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Real Analog - Circuits 1
Chapter 8: Homework
Chapter 8 Homework:
8.1
For the circuit below,
a. Determine the second order differential equation governing v(t).
b. Find R so that the circuit is critically damped.
+
i(t)
R
0.01F
v(t)
1H
-
8.2
For the circuit below,
a. Determine the differential equation that governs vC(t), t>0.
b. Is the system under, over, or critically damped?
t=0
3Ω
1mF
6V
+
-
+
vC(t)
-
1mH
2Ω
8.3
For the circuit below,
a. Determine the differential equation for iL(t), t>0.
b. Determine the initial (t=0+) and final (t) conditions on vC(t) and iL(t).
t=0
3Ω
1V
+
-
+
vC(t)
2Ω
1F
iL(t)
2H
8.4
The switch moves from position A to position B at t=0 seconds.
a. Determine the differential equation that governs iL(t), t>0.
© 2012 Digilent, Inc.
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Real Analog – Circuits 1
Chapter 8: Homework
b. Determine initial (t=0+) and final (t) conditions on vC(t) and iL(t).
10Ω
iL(t)
20V
3Ω
A
B
t=0
+
+
-
1
F
20
4H
+
-
vC(t)
4V
-
8.5
For the circuit below,
a. Determine the differential equation governing i(t).
b. Determine  and n
c. Find the maximum value of current through the resistor in response to a step input
u(t) = 3u0(t) A.
1H
u(t)
8.6
0.01F
4Ω
i(t)
A current in a second order circuit is described by the differential equation
𝑑2 𝑖(𝑡)
𝑑𝑖(𝑡)
+6
+ 100𝑖(𝑡) = 50𝑢0 (𝑡)
𝑑𝑡
𝑑𝑡
a. Determine the damping ratio, undamped natural frequency, and damped natural frequency for
the circuit.
b. Sketch the response of the circuit to a unit step input. Include numerical values for tr, the
maximum value of i(t), and the steady-state value of i(t).
© 2012 Digilent, Inc.
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Real Analog – Circuits 1
Chapter 8: Homework
8.7
For the circuit below, determine
a. The differential equation for iL(t), t>0.
b. The initial (t=0+) and final (t) conditions on vC(t) and iL(t).
t=0
3Ω
iL(t)
2H
3A
+
vC(t)
4Ω
1F
-
8.8
The switch moves from position A to position B at t=0 seconds.
a. Determine the differential equation that governs vC(t), t>0.
b. Determine initial (t=0+) and final (t) conditions on vC(t) and iL(t).
2Ω
t=0
A
+ vc(t) B
10V
+
-
2F
iL(t)
© 2012 Digilent, Inc.
3H
2Ω
3
Real Analog – Circuits 1
Chapter 8: Homework
8.9
The switch moves from position A to position B at t=0 seconds.
a. Determine the differential equation that governs vC(t), t>0.
b. Determine initial (t=0+) and final (t) conditions on vC(t) and iL(t).
4W
t=0
2W
+
vC(t)
2A
iL(t)
2F
1H
8.10 The differential equation governing a voltage vout(t) in a circuit is:
2
d 2 vout ( t )
dt
2
4
dvout ( t )
 50vout ( t )  100vin ( t )
dt
Determine the maximum value of vout(t) resulting from a step voltage input
 0,t  0
.
vin ( t )  
2V ,t  0
8.11 For the circuit below, determine
a. The differential equation for iL(t), t>0
b. The initial (t=0+) and final (t) conditions on vC(t) and iL(t).
2Ω
iL(t)
t=0
B
4H
A
8V
+
-
+
2Ω
0.5F
vc(t)
-
© 2012 Digilent, Inc.
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