Basic Circuit Analysis - AC

CHAPTER -3

Basic Circuit Analysis - AC

INTRODUCTION

Alternating current and voltage sources are widely used in practice. Unlike the DC source, the AC source gives a voltage (or current) that varies with time. The voltage changes not only in magnitude but also in direction (or polarity). In figure 3.1 (a) is plotted a constant DC voltage whereas in figures 3.1 (b), 3.1 (c), 3.1 (d) and 3.1 (e) some alternating voltages are shown.

In figure 3.1 (a) the voltage is constant at V volts and does not change sign or polarity. In figure 3.1 (c) the voltage changes in magnitude while in 3.1 (b), 3.1 (d) and 3.1 (e), the sign also changes. Figure 3.1 (c) represents only time variation, but not change of polarity. An alternating quantity is one which changes sign and magnitude periodically.

Usually the alternating quantities are periodic in nature, i.e., they repeat cyclically after a constant interval of time, say T. Hence,

v(t) = v(t+T) = v (t + 2T) and so on …. (1)

or

v (t) = v (t + nT), n = 0, 1, 2

The time taken to complete one cycle (or the time interval, T after which the waveform repeats itself) is called the time period of the quantity. The number of such cycles occurring per second is called frequency, f. Hence,

f = 1 / T Hz   …… (2)

The maximum value, positive or negative of the alternating quantity is called its amplitude.

EXAMPLE 1: The period of a sine wave is 20 ms. What is its frequency? Represent the sine wave.

Solution: