Introduction to Electric Circuits

76 Single-phase a.c. circuits

i.e.
i = WCVm sin (oJt + 7r/2)
Comparing the current and voltage expressions we see that the current leads
the voltage by 7r/2 (90~ The waveforms and phasor diagrams are given in
Fig. 4.12(a) and (b).

Figure 4.12

v,,i /

t

I

r

(a) Waveforms (b) Phasor diagram

Now Im = wCVm and dividing both sides by ~/2 gives I- ~oCV (I and V are

now rms values). Rearranging we get

VII = 1/~C (4.11)

Now 1/wC is written Xc and is called the capacitive reactance of the capacitor,

for which the unit is the volt per ampere (the ohm). Since Xc = 1/wC = 1/2zrfC

it is dependent upon frequency. Fig. 4.13 shows how the capacitive reactance

and the current in the circuit of Fig. 4.11 vary with frequency.

Figure 4.13

Note that as

Xc~

0 "7

I

0 r f

f-->O so Xc---,~

and that as

and I ---, 0

f---,~ so Xc---'0 and I---,~

Example 4.6

In the circuit of Fig. 4.11, C = 120 IxF and the rms values of V and I are,

respectively, 100 V and 5 A. Calculate the frequency of the sinusoidal supply

voltage.