PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

Alternating Current Analysis 237

where G = 1/R then

i(t) = Vm|Y| cos(t + )

where θ = tan−^1 (−R/ωL).

Clearly, the voltage v(t) across the parallel RL connection shown in Figure 3.5 leads

the current i(t), by a phase angle of θ rad.

R.3.37 Let us now explore the RC parallel case. Evaluate the current i(t) of the parallel RC

circuit, shown in Figure 3.6, assuming that the applied voltage is given by

v(t) = Vm cos(t)

ANALYTICAL Solution

Then the current i(t) is given by i(t) = Vm|Y|cos(ωt + θ), where

Y

R

CC
 R

^1221





 ()

()and tan

Clearly the current i(t) leads the voltage v(t) by an angle θ.

R.3.38 Let us consider now a numerical example. Evaluate for the circuit diagram shown

in Figure 3.7

a. The total admittance Y

b. V, IR, and IC

ANALYTICAL Solution

Part a

Y

RX j

j

T

C

 
 





11 1

12 5

1

25

1

..12 5 25

YT
 

1

12 5

1

25

12 5

25

22

1

.

tan

.















∠ 







YT
89 10* ^3 ∠26 6.°

FIGURE 3.5

RL parallel circuit diagram of R.3.36.

i(t)

R L

+

v(t)

FIGURE 3.6

RC parallel circuit diagram of R.3.37.

i(t)

R C

+

v(t)