Introduction to Electric Circuits

Example 4.19

4.5 Parallel a.c. circuits 93

Determine the magnitude and phase of the current drawn from the supply in

the circuit of Fig. 4.31.

Figure 4.31

Solution

From Equation (4.30) the admittance of the circuit is given by Y = G- jBL.

Now G = 1/R = 1/5 = 0.2 S, and

B L = 1IX L = 1/2.nfL : 1/(2vr 50 • 20 x 10 -3) = 0.16 S

Therefore

Y = (0.2 - j 0.16) S = 0.26/_-38.7 ~ S

Let the voltage be the reference so that V = 20/_0 ~ V. Then the current

I V/Z and since Z = 1//Y

I = VY (4.32)

Therefore

I = 20 x 0.26/_[0 ~ + (-38.7~ = 5.2/_-38.7~ A

The current therefore lags the voltage as expected in an inductive circuit.

Parallel RC circuits

The diagram of Fig. 4.32(a) shows a resistor R in parallel with a capacitor C.
The corresponding phasor diagram is given in Fig. 4.32(b). In this case, with the
voltage V as the reference phasor, we have IR in phase with V and Ic leading V
by 90 ~ From KCL we have that I = IR + Ic phasorially,

=C

I

In V (reference)

(a) (b)

Figure 4.32