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UNIVERSITI TEKNIKAL MALAYSIA MELAKAFACULTY OF ELECTRONIC ENGINEERING AND COMPUTER ENGINEERING

BENT 1123 ELECTRICAL CIRCUIT ANALYSISTUTORIAL 3 (Second-Order Circuits)

Finding Initial and Final Values.

1. For the circuit in Fig. 1, find:

(a) i(0+) and v(0+),

(b) di(0+)/dt and dv(0+)/dt,

(c) i() and v().

Figure 1

Source-Free Series RLC Circuit.

2. The differential equation that describes the voltage in an RLC network is

2

25 4 0

d v dvv

dt dt

Given that v(0) = 0, dv(0)/dt = 5, obtain v(t).

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3. Find i(t) for t > 0 in the circuit of Fig. 2

Figure 2

4. Find the voltage across the capacitor as a function of time for Fig. 3. Assume steady-state conditions exist

Figure 3

Source-Free Parallel RLC Circuit.

5. Assuming R=2 k, design a parallel RLC circuit that has the characteristic equation2 6100 10 0s s .

Step Response of a Series RLC Circuit.

6. A branch voltage in an RLC

v8dt

dv4

dt

vd2

2

If the initial conditions are

20V

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> 0 in the circuit of Fig. 2

Find the voltage across the capacitor as a function of time for t > 0 for the circuit state conditions exist at t = 0-.

Free Parallel RLC Circuit.

, design a parallel RLC circuit that has the characteristic equation100 10 0

RLC Circuit.

RLC circuit is described by

48v

If the initial conditions are v(0) = 0 = dv(0)/dt, find v(t).

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0 for the circuit in

, design a parallel RLC circuit that has the characteristic equation

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7. Refer to the circuit in Fig. 4. Calculate i(t) for t > 0.

Figure 4

Step Response of a Parallel RLC Circuit.

8. In the circuit of Fig. 5, find v(t) and i(t) for t > 0. Assume v(0) = 0 V and i(0) = 1 A.

Figure 5

6(1u(t)) A

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9. Find the output voltage vo(t) in the circuit of Fig. 6.

Figure 6

10. Determine i(t) for t > 0 in the circuit of Fig. 7.

Figure 7

General Second-Order Circuits.

11. After being open for a day, the switch in the circuit of Fig. 8 is closed at t=0. Find the differential equation describing i(t), t >0.

80 t=0

i

120 V 10 mF 0.25 H

Figure 8

+_

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12. For the circuit in Fig. 9, find v(t) for t > 0. Assume that v(0+) = 4 V and i(0+) = 2 A.

Figure 9