.68, 7.87, 8.06, 8.25, 8.45, 8.66, 8.87, 9.09, 9.31, 9.53, 9.76 |

Then by using the appropriate E-series value and adding a multiplication factor to it, any value of resistance within that series can be found. For example, take an E-12 series resistor, 10% tolerance with a preferred value of 3.3, and then the values of resistance for this range are:
|Value x Multiplier = Resistance |
|3.3 x 1 = 3.3Ω |
|3.3 x 10 = 33Ω |
|3.3 x 100 = 330Ω |
|3.3 x 1,000 = 3.3kΩ |
|3.3 x 10,000 = 33kΩ |
|3.3 x 100,000 = 330kΩ |
|3.3 x 1,000,000 = 3.3MΩ |

The mathematical basis behind these preferred values comes from the square root value of the actual series being used. The tolerance series of Preferred Values shown above are manufactured to conform to the British Standard BS 2488 and are ranges of resistor values chosen so that at maximum or minimum tolerance any one resistor overlaps with its neighbouring value.
Surface Mount Resistors
[pic]
4.7kΩ SMD Resistor • Surface Mount Resistors or SMD Resistors are very small rectangular shaped metal oxide film resistor. They have a ceramic substrate body onto which is deposited a thick layer of metal oxide resistance. • “The resistive value of the resistor is controlled by increasing the desired thickness, length or type of deposited film being used and highly accurate low tolerance resistors, down to 0.1% can be produced. “ • They also have metal terminals or caps at either end of the body which allows them to be soldered directly onto printed circuit boards. • Surface Mount Resistors are printed with either a 3 or 4-digit numerical code which is similar to that used on the more common axial type resistors to denote their resistive value. • Standard SMD resistors are marked with a three-digit code, in which the first two digits represent the first two numbers of the resistance value with the third digit being the multiplier, either x1, x10, x100 etc. • Surface mount resistors that have a value of less than 100Ω's are usually written as: "390", "470", "560" with the final zero representing a 10 xo multiplier, which is equivalent to 1. • Resistance values below ten have a letter "R" to denote the position of the decimal point as seen previously in the BS1852 form, so that 4R7 = 4.7Ω. • Surface mount resistors that have a "000" or "0000" markings are zero-Ohm (0Ω) resistors or in other words shorting links, since these components have zero resistance. http://www.electronics-tutorials.ws/resistor/res_2.html

Connecting Resistors Together • Individual resistors can be connected together in a series connection, a parallel connection or combinations of both series and parallel together, to produce more complex networks whose equivalent resistance is a combination of the individual resistors. • Then complicated networks of resistors or impedances can be replaced by a single equivalent resistor or impedance. Whatever the combination or complexity of the circuit, all resistors obey Ohm's Law and Kirchoff's Circuit Laws.
Resistors in Series. ❖ Resistors are said to be connected in "Series", when they are daisy chained together in a single line. Since all the current flowing through the first resistor has no other way to go it must also pass through the second resistor and the third and so on. Then, resistors in series have a Common Current flowing through them as the current that flows through one resistor must also flow through the others as it can only take one path. ❖ Then the amount of current that flows through a set of resistors in series is the same at all points in a series circuit. For instance:
[pic]

Series Resistor Circuit
|[pic] |

As the resistors are connected together in series the same current passes through each resistor in the chain and the total resistance, RT of the circuit must be equal to the sum of all the individual resistors added together.
[pic]

[pic]
Where four, five or even more resistors are all connected together in a series circuit, the total or equivalent resistance of the circuit, RT would still be the sum of all the individual resistors connected together and the more resistors added to the series, the greater the equivalent resistance (no matter what their value). This total resistance is generally known as the Equivalent Resistance and can be defined as;”a single value of resistance that can replace any number of resistors without altering the values of the current or the voltage in the circuit". Then the equation given for calculating total resistance of the circuit when resistors are connected together in series is given as:
Series Resistor Equation
Rtotal = R1 + R2 + R3 + ..... Rn etc. • The total or equivalent resistance, RT has the same effect on the circuit as the original combination of resistors as it is the algebraic sum of the individual resistances. • The total resistance (RT) of any two or more resistors connected together in series will always be GREATER than the value of the largest resistor in the chain.

Series Resistor Voltage
The equation given for calculating the total voltage in a series circuit which is the sum of all the individual voltages added together is given as:
[pic]
Then series resistor networks can also be thought of as "voltage dividers" and a series resistor circuit having N resistive components will have N-different voltages across it while maintaining a common current.
By using Ohm's Law, either the voltage, current or resistance of any series connected circuit can easily be found and resistor of a series circuit can be interchanged without affecting the total resistance, current, or power to each resistor.
The Potential Divider Circuit ✓ Connecting resistors in series like this across a single DC supply voltage has one major advantage, different voltages appear across each resistor with the amount of voltage being determined by the resistors value only because as we now know, the current through a series circuit is common. ✓ This ability to generate different voltages produces a circuit called a Potential or Voltage Divider Network. ✓ Kirchoff's voltage laws states that "the supply voltage in a closed circuit is equal to the sum of all the voltage drops (IR) around the circuit" and this can be used to good effect as this allows us to determine the voltage levels of a circuit without first finding the current.
The basic circuit for a potential divider network (also known as a voltage divider) for resistors in series is shown below.
Potential Divider Network
|[pic] |

In this circuit the two resistors are connected in series across Vin, which is the power supply voltage connected to the resistor, R1, where the output voltage Vout is the voltage across the resistor R2 which is given by the formula. If more resistors are connected in series to the circuit then different voltages will appear across each resistor with regards to their individual resistance R (Ohms law IxR) providing different voltage points from a single supply. However, care must be taken when using this type of network as the impedance of any load connected to it can affect the output voltage The higher the load impedance the less is the loading effect on the output.

Resistors in Series Applications
Resistors in series can be used to produce different voltages across themselves and this type of resistor network is very useful for producing a voltage divider network. If replace one of the resistors in the voltage divider circuit above with a Sensor such as a thermistor, light dependant resistor (LDR) or even a switch, it can be convert an analogue quantity being sensed into a suitable electrical signal which is capable of being measured.
For example, the following thermistor circuit has a resistance of 10KΩ at 25°C and a resistance of 100Ω at 100°C. Calculate the output voltage (Vout) for both temperatures.
Thermistor Circuit
[pic]
At 25°C
[pic]
At 100°C
[pic]
By changing the fixed 1KΩ resistor, R2 in our simple circuit above to a variable resistor or potentiometer, a particular output voltage set point can be obtained over a wider temperature range.
Resistors in Series Summary • When two or more resistors are connected together end-to-end in a single branch they are said to be connected together in series. • Resistors in Series carry the same current, but the potential differences across them are not the same. • In a series circuit the individual resistors add together to give the equivalent resistance, ( RT ) of the series combination. • The resistors in a series circuit can be interchanged without affecting the total resistance, current, or power to each resistor or the circuit. http://www.electronics-tutorials.ws/resistor/res_3.html Resistors in Parallel ▪ Resistors are said to be connected together in "Parallel" when both of their terminals are respectively connected to each terminal of the other resistor or resistors. ▪ Unlike the previous series circuit, in parallel circuits the current can take more than one path and because there are multiple paths the current is not the same at all points in a parallel circuit. ▪ However, the voltage drop across all of the resistors in a parallel circuit is the same. ▪ Then, Resistors in Parallel have a Common Voltage across them and is true for all parallel elements.
Parallel circuits as one were the resistors are connected to the same two points (or nodes) and are identified by the fact that it has more than one current path connected to a common voltage source. In the circuit diagram below the voltage across resistor R1 equals the voltage across resistor R2 which equals the voltage across R3 and all equal the supply voltage and is therefore given as:
[pic]

Parallel Resistor Circuit
|[pic] |

Parallel Resistor Equation
[pic]

The inverse of the equivalent resistance of two or more resistors connected in parallel is the algebraic sum of the inverses of the individual resistances. The equivalent resistance is always less than the smallest resistor in the parallel network so the total resistance, RT will always decrease as additional parallel resistors are added.
Parallel resistance gives us a value known as Conductance, symbol G with the units of conductance being the Siemens, symbol S. Conductance is the reciprocal or the inverse of resistance, (G = 1/R).

The method of calculation can be used for calculating any number of individual resistances connected together within a single parallel network. If however, there are only two individual resistors in parallel then a much simpler and quicker formula can be used to find the total resistance value, and this is given as:
[pic]
❖ Total circuit resistance (RT) of any two resistors connected together in parallel will always be LESS than the value of the smallest resistor. ❖ In other words, the equivalent resistance of a parallel network is always less than the smallest individual resistor in the combination.

