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Calculate i(t) for t>0 in the circuit of Fig. 8.82. 20u(-1) V

Calculate i(t) for t>0 in the circuit of Fig. 8.82. 20u(-1) V

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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why the resistor disappear when t>0

Calculate i(t) for t> 0 in the circuit of Fig. 8.82. F 20u(-1) V Figure 8.82 For Prob. 8.34. Chapter 8, Solution 34. Before t= 0, the capacitor acts like an open circuit while the inductor behaves like a short circuit. i(0) = 0, v(0) = 20 V For t> 0, the LC circuit is disconnected from the voltage source as shown below. V, i (1/16)F () H This is a lossless, source-free, series RLC circuit. 1 a = R/(2L) = 0, w, = 1/ /LC = 1/. V16 1 = 8, s= ±j8 4 Since a is less than o, we have an underdamped response. Therefore, i(t) = Ajcos8t + A2sin8t where i(0) = 0 = A1 di(0)/dt = (1/L)vL(0) = -(1/L)v(0)= -4x20 = -80 However, di/dt = 8A2cos8t, thus, di(0)/dt = -80 = 8A2 which leads to A2 = -10
Transcribed Image Text:Calculate i(t) for t> 0 in the circuit of Fig. 8.82. F 20u(-1) V Figure 8.82 For Prob. 8.34. Chapter 8, Solution 34. Before t= 0, the capacitor acts like an open circuit while the inductor behaves like a short circuit. i(0) = 0, v(0) = 20 V For t> 0, the LC circuit is disconnected from the voltage source as shown below. V, i (1/16)F () H This is a lossless, source-free, series RLC circuit. 1 a = R/(2L) = 0, w, = 1/ /LC = 1/. V16 1 = 8, s= ±j8 4 Since a is less than o, we have an underdamped response. Therefore, i(t) = Ajcos8t + A2sin8t where i(0) = 0 = A1 di(0)/dt = (1/L)vL(0) = -(1/L)v(0)= -4x20 = -80 However, di/dt = 8A2cos8t, thus, di(0)/dt = -80 = 8A2 which leads to A2 = -10
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