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Problem Set 8
Chapter 9: The Complete Response of Circuits with Two
Energy Storage Elements
Due: see website for due date
P 9.2-2
Find the differential equation for iL(t) using the operator method.
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2
8
Answer: 1.1 10 iL  11000siL  s iL  1 10 is
P 9.2-3
Find the differential equation for iL(t) for t > 0 for the circuit.
Answer:
d2iL  R1
R1
R di
1  diL  R1
1 
1 dv s
 


is  1 s 

 iL  
2
dt
R2LC
L dt L dt
 L R2C  dt  R2LC LC 
P 9.3-3
Find the characteristic equation and its roots for the circuit shown.
Answer: s2  102000s  3  108  0; s1  3031, s2  98969
P 9.4-2
The switch has been open for a long time (vC(0−) = 2V) before
closing at t = 0. Determine and plot vC(t). Answer: et  3e3t V
P 9.5-3
Police often use stun guns to incapacitate potentially dangerous felons. The hand-held
device provides a series of high-voltage, low-current pulses. The power of the pulses is
far below lethal levels, but it is enough to cause muscles to contract and put the person
out of action. The device provides a pulse of up to 50,000 V,
and a current of 1 mA flows through an arc. A model of the
circuit for one period is shown. Find v(t) for 0 < t < 1 ms. The
resistor R represents the spark gap. Select C so that the
response is critically damped.
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Answer: 1012 te510
t
1
P 9.6-3
A 240-W power supply circuit is shown. This circuit
employs a large inductor and a large capacitor. Find iL(t)
for t > 0.
Answer: e2 t  4 cos t  2 sin t  A
P 9.8-2
Determine i(t) for t > 0 for the circuit.
Answer: 0.2  0.246 e3.62 t  0.646 e1.38 t A
Hint:
d2i
di
 5  5i  1.
2
dt
dt
P 9.8-8
Find vC(t) for t > 0 for the circuit.
Answer: 0.123 e
5.65 t
 0.877 e
0.35 t
1 V
2
Hint:
d vC
dv
 6 C  2v C  2 .
2
dt
dt
P 9.8-14
Determine vC(t) for t > 0.
Answer:
16  e
2.5 t
 16 cos 9.682 t  4.131sin 9.682 t 
V
SP 9-3
Determine and plot the capacitor voltage v(t) for 0 < t < 300 μs for the circuit shown. The
sources are also shown below.
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