Currents in a Parallel Resistor Circuit o The total current, IT in a parallel resistor circuit is the sum of the individual currents flowing in all the parallel branches. o The amount of current flowing in each parallel branch is not necessarily the same as the value of the resistance in each branch determines the current within that branch. o For instant, although the parallel combination has the same voltage across it, the resistances could be different therefore the current flowing through each resistor would definitely be different as determined by Ohms Law.
The current that flows through each of the resistors connected together in parallel is not necessarily the same value as it depends upon the resistive value of the resistor. Kirchoff's Current Laws. States that "the total current leaving a circuit is equal to that entering the circuit - no current is lost". Thus, the total current flowing in the circuit is given as:
IT = IR1 + IR2

The equation given for calculating the total current flowing in a parallel resistor circuit which is the sum of all the individual currents added together is given as:
Itotal = I1 + I2 + I3 ..... + In “Then parallel resistor networks can also be thought of as a "current divider" because the current splits or divides between the various branches and a parallel resistor circuit having N resistive networks will have N-different current paths while maintaining a common voltage. Parallel resistors can also be interchanged without changing the total resistance or the total circuit current. As the supply voltage is common to all the resistors in a parallel circuit, Ohms Law is used to calculate the individual branch current.”
Resistors in Parallel Summary • When two or more resistors are connected so that both of their terminals are respectively connected to each terminal of the other resistor or resistors, they are said to be connected together in parallel. • The potential differences across each resistor in the parallel combination are the same but the currents flowing through them are not the same. • The equivalent or total resistance, RT of a parallel combination is found through reciprocal addition and the total resistance value will always be less than the smallest individual resistor in the combination. • Parallel resistors can be interchanged within the same combination without changing the total resistance or total circuit current. • Resistors connected together in a parallel circuit will continue to operate even though one resistor may be open-circuited. http://www.electronics-tutorials.ws/resistor/res_4.html Resistor Combinations
Resistor circuits that combine series and parallel resistors circuits together are generally known as Resistor Combination or mixed circuits and the method of calculating their equivalent resistance is the same as that for any individual series or parallel circuit..
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✓ Any complicated circuit consisting of several resistors can be reduced to a simple circuit with only one equivalent resistor by replacing the resistors in series or in parallel using the steps above. ✓ It is sometimes easier with complex resistor combinations to sketch or redraw the new circuit after these changes have been made as a visual aid to the maths. ✓ Then continue to replace any series or parallel combinations until one equivalent resistance is found. http://www.electronics-tutorials.ws/resistor/res_5.html

Potential Difference ➢ The voltage difference between any two points in a circuit is known as the Potential Difference, pd or Voltage Drop and it is the difference between these two points that makes the current flow. Unlike current which flows around a circuit in the form of electrical charge, potential difference does not move it is applied. ➢ The unit of potential difference is the volt and is defined as the potential difference across a resistance of one ohm carrying a current of one ampere. In other words, V = I.R ➢ Ohm's Law states that for a linear circuits the current flowing through it is proportional to the potential difference across it so the greater the potential difference across any two points the bigger will be the current flowing through it. ➢ The voltage at any point in a circuit is always measured with respect to a common point, generally 0V. ➢ For electrical circuits, the earth or ground potential is usually taken to be at zero volts (0V) and everything is referenced to that common point in a circuit. ➢ This is similar in theory to measuring height. Measuringt the height of hills in a similar way by saying that the sea level is at zero feet and then compare other points of the hill or mountain to that level. In the same way we call the common point in a circuit zero volts and give it the name of ground, zero volts or earth, then all other voltage points in the circuit are compared or referenced to that ground point. ➢ The use of a common ground or reference point in electrical schematic drawings allows the circuit to be drawn more simply as it is understood that all connections to this point have the same potential.
Potential Difference
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As the units of measure for Potential Difference are volts, potential difference is mainly called voltage. Individual voltages connected in series can be added together to give us a "total voltage" sum of the circuit. Voltages across components that are connected in parallel will always be of the same value. for series connected voltages,
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Voltage Divider Connecting together resistors in series across a potential difference we can produce a voltage divider circuit giving ratios of voltages with respect to the supply voltage across the series combination. This then produces a Voltage Divider network that only applies to resistors in series as parallel resistors produce a current divider network.

Voltage Division
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The circuit shows the principal of a voltage divider circuit where the output voltage drops across each resistor, R1, R2, R3 and R4 are referenced to a common point. For any number of resistors connected together in series the total resistance, RT of the circuit divided by the supply voltage Vs will give the circuit current as I = Vs/RT, Ohm's Law. Then the individual voltage drops across each resistor can be simply calculated as: V = IxR.
The voltage at each point, P1, P2, P3 etc increases according to the sum of the voltages at each point up to the supply voltage, Vs and also calculate the individual voltage drops at any point without firstly calculating the circuit current by using the following formula.

Voltage Divider Equation
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Where, V(x) is the voltage to be found, R(x) is the resistance producing the voltage, RT is the total series resistance and VS is the supply voltage. • Then by using this equation it can be said that the voltage dropped across any resistor in a series circuit is proportional to the magnitude of the resistor and the total voltage dropped across all the resistors must equal the voltage source as defined by Kirchoff's Voltage Law. • So by using the Voltage Divider Equation, for any number of series resistors the voltage drop across any individual resistor can be found. • Thus, voltage is applied to a resistor or circuit and that current flow through and around a circuit. But there is a third variable we can apply to resistors. • Power is a product of voltage and current and the basic unit of measurement of power is the watt. http://www.electronics-tutorials.ws/resistor/res_6.html

Resistor Power Rating o When an electrical current passes through a resistor, electrical energy is lost by the resistor in the form of heat and the greater this current flow the hotter the resistor will get. o Resistors are rated by the value of their resistance and the power in watts that they can safely dissipate based mainly upon their size. o Every resistor has a maximum power rating which is determined by its physical size as generally, the greater its surface area the more power it can dissipate safely into the ambient air or into a heatsink. o A resistor can be used at any combination of voltage (within reason) and current so long as its "Dissipating Power Rating" is not exceeded with the resistor power rating indicating how much power the resistor can convert into heat or absorb without any damage to itself. o The Resistor Power Rating is sometimes called the Resistors Wattage Rating and is defined as the amount of heat that a resistive element can dissipate for an indefinite period of time without degrading its performance. o The power rating of resistors varies a lot from less than one tenth of a watt to many hundreds of watts depending upon its size, construction and ambient operating temperature. o Most resistors have their maximum resistive power rating given for an ambient temperature of +70oC or below. o Electrical power is the rate in time at which energy is used or consumed (converted into heat).
Resistor Power (P) ▪ It is known from Ohm's Law that when a voltage is dropped across a resistor, a current will be passed through the resistor producing a product of power. ▪ “ In other words, if a resistor is subjected to a voltage, or if it conducts a current, then it will always consume power and we can superimpose these three quantities of power, voltage and current into a triangle called a Power Triangle with the power dissipated as heat in a resistor at the top and the current and the voltage at the bottom as shown.”
The Resistor Power Triangle
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Then by using Ohm's Law again, it is possible to obtain two alternative variations of the above expression for resistive power if the value of two for the voltage, the current or the resistance as follows:
[P = V2 ÷ R] Power = Volts2 ÷ Ohms
[P = I2 x R] Power = Current2 x Ohms
Then the power dissipation of any resistor can be calculated using the following three standard formulas:
[pic]
Where, • V is the voltage across the resistor in volts • I is in current flowing through the resistor in amperes • R is the resistance of the resistor in Ohm´s (Ω)

”As the dissipated power rating of a resistor is linked to their physical size, a 1/4 (0.250)W resistor is physically smaller than a 1W resistor, and resistors that are of the same ohmic value are also available in different power or wattage ratings. Generally, the larger their physical size the higher its wattage rating. However, it is always better to select a particular size resistor that is capable of dissipating two or more times the calculated power. When resistors with higher wattage ratings are required, wirewound resistors are generally used to dissipate the excessive heat."
|Type |Power Rating |Stability |
|Metal Film |Very low at less than 3W |High 1% |
|Carbon |Low at less than 5W |Low 20% |
|Wirewound |High up to 500W |High 1% |

Power Resistors ▪ Wirewound power resistors come in a variety of designs and types, from the standard smaller heatsink mounted aluminium body 25W types as we have seen previously, to the larger tubular 1000W ceramic or porcelain power resistors used for heating elements. ▪ The resistance value of wirewound resistors is very low (low ohmic values) compared to the carbon or metal film types and range from less than 1Ω (R005) up to only 100kΩ´s as larger resistance values would require fine gauge wire that would easily fail. ▪ Low ohmic, low power value resistors are generally used for current sensing applications were, using ohm´s law the current flowing through the resistance gives rise to a voltage drop across it. ▪ This voltage can be measured to determine the value of the current flowing in the circuit. This type of resistor is used in test measuring equipment and controlled power supplies. ▪ The larger wirewound power resistors are made of corrosion resistant wire wound onto a porcelain or ceramic core type former and are generally used to dissipate high inrush currents such as those generated in motor control, electromagnet or elevator/crane control and motor braking circuits. ▪ These types of resistors have standard power ratings up to 500W and are connected together to form resistance banks. ▪ Another useful feature of wirewound power resistors is in the use of heating elements like the ones used for electric fires, toaster, irons etc. ▪ In this type of application the wattage value of the resistance is used to produce heat and the type of alloy resistance wire used is generally made of Nickel-Chrome (Nichrome) allowing temperatures up to 1200oC.All resistors whether carbon, metal film or wirewound obey Ohm´s Law when calculating their maximum power (wattage) value. ▪ It is also worth noting that when two resistors are connected in parallel then their overall power rating is increased. ▪ If both resistors are of the same value and of the same power rating, then the total power rating is doubled. http://www.electronics-tutorials.ws/resistor/res_7.html Resistors in AC Circuits
“In all cases both the voltage and current has been assumed to be of a constant polarity, run and route, in other words Direct Current or DC. But there is another type of supply known as Alternating Current or AC whose voltage switches polarity from positive to negative and back again over time and also whose current with respect to the voltage oscillates back and forth. The oscillating shape of an AC supply follows that of the mathematical form of a "Sine wave" which is commonly called a Sinusoidal Waveform. Therefore, a sinusoidal voltage can be defined as V(t) = Vmax sin ωt.” ▪ When using pure resistors in AC circuits that have negligible values of inductance or capacitance, the same principals of Ohm's Law, circuit rules for voltage, current and power (and even Kirchoff's Laws) apply as they do for DC resistive circuits the only difference this time is in the use of the instantaneous "peak-to-peak" or "rms" quantities. When working with such rules it is usual to use only "rms" values. ▪ Also the symbol used for defining an AC voltage source is that of a "wavy" line as opposed to a battery symbol for DC and this is shown below.
Symbol Representation of DC and AC Supplies
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▪ Resistors are “passive” devices that are they do not produce or consume any electrical energy, but convert electrical energy into heat. In DC circuits the linear ratio of voltage to current in a resistor is called its resistance. ▪ However, in AC circuits this ratio of voltage to current depends upon the frequency and phase difference or phase angle (φ) of the supply. So when using resistors in AC circuits the term Impedance, symbol Z is the generally used and can be said that DC resistance = AC impedance, R = Z. ▪ For resistors in AC circuits the direction of the current flowing through them has no effect on the behavior of the resistor so will rise and fall as the voltage rises and falls. ▪ The current and voltage reach maximum, fall through zero and reach minimum at exactly the same time. i.e, they rise and fall simultaneously and are said to be "in-phase" as shown below.
V-I Phase Relationship and Vector Diagram
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Point along the horizontal axis that the instantaneous voltage and current are in-phase because the current and the voltage reach their maximum values at the same time, that is their phase angle θ is 0o. Then these instantaneous values of voltage and current can be compared to give the ohmic value of the resistance simply by using ohms law. Consider below the circuit consisting of an AC source and a resistor.
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The instantaneous voltage across the resistor, VR is equal to the supply voltage, Vt and is given as:
[pic]

