Alternating Current Analysis
311
P.3.11 Let the impedance of a given circuit be given by Z = 7.05 + j9.7 Ω, and the peak
sinusoidal voltage across be V m = 60 V. Verify the following:
a. Z = 12 ∠54° Ω
b. I m = 5 A
c. V eff = 42.42 V
d. I eff = 3.535 A
e. S = P AP = 150 va
f. P = 88.1 W
g. Q = P reac = 121.2 var
h. p(t) = V m ⋅ I m [cos(θ) sin(2ωt) − (1/2)sin(θ) sin(2ωt)], where cos(θ) = cos(54°) = 0.588
and sin(θ) = sin(54°) = 0.809
i. Evaluate the maximum and minimum of p(t) by solving the equation given
by
dp(t)
_____
dt
= 0
Check if the solutions occur at ωt = 27 rad or 117 rad
and if p max = 238 W
and
p min = −61.7 W
P.3.12 A resistor of 50 Ω and an inductor of L = 0.1 H are connected in series where the
applied voltage is sinusoidal with 110 V RMS , and frequency f = 60 Hz. Verify the
following:
a. v(t) = 156 sin(2π 60t) V
b. Z = 50 + j37.7 Ω
c. Z = 62.5 ∠37° Ω
d. I = 2.5 ∠–37° A
e. i(t) = 2.5 sin(2π 60 t − 37°) A
f. I RMS = 1.76 A
g. |Z| = 62.5 Ω
P.3.13 A series RC circuit consisting of a resistor R = 10 KΩ and a capacitor C = 10 µF, with
an applied voltage given by sine wave of 10 V, with a frequency of 1 kHz. Verify the
following:
a. v(t) = 14.14 sin 6283t V
b. Z = 10,000 − j15,900 Ω
c. Z = 18,800 ∠−58° Ω
d. I = 0.752 ∠58° mA
e. i(t) = 0.752 sin(6283t + 58°) mA
f. I RMS = 0.532 mA
g. V R(peak) = 7.52 V
h. V R(RMS) = 5.32 V
i. V C(peak) = 11.96 V
j. V C(RMS) = 8.46 V
CRC_47760_CH003.indd 311
CRC_47760_CH003.indd 311
7/23/2008 1:27:54 PM
7/23/2008 1:27:54 PM