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Resistors in series and parallel.

By staffy Aug 25, 2005 1193 Words
Title: Resistors in Series and Parallel

Date: 17/7/05

Aim:

The aim of this experiment is to compare the predicted and actual resistance in a circuit of resistor combinations in series and in parallel.

Background:

A resistor is an electrical component/device that has electrical resistance. Resistors can be used in electric circuits for protection of components, voltage division or current control. In an ideal resistor the resistance remains constant regardless of the applied voltage or current, or the rate of change in the current (Resistor, 2005, Wikipedia).

Electrical resistance is a measure of the ability of an object to oppose the passage of an electric current. The electrical resistance of an electrical component can be found by using Ohm's law. Ohm's law states that the potential difference (voltage) between the ends of a conductor (e.g. a resistor) and the current flowing through the conductor are proportional at a given temperature (Storen & Martine, 2000, p221-226). This law can be written as: R=V .

I

The SI unit used for electrical resistance is an ohm. An electrical device that has an electrical resistance of 1 ohm will cause a current of 1 amp to flow through it if a voltage of 1V is passed through it.

From previous scientific research it has been determined that the general law for resistors in series is: Rseries = R1 + R2 + R3+Rn

It has also been determined that the general law for resistors in parallel is

Rparallel =

Hypothesis:

From the formulas stated in the Background of this report it can be seen that the total resistance of resistors in series can be found by adding together the individual resistances of each component. It can also be seen that the total resistance of resistors in parallel can be found by adding together the individual reciprocals of each component's resistance and then taking the reciprocal.

Predictions:

By knowing the individual resistor values we can accurately determine the total resistance of resistor combinations. Please refer to the Results section of experiment for more detail.

Materials:

-Seven resistors

-12v power pack

-Multimeter

-2 alligator clips

-Small lengths of thin copper wire

Method:

1.The circuit shown in Diagram 1 (see Results) was set up using the appropriate electrical components.

2.The 12v power supply was turned on and set to 6v.

3.The amperage, voltage and resistance of the three resistor combinations (see results) within the circuit were found, as well as the total amounts for the whole circuit by using the multimeter.

4.The voltage and amperage of each resistor was then found by using the multimeter.

Results and Calculations:

Diagram 1: Circuit Setup

Table 1: Resistor Values

All actual resistances obtained were within the relevant upper and lower tolerance values stated above except for the resistance obtained for R4.

Prediction calculations:

Total Resistance (Equivalent to Resistor Combination 3) (See Image 1)

R total lower:

= 1847.3 ohms

R total upper:

= 2319.20 ohms

(The actual value should therefore be between 2319.20 and 1847.3 ohms.)

Resistor Combination 1 (See Image 2)

R lower:

= 245.51 ohms

R upper:

= 271.36 ohms

(Actual value should therefore be between 271.36 and 245.51 ohms)

Resistor Combination 2 (see Image 3)

Rlower

R lower: 1664.24 ohms

Rupper

R upper: 1846.36 ohms

(Actual value should therefore between 1664.24-1846.36 ohms)

Resistor Combination 3 (Equivalent to Total Resistance)

Refer to Total Resistance

Experimental measurements:

Data for Total Circuit (see diagram 1):

Amperage= 0.01 amps Resistance= 2538 ohms

Voltage from power supply = 6.04V

Diagram 2: Resistor Combination 1

Data for Resistor Combination 1 (see diagram 2):

Voltage= 0.72V Amperage= 0.01 amps Resistance= 270 ohms

Diagram 3: Resistor Combination 2

Data for Resistor Combination 2 (see diagram 3):

Voltage= 4.14V Amperage= 0.01 amps Resistance= 2033 ohms

Diagram 4: Resistor Combination 3

Data for Resistor Combination 3 (see diagram 4):

Voltage= 1.23V Amperage= 0.01 amps Resistance= 2491 ohms

Discussion:

Resistors are used in various real life applications to perform tasks that involve: limiting the current that goes through a section of a circuit, introducing a voltage drop in a circuit, generating heat and the protection of components of a circuit. It is important to calculate the resistance of resistors so that the electrical circuits produced using them will perform in the manner that their manufacturer wanted them to. If the wrong resistance/resistor is used then delicate components that need only a relatively small amount of current may be destroyed.

All resistors have a level of tolerance. This is to allow for imperfections in the manufactured object. It was determined through experimentation that all of the resistors that were used in this experiment were within their tolerance range with the exception of R4 (See Table 1). This resistor had a nominal value of 1600 ohms and a tolerance of +/-5%. This means that this resistor should have had a value within the range of 1520-1680 ohms, however the actual resistance was found to be 1798 ohms. It is possible that this may have been due to a manufacturing fault or a labelling error.

The total predicted resistance was determined by using the series and parallel resistor laws and the resistance values of the various components of the circuit. The tolerance range for the circuit was predicted to be between 1847.3-2319.2 ohms. Through experimentation the actual total resistance for the circuit was 2216.62 ohms, this value was within the predicted range.

The actual resistance value of component 1 was 263.26 ohms; this was within the predicted range (271.36-245.51 ohms).

The actual resistance value of component 2 was 1764.26 ohms; this was within the predicted range (1664.24-1846.36 ohms).

The actual resistance value of component 3 was 2216.62 ohms; this was within the predicted range (2319.20 and 1847.3 ohms).

The actual resistance of the resistors was found by using a multimeter. Some systematic error may have occurred in this experiment if the multimeter was not calibrated correctly during testing.

Temperature fluctuations may have caused inconsistencies in this experiment. The reason why resistance occurs is that a metal consists of lattice of atoms that each has a shell of electrons. The metal is a conductor because the electrons are free to dissociate from their parent atoms and travel through the lattice. When a voltage is applied the electrons drift from one side of the metal to the other. In real material imperfections scatter the electrons resulting in resistance. Temperature is able to affect resistance because temperature causes the atoms to vibrate more strongly creating even more collisions and further increasing the resistance.

Conclusion:

The aim of the experiment was to compare the predicted and actual resistance in the circuit of resistor combinations in series and parallel. The results of this experiment found that the series and parallel resistor laws were reasonably good indicators of the "real world" values of resistance for circuits that contained resistors in series and parallel. One example of this was that the total resistance of the circuit made was found to be 2216.62 ohms which was within the predicted range (this predicted range was calculated by using the upper and lower tolerance values for the resistors used in the circuit. From the data obtained it can therefore be seen that all three resistor laws stated in the Background section of this report are quite useful in calculating theoretical values for the resistance of circuits in series and parallel that are close to the "real world" values.

Bibliography:

"resistor." Wikipedia. Wikipedia, 2005.

"resistor." WordNet 1.7.1. Princeton University, 2001.

"resistor." Electronics. Twysted Pair, 2001.

Storen, A and Martine, R. (2000) Nelson Physics VCE Units 3 and 4. Nelson Publishing: Sydney. (pp 221-226)

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