Question

PART 1-SOURCE FREE RLC 1. A parallel RLC circuit has the following circuit parameters: R = 1 \Omega, L = 2 H, and C = 2 F. Calculate the damping ratio and the undamped natural frequency of this network. ANSWER: \zeta = 0.5; \omega_0 = 0.5 rad/s. 2. A series RLC circuit consists of R = 2 \Omega, L = 1 H, and a capacitor. Determine the type of response exhibited by the network if (a) C = 1/2 F, (b) C = 1 F, and (c) C = 2 F. ANSWER: (a) underdamped; (b) critically damped; (c) overdamped. 3. The switch in the network in Fig. 1 opens at t = 0. Find i(t) for t > 0. Figure 1 1F 6\Omega 3\Omega t=0 2H +12V $i(t)$ ANSWER: i(t) = -2e^{-t/2} + 4e^{-t} A. 4. The switch in the network in Fig.2. moves from position 1 to position 2 at t = 0. Find v_o(t) for t > 0. 1/2 H 2/3 F 1 2 t=0 2A 2\Omega v_o(t) Figure 2 ANSWER: v_o(t) = 2(e^{-t} - 3e^{-3t}) V.

          PART 1-SOURCE FREE RLC
1. A parallel RLC circuit has the following circuit parameters: R = 1 \Omega, L = 2 H, and C = 2
F. Calculate the damping ratio and the undamped natural frequency of this network.
ANSWER: \zeta = 0.5; \omega_0 = 0.5 rad/s.
2. A series RLC circuit consists of R = 2 \Omega, L = 1 H, and a capacitor. Determine the type of
response exhibited by the network if (a) C = 1/2 F, (b) C = 1 F, and (c) C = 2 F.
ANSWER: (a) underdamped; (b) critically damped; (c) overdamped.
3. The switch in the network in Fig. 1 opens at t = 0. Find i(t) for t > 0.
Figure 1
1F
6\Omega
3\Omega
t=0
2H
+12V
$i(t)$
ANSWER: i(t) = -2e^{-t/2} + 4e^{-t} A.
4. The switch in the network in Fig.2. moves from position 1 to position 2 at t = 0. Find v_o(t)
for t > 0.
1/2 H
2/3 F
1
2
t=0
2A
2\Omega
v_o(t)
Figure 2
ANSWER: v_o(t) = 2(e^{-t} - 3e^{-3t}) V.

PART 1-SOURCE FREE RLC
1. A parallel RLC circuit has the following circuit parameters: R = 1 Ω, L = 2 H, and C = 2
F. Calculate the damping ratio and the undamped natural frequency of this network.
ANSWER: ζ= 0.5; ω0 = 0.5 rad/s.
2. A series RLC circuit consists of R = 2 Ω, L = 1 H, and a capacitor. Determine the type of
response exhibited by the network if (a) C = 1/2 F, (b) C = 1 F, and (c) C = 2 F.
ANSWER: (a) underdamped; (b) critically damped; (c) overdamped.
3. The switch in the network in Fig. 1 opens at t = 0. Find i(t) for t > 0.
Figure 1
1F
6Ω3Ωt=0
2H
+12V
i(t)
ANSWER: i(t) = -2e^-t/2 + 4e^-t A.
4. The switch in the network in Fig.2. moves from position 1 to position 2 at t = 0. Find vo(t)
for t > 0.
1/2 H
2/3 F
1
2
t=0
2A
2Ωvo(t)
Figure 2
ANSWER: vo(t) = 2(e^-t - 3e^-3t) V.

Added by Mark A.

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