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
.
∠
YT89 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)