EE2001 Circuit Analysis

2012/2013

Circuit Theorems

Prepared by John Chan

Email:ecychan@ntu.edu.sg

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- A simple electric circuit is shown in Fig. 1. - It consists of three basic elements: a battery, a lamp, and connecting wires.

- In this course, we are going to learn various analytical techniques for describing the behavior of a circuit like this. - Our major concern is the analysis of circuits, meaning the study of the behavior of the circuit.

Fig. 1. A simple electric circuit.

- A more complicated real circuit is displayed in Fig. 2, representing the schematic diagram for a radio receiver.

Fig. 2. Electric circuit of a radio receiver.

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Basic Concepts Electric charge and Current - Electric charge and its movement are the most basic items of interest in electrical engineering. - The magnitude of the electron’s charge is 1.602 x 10-19 coulomb (unit is C). - A unique feature of electric charge is that it is mobile, meaning it can be transferred from one place to another. - When a conducting wire is connected to a battery, the charge are compelled to move; +ve charges move in one direction and –ve charges move in the opposite direction. - When there is a net flow of charge across any area, we say that there is a current across the area.

Electric current is the time rate of change of charge, measured in amperes (A). - The movement of 1 C of charge through a cross section of a conductor in 1 sec produces an electric current of 1 A. - The direction of current flow is taken by convention as opposite to the direction of electron flow (see Fig. 3).

Fig. 3. Electric current due to flow of electronic charge in a conductor.

- The relationship between current i, and charge q, and time t is . 5

(a)

(b)

Fig. 4. Conventional current flow: (a) +ve current flow, (b) –ve current flow. 6

Types of current A direct current (dc) is a current that remains constant with time.

Voltage

An alternating current (ac) is a current that varies sinusoidally with time.

Keep in mind that electric current is always through an element.

- To move the electron in a conductor in a particular direction requires some work or energy transfer. - This work is performed by an external electromotive force (emf), typically represented by the battery. - The emf is not a force, but called a force because it forces current to flow in a circuit. - The emf is also known as voltage or potential difference (p.d.). - The voltage between two points a and b in a circuit is the energy (or work) needed to move a unit charge from a to b. - The relationship between the energy w (in joules, J) and the charge (in C) is . - Thus, voltage is the energy required to move a unit charge through an element, measured in volts (V). So, 1 V = 1 J/C.

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Fig. 5 shows the voltage across an element (represented by a rectangular block) connected to points a and b.

Fig. 5. Polarity of

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- The + and – signs are used to designate which point is at the assumed higher potential (the + point). - The can be interpreted as: point a is at a potential of volts higher than point b, or the potential at point a with respect to . point b is - An arrow is used to point to the terminal of assumed higher potential (the + point).

Types of voltage - A constant voltage is called a...