The instantaneous current flowing in the resistor will therefore be:
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As the voltage across a resistor is given as VR = I.R, the instantaneous voltage across the resistor above can also be given as:
[pic]
• In purely resistive series AC circuits, all the voltage drops across the resistors can be added together to find the total circuit voltage as all the voltages are in-phase with each other. • Likewise, in a purely resistive parallel AC circuit, all the individual branch currents can be added together to find the total circuit current because all the branch currents are in-phase with each other. “Since for resistors in AC circuits the phase angle φ between the voltage and the current is zero, then the power factor of the circuit is given as cos 0o = 1.0. The power in the circuit at any instant in time can be found by multiplying the voltage and current at that instant. Then the power (P), consumed by the circuit is given as P = Vrms Ι cos Φ in watt's. But since cos Φ = 1 in a purely resistive circuit, the power consumed is simply given as, P = Vrms Ι the same as for Ohm's Law.” • This then gives us the "Power" waveform and which is shown below as a series of positive pulses because when the voltage and current are both in their positive half of the cycle the resultant power is positive. • When the voltage and current are both negative, the product of the two negative values gives a positive power pulse.
Power Waveform in a Pure Resistance
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Then the power dissipated in a purely resistive load fed from an AC rms supply is the same as that for a resistor connected to a DC supply and is given as:
[pic]
Where, • P is the average power in Watts • Vrms is the rms supply voltage in Volts • Irms is the rms supply current in Amps • R is the resistance of the resistor in Ohm's (Ω) - should really be Z to indicate impedance
The heating effect produced by an AC current with a maximum value of Imax is not the same as that of a DC current of the same value. To compare the AC heating effect to an equivalent DC the rms values must be used. Any resistive heating element such as Electric Fires, Toasters, Kettles, Irons, Water Heaters etc can be classed as a resistive AC circuit and can use resistors in AC circuits to heat our homes and water. http://www.electronics-tutorials.ws/resistor/res_8.html Resistors Summary
• The work of a Resistor is to bind the current flow through an electrical circuit.
• Resistance is measured in Ohm's and is given the symbol Ω
• Carbon, Film and Wirewound are all types of resistors.
• Resistor colour codes are used to identify the resistance and tolerance rating of small resistors.
• The BS1852 Standard uses letters and is used to identify large size resistors.
• Tolerance is the percentage measure of the accuracy of a resistor from its preferred value with the E6 (20%), E12 (10%), E24 (5%) and E96 (1%) series of tolerance values available.

Series Resistors
• Resistors that are daisy chained together in a single line are said to be connected in SERIES.
• Series connected resistors have a common Current flowing through them. • Itotal = I1 = I2 = I3 .... etc
• The total circuit resistance of series resistors is equal to.
• Rtotal = R1 + R2 + R3 + ..... Rn etc. •
• Total circuit voltage is equal to the sum of all the individual voltage drops. • Vtotal = V1 + V2 + V3.... etc •
• The total resistance of a series connected circuit will always be greater than the highest value resistor.

Parallel Resistors
• Resistors that have both of their respective terminals connected to each terminal of another resistor or resistors are said to be connected in PARALLEL.
• Parallel resistors have a common Voltage across them. • VS = V1 = V2 = V3.... etc •
• Total resistance of a parallel circuit is equal to.
• [pic] •
• Total circuit current flow is equal to the sum of all the individual branch currents added together. • Itotal = I1 + I2 + I3.... etc •
• The total resistance of a parallel circuit will always be less than the value of the smallest resistor.

Resistor Power Rating
• The larger the power rating, the greater the physical size of the resistor.
• All resistors have a maximum power rating and if exceeded will result in the resistor overheating and becoming damaged.
• Standard resistor power rating sizes are 1/8 W, 1/4 W, 1/2 W, 1 W, and 2 W.
• Low ohmic value power resistors are generally used for current sensing or power supply applications.
• The power rating of resistors can be calculated using the formula.
• [pic] •
• In AC Circuits the voltage and current flowing in a pure resistor are always "in-phase" producing 0o phase shift..
• When used in AC Circuits the AC impedance of a resistor is equal to its DC Resistance.
• The AC circuit impedance for resistors is given the symbol Z. http://www.electronics-tutorials.ws/resistor/res_9.html

Capacitors • Capacitor, at times referred to as a Condenser, is a passive device, and one which stores its energy in the form of an electrostatic field produce a potential difference (Static Voltage) across its plates. • In its essential form a capacitor consists of two or more parallel conductive (metal) plates that do not contact or are connected but are electrically separated either by air or by some form of insulating material such as paper, mica or ceramic called the Dielectric. • The conductive plates of a capacitor can be square, circular or rectangular, or be of a cylindrical or spherical shape with the shape and construction of a parallel plate capacitor depending on its application and voltage rating. • “When used in a direct-current or DC circuit, a capacitor blocks the flow of current through it, but when it is connected to an alternating-current or AC circuit, the current appears to pass straight through it with little or no resistance. If a DC voltage is applied to the capacitors conductive plates, current flows charging up the plates with electrons giving one plate a positive charge and the other plate an equal and opposite negative charge. “ • This flow of electrons to the plates is known as the Charging Current and continues to flow until the voltage across both plates (and hence the capacitor) is equal to the applied voltage Vc. • At this point the capacitor is said to be fully charged with electrons with the strength of this charging current at its maximum when the plates are fully discharged and slowly reduces in value to zero as the plates charge up to a potential difference equal to the applied supply voltage and this is illustrated below.

