Find v(1) and i(t) in the circuit shown in

Power System Analysis and Design (MindTap Course List)
6th Edition
ISBN:9781305632134
Author:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma
Publisher:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma
Chapter2: Fundamentals
Section: Chapter Questions
Problem 2.7P: Let a 100V sinusoidal source be connected to a series combination of a 3 resistor, an 8 inductor,...
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Find v(1) and i(t) in the circuit shown in
olution:
on the voltage source 10 cos 4r, w = 4.
V. = 10/0°V
impedance is
Z=5+
ence the current
jwC
V = IZC
+
10/0°
Z
5 - j2.5
= 1.6 + j0.8 =
he voltage across the capacitor is
I
jwC
1
j4 x 0.1
E
1.789/26.57°
j4 x 0.1
1.789/26.57°
0.4/90°
and
10(5 + £2.5)
5² +2.5²
1.789/26.57° A
5-j2.50
nverting I and V in Eqs.
i(t)
1.789 cos(41+ 26.57°) A
u(t) = 4.47 cos(41- 63.43°) V
4-10 cos 4r
ice that i(t) leads vir) by 90° as expected.
4.47/-63.43° V
to the time domain, we get
a
prime
video
X
502
ww
0.1 F
+
8
Transcribed Image Text:Find v(1) and i(t) in the circuit shown in olution: on the voltage source 10 cos 4r, w = 4. V. = 10/0°V impedance is Z=5+ ence the current jwC V = IZC + 10/0° Z 5 - j2.5 = 1.6 + j0.8 = he voltage across the capacitor is I jwC 1 j4 x 0.1 E 1.789/26.57° j4 x 0.1 1.789/26.57° 0.4/90° and 10(5 + £2.5) 5² +2.5² 1.789/26.57° A 5-j2.50 nverting I and V in Eqs. i(t) 1.789 cos(41+ 26.57°) A u(t) = 4.47 cos(41- 63.43°) V 4-10 cos 4r ice that i(t) leads vir) by 90° as expected. 4.47/-63.43° V to the time domain, we get a prime video X 502 ww 0.1 F + 8
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