Capacitor Construction
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• The parallel plate capacitor is the simplest form of capacitor and its capacitance value is fixed by the surface area of the conductive plates and the distance or separation between them. • Altering any two of these values alters the value of its capacitance and this forms the basis of operation of the variable capacitors. • Also, because capacitors store the energy of the electrons in the form of an electrical charge on the plates the larger the plates and/or smaller their separation the greater will be the charge that the capacitor holds for any given voltage across its plates. In other words, larger plates, smaller distance, more capacitance. • “A voltage to a capacitor and measuring the charge on the plates, the ratio of the charge Q to the voltage V will give the capacitance value of the capacitor and is therefore given as: C = Q/V this equation can also be re-arranged to give the more familiar formula for the quantity of charge on the plates as: Q = C x V”
The charge is stored on the plates of a capacitor, it is more correct to say that the energy within the charge is stored in an "electrostatic field" between the two plates. When an electric current flows into the capacitor, charging it up, the electrostatic field becomes more stronger as it stores more energy. Likewise, as the current flows out of the capacitor, discharging it, the potential difference between the two plates decreases and the electrostatic field decreases as the energy moves out of the plates.
The property of a capacitor to store charge on its plates in the form of an electrostatic field is called the Capacitance of the capacitor. Not only that, but capacitance is also the property of a capacitor which resists the change of voltage across it.
The Capacitance of a Capacitor
The unit of capacitance is the Farad (abbreviated to F) named after the British physicist Michael Faraday and is defined as a capacitor has the capacitance of One Farad when a charge of One Coulomb is stored on the plates by a voltage of One volt. Capacitance, C is always positive and has no negative units. However, the Farad is very large units of measurement to use on its own so sub-multiples of the Farad are generally used such as micro-farads, nano-farads and pico-farads, for example.
The capacitance of a parallel plate capacitor is proportional to the area, A of the plates and inversely proportional to their distance or separation, d (i.e. the dielectric thickness) giving us a value for capacitance of C = k( A/d ) where in a vacuum the value of the constant k is 8.84 x 10-12 F/m or 1/4.π.9 x 109, which is the permittivity of free space. Generally, the conductive plates of a capacitor are separated by air or some kind of insulating material or gel rather than the vacuum of free space.
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The Dielectric of a Capacitor
As well as the overall size of the conductive plates and their distance or spacing apart from each other, another factor which affects the overall capacitance of the device is the type of dielectric material being used. In other words the "Permittivity" (ε) of the dielectric. The conductive plates are generally made of a metal foil or a metal film but the dielectric material is an insulator. The various insulating materials used as the dielectric in a capacitor differ in their ability to block or pass an electrical charge. This dielectric material can be made from a number of insulating materials or combinations of these materials with the most common types used being: air, paper, polyester, polypropylene, Mylar, ceramic, glass, oil, or a variety of other materials.
The factor by which the dielectric material, or insulator, increases the capacitance of the capacitor compared to air is known as the Dielectric Constant, k and a dielectric material with a high dielectric constant is a better insulator than a dielectric material with a lower dielectric constant. Dielectric constant is a dimensionless quantity since it is relative to free space. The actual permittivity or "complex permittivity" of the dielectric material between the plates is then the product of the permittivity of free space (εo) and the relative permittivity (εr) of the material being used as the dielectric and is given as:
Complex Permittivity
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As the permittivity of free space, εo is equal to one, the value of the complex permittivity will always be equal to the relative permittivity. This then a final equation for the capacitance of a capacitor as:
[pic]
One method used to increase the overall capacitance of a capacitor is to "interleave" more plates together within a single capacitor body. Instead of just one set of parallel plates, a capacitor can have many individual plates connected together thereby increasing the area, A of the plate. For example, a capacitor with 10 interleaved plates would produce 9 (10 - 1) mini capacitors with an overall capacitance nine times that of a single parallel plate.
[pic]
Modern capacitors can be classified according to the characteristics and properties of their insulating dielectric: • Low Loss, High Stability such as Mica, Low-K Ceramic, Polystyrene. • • Medium Loss, Medium Stability such as Paper, Plastic Film, High-K Ceramic. • • Polarized Capacitors such as Electrolytic's, Tantalum's.
Voltage Rating of a Capacitor
All capacitors have a maximum voltage rating and when selecting a capacitor consideration must be given to the amount of voltage to be applied across the capacitor. The maximum amount of voltage that can be applied to the capacitor without damage to its dielectric material is generally given in the data sheets as: WV, (working voltage) or as WV DC, (DC working voltage). If the voltage applied across the capacitor becomes too great, the dielectric will break down (known as electrical breakdown) and arcing will occur between the capacitor plates resulting in a short-circuit. The working voltage of the capacitor depends on the type of dielectric material being used and its thickness.
The DC working voltage of a capacitor is just that, the maximum DC voltage and NOT the maximum AC voltage as a capacitor with a DC voltage rating of 100 volts DC cannot be safely subjected to an alternating voltage of 100 volts. Since an alternating voltage has an r.m.s. value of 100 volts but a peak value of over 141 volts!. Then a capacitor which is required to operate at 100 volts AC should have a working voltage of at least 200 volts. In practice, a capacitor should be selected so that its working voltage either DC or AC should be at least 50 percent greater than the highest effective voltage to be applied to it.
Another factor which affects the operation of a capacitor is Dielectric Leakage. Dielectric leakage occurs in a capacitor as the result of an unwanted leakage current which flows through the dielectric material. Generally, it is assumed that the resistance of the dielectric is extremely high and a good insulator blocking the flow of DC current through the capacitor (as in a perfect capacitor) from one plate to the other. However, if the dielectric material becomes damaged due excessive voltage or over temperature, the leakage current through the dielectric will become extremely high resulting in a rapid loss of charge on the plates and an overheating of the capacitor eventually resulting in premature failure of the capacitor. Then never use a capacitor in a circuit with higher voltages than the capacitor is rated for otherwise it may become hot and explode.

Summary
The job of a capacitor is to store charge onto its plates. The amount of electrical charge that a capacitor can store on its plates is known as its Capacitance value and depends upon three main factors.
• The surface area, A of the two conductive plates which make up the capacitor, the larger the area the greater the capacitance.
• The distance, d between the two plates, the smaller the distance the greater the capacitance.
• The type of material which separates the two plates called the "dielectric", the higher the permittivity of the dielectric the greater the capacitance.
The dielectric of a capacitor is a non-conducting insulating material, such as waxed paper, glass, mica different plastics etc, and provides the following advantages.
• The dielectric constant is the property of the dielectric material and varies from one material to another increasing the capacitance by a factor of k.
• The dielectric provides mechanical support between the two plates allowing the plates to be closer together without touching.
• Permittivity of the dielectric increases the capacitance.
• The dielectric increases the maximum operating voltage compared to air.
All capacitors have a maximum working voltage rating, its WV DC so select a capacitor with a rating at least 50% more than the supply voltage. There are a large variety of capacitor styles and types, each one having its own particular advantage, disadvantage and characteristics. http://www.electronics-tutorials.ws/capacitor/cap_1.html

Types of Capacitor
There are a very, very large variety of different types of capacitor available in the market place and each one has its own set of characteristics and applications from small delicate trimming capacitors up to large power metal-can type capacitors used in high voltage power correction and smoothing circuits. Like resistors, there are also variable types of capacitors which allow us to vary their capacitance value for use in radio or "frequency tuning" type circuits.
Commercial types of capacitor are made from metallic foil interlaced with thin sheets of either paraffin-impregnated paper or Mylar as the dielectric material. Some capacitors look like tubes, this is because the metal foil plates are rolled up into a cylinder to form a small package with the insulating dielectric material sandwiched in between them. Small capacitors are often constructed from ceramic materials and then dipped into an epoxy resin to seal them. Either way, capacitors play an important part in electronic circuits so here are a few of the more "common" types of capacitor available.
Dielectric Capacitor
Dielectric Capacitors are usually of the variable type were a continuous variation of capacitance is required for tuning transmitters, receivers and transistor radios. Variable dielectric capacitors are multi-plate air-spaced types that have a set of fixed plates (the stator vanes) and a set of movable plates (the rotor vanes) which move in between the fixed plates. The position of the moving plates with respect to the fixed plates determines the overall capacitance value. The capacitance is generally at maximum when the two sets of plates are fully meshed together. High voltage type tuning capacitors have relatively large spacing or air-gaps between the plates with breakdown voltages reaching many thousands of volts.
Variable Capacitor Symbols
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As well as the continuously variable types, preset type variable capacitors are also available called Trimmers. These are generally small devices that can be adjusted or "pre-set" to a particular capacitance value with the aid of a small screwdriver and are available in very small capacitances of 500pF or less and are non-polarized.
Film Capacitor
Film Capacitors are the most commonly available of all types of capacitors, consisting of a relatively large family of capacitors with the difference being in their dielectric properties. These include polyester (Mylar), polystyrene, polypropylene, polycarbonate, metallised paper, Teflon etc. Film type capacitors are available in capacitance ranges from as small as 5pF to as large as 100uF is depending upon the actual type of capacitor and its voltage rating. Film capacitors also come in an assortment of shapes and case styles which include: • Wrap & Fill (Oval & Round) - where the capacitor is wrapped in a tight plastic tape and have the ends filled with epoxy to seal them. • • Epoxy Case (Rectangular & Round) - where the capacitor is encased in a moulded plastic shell which is then filled with epoxy. • • Metal Hermetically Sealed (Rectangular & Round) - where the capacitor is encased in a metal tube or can and again sealed with epoxy.
With all the above case styles available in both Axial and Radial Leads.
Film Capacitors which use polystyrene, polycarbonate or Teflon as their dielectrics are sometimes called "Plastic capacitors". The construction of plastic film capacitors is similar to that for paper film capacitors but use a plastic film instead of paper. The main advantage of plastic film capacitors compared to impregnated-paper types is that they operate well under conditions of high temperature, have smaller tolerances, a very long service life and high reliability. Examples of film capacitors are the rectangular metallised film and cylindrical film & foil types as shown below.
Radial Lead Type
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Axial Lead Type
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The film and foil types of capacitors are made from long thin strips of thin metal foil with the dielectric material sandwiched together which are wound into a tight roll and then sealed in paper or metal tubes. These film types require a much thicker dielectric film to reduce the risk of tears or puncture in the film, and are therefore more suited to lower capacitance values and larger case sizes.
Metallised foil capacitors have the conductive film metallised sprayed directly onto each side of the dielectric which gives the capacitor self-healing properties and can therefore use much thinner dielectric films. This allows for higher capacitance values and smaller case sizes for a given capacitance. Film and foil capacitors are generally used for higher power and more precise applications.

Ceramic Capacitors
Ceramic Capacitors or Disc Capacitors as they are generally called, are made by coating two sides of a small porcelain or ceramic disc with silver and are then stacked together to make a capacitor. • For very low capacitance values a single ceramic disc of about 3-6mm is used. Ceramic capacitors have a high dielectric constant (High-K) and are available so that relatively high capacitances can be obtained in a small physical size. • They exhibit large non-linear changes in capacitance against temperature and as a result are used as de-coupling or by-pass capacitors as they are also non-polarized devices. Ceramic capacitors have values ranging from a few picofarads to one or two microfarads but their voltage ratings are generally quite low.
[pic]
Ceramic Capacitor
Ceramic types of capacitors generally have a 3-digit code printed onto their body to identify their capacitance value in pico-farads. Generally the first two digits indicate the capacitors value and the third digit indicates the number of zero's to be added. On the image of a ceramic capacitor above the numbers 154 indicate 15 and 4 zero's in pico-farads which is equivalent to 150,000 pF or 150nF. Letter codes are sometimes used to indicate their tolerance value such as: J = 5%, K = 10% or M = 20% etc.
Electrolytic Capacitors
Electrolytic Capacitors are generally used when very large capacitance values are required. Here instead of using a very thin metallic film layer for one of the electrodes, a semi-liquid electrolyte solution in the form of a jelly or paste is used which serves as the second electrode (usually the cathode). • The dielectric is a very thin layer of oxide which is grown electro-chemically in production with the thickness of the film being less than ten microns. • This insulating layer is so thin that it is possible to make capacitors with a large value of capacitance for a small physical size as the distance between the plates, d is very small.
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Electrolytic Capacitor
The majority of electrolytic types of capacitors are Polarised, that is the DC voltage applied to the capacitor terminals must be of the correct polarity, i.e. positive to the positive terminal and negative to the negative terminal as an incorrect polarisation will break down the insulating oxide layer and permanent damage may result. • All polarised electrolytic capacitors have their polarity clearly marked with a negative sign to indicate the negative terminal and this polarity must be followed. • Electrolytic Capacitors are generally used in DC power supply circuits due to their large capacitances and small size to help reduce the ripple voltage or for coupling and decoupling applications. • One main disadvantage of electrolytic capacitors is their relatively low voltage rating and due to the polarisation of electrolytic capacitors, it follows then that they must not be used on AC supplies. Electrolytic generally come in two basic forms; Aluminum Electrolytic Capacitors and Tantalum Electrolytic Capacitors.
Electrolytic Capacitor
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1. Aluminium Electrolytic Capacitors
There are basically two types of Aluminium Electrolytic Capacitor, the plain foil type and the etched foil type. The thickness of the aluminium oxide film and high breakdown voltage give these capacitors very high capacitance values for their size. • The foil plates of the capacitor are anodized with a DC current. This anodizing process sets up the polarity of the plate material and determines which side of the plate is positive and which side is negative. • The etched foil type differs from the plain foil type in that the aluminium oxide on the anode and cathode foils has been chemically etched to increase its surface area and permittivity. • This gives a smaller sized capacitor than a plain foil type of equivalent value but has the disadvantage of not being able to withstand high DC currents compared to the plain type. Also their tolerance range is quite large at up to 20%. Typical values of capacitance for an aluminium electrolytic capacitor range from 1uF up to 47,000uF.
Etched foil electrolytic's are best used in coupling, DC blocking and by-pass circuits while plain foil types are better suited as smoothing capacitors in power supplies. But aluminium electrolytic's is "polarised" devices so reversing the applied voltage on the leads will cause the insulating layer within the capacitor to become destroyed along with the capacitor. • However, the electrolyte used within the capacitor helps heal a damaged plate if the damage is small. Since the electrolyte has the properties to self-heal a damaged plate, it also has the ability to re-anodize the foil plate. • As the anodizing process can be reversed, the electrolyte has the ability to remove the oxide coating from the foil as would happen if the capacitor was connected with a reverse polarity.
Since the electrolyte has the ability to conduct electricity, if the aluminum oxide layer was removed or destroyed, the capacitor would allow current to pass from one plate to the other destroying the capacitor, "so be aware".
2. Tantalum Electrolytic Capacitors
Tantalum Electrolytic Capacitors and Tantalum Beads are available in both wet (foil) and dry (solid) electrolytic types with the dry or solid tantalum being the most common. • Solid tantalum capacitors use manganese dioxide as their second terminal and are physically smaller than the equivalent aluminium capacitors. • The dielectric properties of tantalum oxide is also much better than those of aluminium oxide giving a lower leakage currents and better capacitance stability which makes them suitable for use in blocking, by-passing, decoupling, filtering and timing applications. • Also, Tantalum Capacitors although polarised, can tolerate being connected to a reverse voltage much more easily than the aluminium types but are rated at much lower working voltages. • Solid tantalum capacitors are usually used in circuits where the AC voltage is small compared to the DC voltage.
However, some tantalum capacitor types contain two capacitors in-one, connected negative-to-negative to form a "non-polarised" capacitor for use in low voltage AC circuits as a non-polarised device. Generally, the positive lead is identified on the capacitor body by a polarity mark, with the body of a tantalum bead capacitor being an oval geometrical shape. Typical values of capacitance range from 47nF to 470uF.

Aluminium & Tantalum Electrolytic Capacitor
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Electrolytic's are widely used capacitors due to their low cost and small size but there are three easy ways to destroy an electrolytic capacitor:
• Over-voltage - excessive voltage will cause current to leak through the dielectric resulting in a short circuit condition.
• Reversed Polarity - reverse voltage will cause self-destruction of the oxide layer and failure.
• Over Temperature - excessive heat dries out the electrolytic and shortens the life of an electrolytic capacitor. http://www.electronics-tutorials.ws/capacitor/cap_2.html

Capacitor Characteristics
There are a bewildering array of capacitor characteristics and specifications associated with the humble capacitor and reading the information printed onto the body of a capacitor can sometimes be difficult especially when colours or numeric codes are used. • Each family or type of capacitor uses its own unique identification system with some systems being easy to understand, and others that use misleading letters, colours or symbols. • The best way to figure out what a capacitor label means is to first figure out what type of family the capacitor belongs to whether it is ceramic, film, plastic or electrolytic. • Even though two capacitors may have exactly the same capacitance value, they may have different voltage ratings. • If a smaller rated voltage capacitor is substituted in place of a higher rated voltage capacitor, the increased voltage may damage the smaller capacitor. • With a polarised electrolytic capacitor, the positive lead must go to the positive connection and the negative lead to the negative connection otherwise it may again become damaged.
So it is always better to substitute an old or damaged capacitor with the same type as the specified one. An example of capacitor markings is given below.
Capacitor Characteristics
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The capacitor, as with any other electronic component, comes defined by a series of characteristics. These Capacitor Characteristics can always be found in the datasheets that the capacitor manufacturer provides to us so here are just a few of the more important ones.

1. Nominal Capacitance, (C)
The nominal value of the Capacitance, C of a capacitor is measured in pico-Farads (pF), nano-Farads (nF) or micro-Farads (µF) and is marked onto the body of the capacitor as numbers, letters or coloured bands. • The capacitance of a capacitor can change value with the circuit frequency (Hz) y with the ambient temperature. • “ Smaller ceramic capacitors can have a nominal value as low as one pico-Farad, (1pF) while larger electrolytic does can have a nominal capacitance value of up to one Farad, (1F). All capacitors have a tolerance rating that can range from -20% to as high as +80% for aluminium electrolytic's affecting its actual or real value.” The choice of capacitance is determined by the circuit configuration but the value read on the side of a capacitor may not necessarily be its actual value.
2. Working Voltage, (WV)
The Working Voltage is the maximum continuous voltage either DC or AC that can be applied to the capacitor without failure during its working life. • Generally, the working voltage printed onto the side of a capacitors body refers to its DC working voltage, (WV-DC). DC and AC voltage values are usually not the same for a capacitor as the AC voltage value refers to the r.m.s. value and NOT the maximum or peak value which is 1.414 times greater. • Also, the specified DC working voltage is valid within a certain temperature range, normally - 30°C to + 70°C. Any DC voltage in excess of its working voltage or an excessive AC ripple current may cause failure. It follows therefore, that a capacitor will have a longer working life if operated in a cool environment and within its rated voltage. Common working DC voltages are 10V, 16V, 25V, 35V, 50V, 63V, 100V, 160V, 250V, 400V and 1000V and are printed onto the body of the capacitor.

3. Tolerance, (±%)
As with resistors, capacitors also have a Tolerance rating expressed as a plus-or-minus value either in picofarad's (±pF) for low value capacitors generally less than 100pF or as a percentage (±%) for higher value capacitors generally higher than 100pF. • The tolerance value is the extent to which the actual capacitance is allowed to vary from its nominal value and can range anywhere from -20% to +80%. • Thus a 100µF capacitor with a ±20% tolerance could legitimately vary from 80µF to 120µF and still remain within tolerance. • Capacitors are rated according to how near to their actual values they are compared to the rated nominal capacitance with coloured bands or letters used to indicated their actual tolerance.
The most common tolerance variation for capacitors is 5% or 10% but some plastic capacitors are rated as low as ±1%.
4. Leakage Current
The dielectric used inside the capacitor to separate the conductive plates is not a perfect insulator resulting in a very small current flowing or "leaking" through the dielectric due to the influence of the powerful electric fields built up by the charge on the plates when applied to a constant supply voltage. • This small DC current flow in the region of nano-amps (nA) is called the capacitors Leakage Current. • Leakage current is a result of electrons physically making their way through the dielectric medium, around its edges or across its leads and which will over time fully discharging the capacitor if the supply voltage is removed.
When the leakage is very low such as in film or foil type capacitors it is generally referred to as "insulation resistance" ( Rp ) and can be expressed as a high value resistance in parallel with the capacitor as shown. When the leakage current is high as in electrolytic's it is referred to as a "leakage current" as electrons flow directly through the electrolyte. Capacitor leakage current is an important parameter in amplifier coupling circuits or in power supply circuits, with the best choices for coupling and/or storage applications being Teflon and the other plastic capacitor types (polypropylene, polystyrene, etc) because the lower the dielectric constant, the higher the insulation resistance. Electrolytic-type capacitors (tantalum and aluminum) on the other hand may have very high capacitances, but they also have very high leakage currents due to their poor isolation resistance, and are therefore not suited for storage or coupling applications. Also, the flow of leakage current for aluminium electrolytic's increases with temperature.
5. Working Temperature, (T)
Changes in temperature around the capacitor affect the value of the capacitance because of changes in the dielectric properties. • If the air or surrounding temperature becomes to hot or to cold the capacitance value of the capacitor may change so much as to affect the correct operation of the circuit. • The normal working range for most capacitors is -30°C to +125°C with nominal voltage ratings given for a Working Temperature of no more than +70°C especially for the plastic capacitor types. • Generally for electrolytic capacitors and especially aluminium electrolytic capacitor, at high temperatures (over +85°C the liquids within the electrolyte can be lost to evaporation, and the body of the capacitor (especially the small sizes) may become deformed due to the internal pressure and leak outright. Also, electrolytic capacitors can not be used at low temperatures, below about -10°C, as the electrolyte jelly freezes.
6. Temperature Coefficient, (TC)
The Temperature Coefficient of a capacitor is the maximum change in its capacitance over a specified temperature range. • The temperature coefficient of a capacitor is generally expressed linearly as parts per million per degree centigrade (PPM/°C), or as a percent change over a particular range of temperatures. • Some capacitors are non linear (Class 2 capacitors) and increase their value as the temperature rises giving them a temperature coefficient that is expressed as a positive "P". Some capacitors decrease their value as the temperature rises giving them a temperature coefficient that is expressed as a negative "N".
However, some capacitors do not change their value and remain constant over a certain temperature range; such capacitors have a zero temperature coefficient or "NPO". These types of capacitors such as Mica or Polyester are generally referred to as Class 1 capacitors. • Most capacitors, especially electrolytic's lose their capacitance when they get hot but temperature compensating capacitors are available in the range of at least P1000 through to N5000 (+1000 ppm/C through to -5000 ppm/C). • It is also possible to connect a capacitor with a positive temperature coefficient in series or parallel with a capacitor having a negative temperature coefficient the net result being that the two opposite effects will cancel each other out over a certain range of temperatures. • Another useful application of temperature coefficient capacitors is to use them to cancel out the effect of temperature on other components within a circuit, such as inductors or resistors etc.
7. Polarization
Capacitor Polarization generally refers to the electrolytic type capacitors but mainly the Aluminium Electrolytic's, with regards to their electrical connection. The majority are polarized types, that are the voltage connected to the capacitor terminals must have the correct polarity, i.e. positive to positive and negative to negative. Incorrect polarization can cause the oxide layer inside the capacitor to break down resulting in very large currents flowing through the device resulting in destruction as we have mentioned earlier. The majority of electrolytic capacitors have their negative, -ve terminal clearly marked with either a black stripe, band, arrows or chevrons down one side of their body as shown, to prevent any incorrect connection to the DC supply. Some larger electrolytic's have their metal can or body connected to the negative terminal but high voltage types have their metal can insulated with the electrodes being brought out to separate spade or screw terminals for safety. Also, when using aluminium electrolytic's in power supply smoothing circuits care should be taken to prevent the sum of the peak DC voltage and AC ripple voltage from becoming a "reverse voltage".

8. Equivalent Series Resistance, (ESR)
The Equivalent Series Resistance or ESR, of a capacitor is the AC impedance of the capacitor when used at high frequencies and includes the resistance of the dielectric material, the DC resistance of the terminal leads, the DC resistance of the connections to the dielectric and the capacitor plate resistance all measured at a particular frequency and temperature.
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ESR Model
In some ways, ESR is the opposite of the insulation resistance which is presented as a pure resistance (no capacitive or inductive reactance) in parallel with the capacitor. • An ideal capacitor would have only capacitance but ESR is presented as a pure resistance (less than 0.1Ω) in series with the capacitor (hence the name Equivalent Series Resistance), and which is frequency dependant making it a "DYNAMIC" quantity. • As ESR defines the energy losses of the "equivalent" series resistance of a capacitor it must therefore determine the capacitor's overall I2R heating losses especially when used in power and switching circuits. Capacitors with a relatively high ESR have less ability to pass current to and from its plates to the external circuit because of their longer charging and discharging RC time constant. • The ESR of electrolytic capacitors increases over time as their electrolyte dries out. Capacitors with very low ESR ratings are available and are best suited when using the capacitor as a filter. • Capacitors with small capacitances (less than 0.01 uF) generally do not pose much danger to humans. However, when the capacitances start to exceed 0.1 uF, touching the capacitor leads can be a shocking experience. • As a rule, never touch the leads of large capacitors. If in question, discharge the capacitor first by shorting the leads together with a screwdriver tip before handling it. http://www.electronics-tutorials.ws/capacitor/cap_3.html Capacitance and Charge
A Capacitor consists of two parallel conductive plates (usually a metal) which are prevented from touching each other (separated) by an insulating material called the "dielectric". And when a voltage is applied to these plates an electrical current flows charging up one plate with a positive charge with respect to the supply voltage and the other plate with an equal and opposite negative charge. • Then, a capacitor has the ability of being able to store an electrical charge Q (units in Coulombs) of electrons. • When a capacitor is fully charged there is a potential difference, p.d. between its plates, and the larger the area of the plates and/or the smaller the distance between them (known as separation) the greater will be the charge that the capacitor can hold and the greater will be its Capacitance.
The Capacitors ability to store this electrical charge (Q) between its plates is proportional to the applied voltage, V for a capacitor of known capacitance in Farads. Capacitance C is always positive. The greater the applied voltage the greater will be the charge stored on the plates of the capacitor. Likewise, the smaller the applied voltage the smaller the charge. Therefore, the actual charge Q on the plates of the capacitor and can be calculated as:

Charge on a Capacitor
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Transposing the above equation gives us: Units of: Q measured in Coulombs, V in volts and C in Farads. • Then from above we can define the unit of Capacitance as being a constant of proportionality being equal to the coulomb/volt which is also called a Farad, unit F. • “ As capacitance represents the capacitors ability (capacity) to store an electrical charge on its plates we can define one Farad as the "capacitance of a capacitor which requires a charge of one coulomb to establish a potential difference of one volt between its plates" as firstly described by Michael Faraday. So the larger the capacitance, the higher is the amount of charge stored on a capacitor for the same amount of voltage."
The ability of a capacitor to store a charge on its conductive plates gives it its Capacitance value. Capacitance can also be determined from the dimensions or area, A of the plates and the properties of the dielectric material between the plates. A measure of the dielectric material is given by the permittivity, ( ε ), or the dielectric constant. So another way of expressing the capacitance of a capacitor is;

With Air as its dielectric
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with a Solid as its dielectric
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Where A is the area of the plates in square meters, m2 with the larger the area, the more charge the capacitor can store. d is the distance or separation between the two plates. The smaller is this distance, the higher is the ability of the plates to store charge, since the -ve charge on the -Q charged plate has a greater effect on the +Q charged plate, resulting in more electrons being repelled off of the +Q charged plate, and thus increasing the overall charge. ε0 (epsilon) is the value of the permittivity for air which is 8.84 x 10-12 F/m, and εr is the permittivity of the dielectric medium used between the two plates.

Parallel Plate Capacitor
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• The capacitance of a parallel plate capacitor is proportional to the surface area A and inversely proportional to the distance, d between the two plates and this is true for dielectric medium of air. However, the capacitance value of a capacitor can be increased by inserting a solid medium in between the conductive plates which has a dielectric constant greater than that of air. Typical values of epsilon ε for various commonly used dielectric materials are: Air = 1.0, Paper = 2.5 - 3.5, Glass = 3 - 10, Mica = 5 - 7 etc. • The factor by which the dielectric material, or insulator, increases the capacitance of the capacitor compared to air is known as the Dielectric Constant, k. k is the ratio of the permittivity of the dielectric medium being used to the permittivity of free space otherwise known as a vacuum. • Therefore, all the capacitance values are related to the permittivity of vacuum. A dielectric material with a high dielectric constant is a better insulator than a dielectric material with a lower dielectric constant.
Dielectric constant is a dimensionless quantity since it is relative to free space.

Charging & Discharging of a Capacitor
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Assume that the capacitor is fully discharged and the switch connected to the capacitor has just been moved to position A. The voltage across the 100uf capacitor is zero at this point and a charging current ( i ) begins to flow charging up the capacitor until the voltage across the plates is equal to the 12v supply voltage. The charging current stops flowing and the capacitor is said to be "fully-charged".
Then, Vc = Vs = 12v. • Once the capacitor is "fully-charged" in theory it will maintain its state of voltage charge even when the supply voltage has been disconnected as they act as a sort of temporary storage device. • However, while this may be true of an "ideal" capacitor, a real capacitor will slowly discharge itself over a long period of time due to the internal leakage currents flowing through the dielectric. • This is an important point to remember as large value capacitors connected across high voltage supplies can still maintain a significant amount of charge even when the supply voltage is switched "OFF".
If the switch was disconnected at this point, the capacitor would maintain its charge indefinitely, but due to internal leakage currents flowing across its dielectric the capacitor would very slowly begin to discharge itself as the electrons passed through the dielectric. The time taken for the capacitor to discharge down to 37% of its supply voltage is known as its Time Constant.
If the switch is now moved from position A to position B, the fully charged capacitor would start to discharge through the lamp now connected across it, illuminating the lamp until the capacitor was fully discharged as the element of the lamp has a resistive value. The brightness of the lamp and the duration of illumination would ultimately depend upon the capacitance value of the capacitor and the resistance of the lamp (t = C x R). The larger the value of the capacitor the brighter and longer will be the illumination of the lamp as it could store more charge.
Current through a Capacitor
The current that flows through a capacitor is directly related to the charge on the plates as current is the rate of flow of charge with respect to time. As the capacitors ability to store charge (Q) between its plates is proportional to the applied voltage (V), the relationship between the current and the voltage that is applied to the plates of a capacitor becomes:
Current-voltage Relationship
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As the voltage across the plates increases (or decreases) over time, the current flowing through the capacitance deposits (or removes) charge from its plates with the amount of charge being proportional to the applied voltage. • Then both the current and voltage applied to a capacitance are functions of time and are denoted by the symbols, i(t) and v(t). • However, from the above equation we can also see that if the voltage remains constant, the charge will become constant and therefore the current will be zero!.
In other words, no change in voltage, no movement of charge and no flow of current. This is why a capacitor appears to "block" current flow when connected to a steady state DC voltage.
The Farad
The ability of a capacitor to store a charge gives it its capacitance value C, which has the unit of the Farad, F. But the farad is an extremely large unit on its own making it impractical to use, so submultiples or fractions of the standard Farad unit are used instead. To get an idea of how big a Farad really is, the surface area of the plates required producing a capacitor with a value of one Farad with a reasonable plate separation of just 1mm operating in a vacuum and rearranging the equation for capacitance above would be:
A = Cd ÷ 8.85pF/m = (1 x 0.001) ÷ 8.85x10-12 = 112,994,350 m2 or 113 million m2 which would be equivalent to a plate of more than 10 kilometers x 10 kilometers square.
Then capacitors which have a value of one Farad are very rare and have a solid dielectric. • As one Farad is such a large and an unpractical unit to use, prefixes are used instead in electronic formulas with component values given in micro-Farads (μF), nano-Farads (nF) and the pico-Farads (pF).
Energy
When a capacitor charges up from the power supply connected to it, an electrostatic field is established which stores energy in the capacitor. The amount of energy in Joules that is stored in this electrostatic field is equal to the energy the voltage supply exerts to maintain the charge on the plates of the capacitor and is given by the formula:
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So the energy stored in the 100uF capacitor circuit above is calculated as:
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http://www.electronics-tutorials.ws/capacitor/cap_4.html

Capacitor Colour Codes
Generally, the actual values of Capacitance, Voltage or Tolerance are marked onto the body of the capacitors in the form of alphanumeric characters. However, when the value of the capacitance is of a decimal value problems arise with the marking of a "Decimal Point" as it could easily not be noticed resulting in a misreading of the actual value. Instead letters such as p (pico) or n (nano) are used in place of the decimal point to identify its position and the weight of the number. Also, sometimes capacitors are marked with the capital letter K to signify a value of one thousand pico-Farads.
To reduce the confusion regarding letters, numbers and decimal points, an International colour coding scheme was developed many years ago as a simple way of identifying capacitor values and tolerances. It consists of coloured bands (in spectral order) known commonly as the Capacitor Colour Code system and whose meanings are illustrated below:
Capacitor Colour Code Table
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Disc & Ceramic Capacitors
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The Capacitor Colour Code system was used for many years on unpolarised polyester and mica moulded capacitors. This system of colour coding is now obsolete but there are still many "old" capacitors around. Nowadays, small capacitors such as film or disk types conform to the BS1852 Standard and its new replacement, BS EN 60062, were the colours have been replaced by a letter or number coded system. The code consists of 2 or 3 numbers and an optional tolerance letter code to identify the tolerance. Where a two number code is used the value of the capacitor only is given in picofarads, for example, 47 = 47 pF and 100 = 100pF etc. A three letter code consists of the two value digits and a multiplier much like the resistor colour codes in the resistors section. For example, the digits 471 = 47*10 = 470pF. Three digit codes are often accompanied by an additional tolerance letter code as given below.
Capacitor Tolerance Letter Codes Table
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When capacitors are connected together in parallel the total or equivalent capacitance, CT in the circuit is equal to the sum of all the individual capacitors added together. The currents flowing through each capacitor and as we saw in the previous tutorial are related to the voltage. Then by applying Kirchoff's Current Law, (KCL) to the above circuit, we have
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and this can be re-written as:
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Then it can be define the total or equivalent circuit capacitance, CT as being the sum of all the individual capacitances add together giving us the generalized equation of

Parallel Capacitors Equation
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When adding together capacitors in parallel, they must all be converted to the same capacitance units, whether it is uF, nF or pF. Also, we can see that the current flowing through the total capacitance value, CT is the same as the total circuit current, iT
The total capacitance of the parallel circuit is defined from the from the total stored charge using the Q = CV equation for charge on a capacitors plates. The total charge QT stored on all the plates equals the sum of the individual stored charges on each capacitor therefore,
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This will divide through by the voltage, (V) this is because it is common to both sides. Also, the number of Capacitors in Parallel is not important for this equation, and can therefore be generalized for any number of parallel capacitors connected together. • One important point about parallel connected capacitor circuits is that, the total capacitance (CT) of any two or more capacitors connected together in parallel will always be GREATER than the value of the largest capacitor in the group and in our example above CT = 0.6uF whereas the largest value capacitor is only 0.3uF.
When 4, 5, 6 or even more capacitors are connected together the total capacitance of the circuit CT would still be the sum of all the individual capacitors added together and the total capacitance of a parallel circuit is always greater than the highest value capacitor. This is because we have increased the total surface area of the plates. Hence, this with two identical capacitors, we have effectively doubled the surface area of the plates and this doubles the capacitance of the combination and so on. http://www.electronics-tutorials.ws/capacitor/cap_6.html Capacitors in Series
Capacitors are said to be connected together "in series" when they are effectively "daisy chained" together in a single line. The charging current (ic) flowing through the capacitors is THE SAME for all capacitors as it only has one path to follow and iT = i1 = i2 = i3 etc. Then, Capacitors in Series all have the same current so each capacitor stores the same amount of charge regardless of its capacitance. This is because the charge stored by a plate of any one capacitor must have come from the plate of its adjacent capacitor therefore,
QT = Q1 = Q2 = Q3 ....etc
In the following circuit, capacitors, C1, C2 and C3 are all connected together in a series branch between points A and B.
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In the previous parallel circuit, the total capacitance, CT of the circuit was equal to the sum of all the individual capacitors added together. In a series connected circuit however, the total or equivalent capacitance CT is calculated differently. The voltage drop across each capacitor will be different depending upon the values of the individual capacitances. Then by applying Kirchoff's Voltage Law, (KVL) to the above circuit, we get:
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Since Q = CV or V = Q/C, substituting Q/C for each capacitor voltage VC in the above KVL equation gives us
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Dividing each term through by Q gives

Series Capacitors Equation
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When adding together Capacitors in Series, the reciprocal (1/C) of the individual capacitors are all added together (just like resistors in parallel) instead of the capacitances themselves. Then the total value for capacitors in series equals the reciprocal of the sum of the reciprocals of the individual capacitances. • Capacitors that are connected together in a series configuration, is that the total circuit capacitance (CT) of any number of capacitors connected together in series will always be LESS than the value of the smallest capacitor in the series.
This reciprocal method of calculation can be used for calculating any number of capacitors connected together in a single series network. If however, there are only two capacitors in series, then a much simpler and quicker formula can be used and is given as:
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http://www.electronics-tutorials.ws/capacitor/cap_7.html

Capacitance in AC Circuits
When capacitors are connected across a direct current DC supply voltage they become charged to the value of the applied voltage, acting like temporary storage devices and maintain or hold this charge indefinitely as long as the supply voltage is present. During this charging process, a charging current, (i) will flow into the capacitor opposing any changes to the voltage at a rate that is equal to the rate of change of the electrical charge on the plates. This charging current can be defined as: i = CdV/dt. Once the capacitor is "fully-charged" the capacitor blocks the flow of any more electrons onto its plates as they have become saturated. However, if we apply an alternating current or AC supply, the capacitor will alternately charge and discharge at a rate determined by the frequency of the supply. Then the Capacitance in AC circuits varies with frequency as the capacitor is being constantly charged and discharged. • The flow of electrons through the capacitor is directly proportional to the rate of change of the voltage across the plates. • Then, capacitors in AC circuits like to pass current when the voltage across its plates is constantly changing with respect to time such as in AC signals, but it does not like to pass current when the applied voltage is of a constant value such as in DC signals. Consider the circuit below.
AC Capacitor Circuit
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In the purely capacitive circuit above, the capacitor is connected directly across the AC supply voltage. As the supply voltage increases and decreases, the capacitor charges and discharges with respect to this change. • The charging current is directly proportional to the rate of change of the voltage across the plates with this rate of change at its greatest as the supply voltage crosses over from its positive half cycle to its negative half cycle or vice versa at points, 0o and 180o along the sine wave.
Consequently, the least voltage change occurs when the AC sine wave crosses over at its maximum or minimum peak voltage level, (Vm). At these positions in the cycle the maximum or minimum currents are flowing through the capacitor circuit and this is shown below.

AC Capacitor Phasor Diagram
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At 0o the rate of change of the supply voltage is increasing in a positive direction resulting in a maximum charging current at that instant in time. As the applied voltage reaches its maximum peak value at 90o for a very brief instant in time the supply voltage is neither increasing nor decreasing so there is no current flowing through the circuit. • As the applied voltage begins to decrease to zero at 180o, the slope of the voltage is negative so the capacitor discharges in the negative direction. • At the 180o point along the line the rate of change of the voltage is at its maximum again so maximum current flows at that instant and so on. Then capacitors in AC circuits the instantaneous current is at its minimum or zero whenever the applied voltage is at its maximum and likewise the instantaneous value of the current is at its maximum or peak value when the applied voltage is at its minimum or zero. • From the waveform above, we can see that the current is leading the voltage by 1/4 cycle or 90o as shown by the vector diagram. Then we can say that in a purely capacitive circuit the alternating voltage lags the current by 90o.
The current flowing through the capacitance in AC circuits is in opposition to the rate of change of the applied voltage but just like resistors, capacitors also offer some form of resistance against the flow of current through the circuit, but with capacitors in AC circuits this AC resistance is known as Reactance or more commonly in capacitor circuits, Capacitive Reactance, so capacitance in AC circuits suffers from Capacitive Reactance.

Capacitive Reactance
Capacitive Reactance in a purely capacitive circuit is the opposition to current flow in AC circuits only. Like resistance, reactance is also measured in Ohm's but is given the symbol X to distinguish it from a purely resistive value. As reactance can also be applied to Inductors as well as Capacitors it is more commonly known as Capacitive Reactance for capacitors in AC circuits and is given the symbol Xc so we can actually say that Capacitive Reactance is Resistance that varies with frequency. Also, capacitive reactance depends on the value of the capacitor in Farads as well as the frequency of the AC waveform and the formula used to define capacitive reactance is given as:
Capacitive Reactance
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Where: F is in Hertz and C is in Farads. 2πF can also be expressed collectively as the Greek letter Omega, ω to denote an angular frequency.
From the capacitive reactance formula above, it can be seen that if either of the Frequency or Capacitance where to be increased the overall capacitive reactance would decrease. As the frequency approaches infinity the capacitors reactance would reduce to zero acting like a perfect conductor. However, as the frequency approaches zero or DC, the capacitors reactance would increase up to infinity, acting like a very large resistance. This means then that capacitive reactance is "Inversely proportional" to frequency for any given value of Capacitance and this shown below:

Capacitive Reactance against Frequency
|[pic] |The capacitive reactance of the capacitor decreases as the |
| |frequency across it increases therefore capacitive reactance |
| |is inversely proportional to frequency. |
| |The opposition to current flow, the electrostatic charge on |
| |the plates (its AC capacitance value) remains constant as it |
| |becomes easier for the capacitor to fully absorb the change in|
| |charge on its plates during each half cycle. |
| |Also as the frequency increases the current flowing through |
| |the capacitor increases in value because the rate of voltage |
| |change across its plates increases. |

So, the Capacitance in AC circuits varies with frequency as the capacitor is being constantly charged and discharged with the AC resistance of a capacitor being known as Reactance or more commonly in capacitor circuits, Capacitive Reactance. • This capacitive reactance is inversely proportional to frequency and produces the opposition to current flow around a capacitive AC circuit as we looked at in the AC Capacitance tutorial in the AC Theory section. http://www.electronics-tutorials.ws/capacitor/cap_8.html

Capacitors Summary
• A capacitor consists of two metal plates separated by a dielectric.
• The dielectric can be made of many insulating materials such as air, glass, paper, plastic etc.
• A capacitor is capable of storing electrical charge and energy.
• The higher the value of capacitance, the more charge the capacitor can store.
• The larger the area of the plates or the smaller their separation the more charge the capacitor can store.
• A capacitor is said to be "Fully Charged" when the voltage across its plates equals the supply voltage.
• The symbol for electrical charge is Q and its unit is the Coulomb.
• Electrolytic capacitors are polarized. They have a +ve and a -ve terminal.
• Capacitance is measured in Farads, which is a very large unit so micro-Farad (uF), nano-Farad (nF) and pico-Farad (pF) are generally used.
• Capacitors that are daisy chained together in a line are said to be connected in Series.
• Capacitors that have both of their respective terminals connected to each terminal of another capacitor are said to be connected in Parallel.
• Parallel connected capacitors have a common supply voltage across them.
• Series connected capacitors have a common current flowing through them.
• Capacitive reactance is the opposition to current flow in AC circuits.
• In AC capacitive circuits the voltage "lags" the current by 90o. http://www.electronics-tutorials.ws/capacitor/cap_9.html The Inductor
In its most essential form, an Inductor is simply a coil of wire. For most coils the current, (i) flowing through the coil produces a magnetic flux, (NΦ) that is proportional to this flow of electrical current. • When electrons flow through a conductor a magnetic flux is developed around the conductor producing a relationship between the direction of this flux around the conductor and the direction of the electrons flowing through the conductor, with this relationship being called, "Fleming's Left Hand Rule". • But another important property of a wound coil exists, and that is a voltage is induced into the coil by this magnetic flux as it opposes or resists any changes in the electrical current flowing it.
The Inductor, also called a choke, is another passive type electrical component designed to take advantage of this relationship by producing a much stronger magnetic field than one that would be produced by a simple coil. • Inductors are formed with wire tightly wrapped around a solid central core which can be either a straight cylindrical rod or a continuous loop or ring to concentrate their magnetic flux. The schematic symbol for an inductor is that of a coil of wire so therefore, a coil of wire can also be called an Inductor. • Inductors are categorized according to the type of inner core with the different core types being distinguished by adding continuous or dotted parallel lines next to the wire coil as shown below.
Inductor Symbols
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o The current, i that flows through an inductor produces a magnetic flux that is proportional to it. o An inductor opposes the rate of change of current flowing through it due to the build up of self-induced energy within its magnetic field. o In other words, “inductors resist or oppose changes of current but will easily pass a steady state DC current. This ability of an inductor to resist changes in current and which also relates current, i with its magnetic flux linkage, NΦ as a constant of proportionality is called Inductance which is given the symbol L with units of Henry, (H) after Joseph Henry. Because the Henry is a relatively large unit of inductance in its own right, for the smaller inductors sub-units of the Henry are used to denote its value.”
Inductors or coils are very common in electrical circuits and there are many factors which determine the inductance of a coil such as the shape of the coil, the number of turns of the insulated wire, the number of layers of wire, the spacing between the turns, the permeability of the core material, the size or cross-sectional area of the core etc, to name a few.
“An inductor coil has a central core area, (A) with a constant number of turns of wire per unit length, (l). So if a coil of N turns is linked by an amount of magnetic flux, Φ then the coil has a flux linkage of NΦ and any current, (i) that flows through the coil will produce an induced magnetic flux in the opposite direction to the flow of current. Then according to Faraday's Law, any change in this magnetic flux linkage produces a self-induced voltage in the single coil of:”
|[pic] |

Where: • N is the number of turns • A is the cross-sectional Area in m2 • Φ is the amount of flux in Webers • μ is the Permeability of the core material • l is the Length of the coil in metres • di/dt is the Currents rate of change in amps/second
A time varying magnetic field induces a voltage that is proportional to the rate of change of the current producing it with a positive value indicating an increase in emf and a negative value indicating a decrease in emf. The equation relating this self-induced voltage, current and inductance can be found by substituting the μN2A / l with L denoting the constant of proportionality called the Inductance of the coil. o The relation between the flux in the inductor and the current flowing through the inductor is given as: Φ = Li. o As an inductor consists of a coil of conducting wire, this then reduces the above equation to give the self-induced emf, sometimes called the back emf induced in the coil too:
The back emf Generated by an Inductor
[pic]
• Where: L is the self-inductance and di/dt the rate of current change.

So from this equation we can say that the "self-induced emf = inductance x rate of current change" and a
[pic]
Inductor Coil
Circuit has an inductance of one Henry will have an emf of one volt induced in the circuit when the current flowing through the circuit changes at a rate of one ampere per second. ➢ It only relates the emf produced across the inductor to changes in current because if the flow of inductor current is constant and not changing such as in a steady state DC current, then the induced emf voltage will be zero because the instantaneous rate of current change is zero, di/dt = 0. With a steady state DC current flowing through the inductor and therefore zero induced voltage across it, the inductor acts as a short circuit equal to a piece of wire, in the presence of a continuous current. In other words, the opposition to the flow of current offered by an inductor is different between AC and DC circuits.
The Time Constant of an Inductor
The current can not change instantaneously in an inductor because for this to occur, the current would need to change by a finite amount in zero time which would result in the rate of current change being infinite, di/dt = ∞, making the induced emf infinite as well and infinite voltages do no exist. However, if the current flowing through an inductor changes very rapidly, such as with the operation of a switch, high voltages can be induced across the inductors coil.
[pic]
Consider the circuit of the inductor on the right. With the switch, (S1) open no current flows through the inductor coil, so the rate of change of current change (di/dt) in its coil is zero and therefore, zero self-induced emf exists across the inductor, (VL = 0).
If we now close the switch (t = 0), a current will flow through the circuit and slowly rise to its maximum value at a rate determined by the inductance of the inductor. This rate of current flowing through the inductor multiplied by the inductors inductance in Henry's, results in some fixed value self-induced emf being produced across the coil as determined by Faraday's equation above, VL = Ldi/dt. ❖ This self-induced emf across the inductors coil, (VL) fights against the applied voltage until the current reaches its maximum value and a steady state condition is reached. ❖ The current which now flows through the coil is determined only by the DC or "pure" resistance of the coils windings as the reactance value of the coil has decreased to zero because the rate of change of current (di/dt) is zero in steady state. ❖ In other words, only the coils DC resistance now exists to oppose the flow of current.
Likewise, if switch, (S1) is opened, the current flowing through the coil will start to fall but the inductor will again fight against this change and try to keep the current flowing at its previous value by inducing a voltage in the other direction. The slope of the fall will be negative and related to the inductance of the coil as shown below.
Current and Voltage in an Inductor
|[pic] |

How much induced voltage will be produced by the inductor depends upon the rate of current change. ✓ An induced emf will always OPPOSE the motion or change which started the induced emf in the first place. ✓ So with a decreasing current the voltage polarity will be acting as a source and with an increasing current the voltage polarity will be acting as a load. ✓ Hences, the same rate of current change through the coil, either increasing or decreasing the magnitude of the induced emf will be the same.

Power and Energy in an Inductor
Power in an Inductor
An inductor in a circuit opposes the flow of current, ( i ) through it because the flow of this current induces an emf that opposes it, Lenz's Law. Then work has to be done by the external battery source in order to keep the current flowing against this induced emf. The instantaneous power used in forcing the current, (i) against this self-induced emf, ( VL ) is given from above as:
[pic]
Power in a circuit is given as, P = V.I therefore:
[pic]
An ideal inductor has no resistance only inductance so R = 0 Ω's and therefore no power is dissipated within the coil, so an ideal inductor has zero power loss.
Energy in an Inductor ✓ When power flows into an inductor, energy is stored in its magnetic field. When the current flowing through the inductor is increasing and di/dt becomes greater than zero, the instantaneous power in the circuit must also be greater than zero, (P > 0) i.e., positive which means that energy is being stored in the inductor. ✓ Likewise, if the current through the inductor is decreasing and di/dt is less than zero then the instantaneous power must also be less than zero, (P