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The capacitor voltage of the RC circuit depicted in Fig Q3 is denoted by V.(t). Vin R Vc(s) = 1(t) 7 Fig. Q3 RC circuit R=4000 2 is the resistance, C = 2 x 106 F is the capacitance, Vin (t) is the input voltage and I(t) is the electric current. The capacitor voltage Ve(t)is given by the solution of the equation RCVc(t) + Vc(t) = Vin(t). The capacitor voltage is related to the current through the equation I(t) = CVc(t). a) It is assumed that the input voltage is Vin (t) = t-e-4t and the initial capacitor voltage and initial current are both zero. By calculating the Laplace Transform of Equation (3.1), show that the capacitor Vc(s) in the frequency domain is Vc(t) -125 (8²-8-4) 8² (8+4)(8 +125) b) Calculate the electric current 1(s) in the frequency domain. c) Using the final value theorem, calculate the limit electric current as t goes to infinity. d) Derive I(t) by inverse Laplace transform. e) Using I(t) calculated in Q3-d, calculate the limit electric current as t goes to infinity. f) Using I(t) calculated in Q3-d, calculate Ve(t).

The capacitor voltage of the RC circuit depicted in Fig Q3 is denoted by V.(t). Vin R Vc(s) = 1(t) 7 Fig. Q3 RC circuit R=4000 2 is the resistance, C = 2 x 106 F is the capacitance, Vin (t) is the input voltage and I(t) is the electric current. The capacitor voltage Ve(t)is given by the solution of the equation RCVc(t) + Vc(t) = Vin(t). The capacitor voltage is related to the current through the equation I(t) = CVc(t). a) It is assumed that the input voltage is Vin (t) = t-e-4t and the initial capacitor voltage and initial current are both zero. By calculating the Laplace Transform of Equation (3.1), show that the capacitor Vc(s) in the frequency domain is Vc(t) -125 (8²-8-4) 8² (8+4)(8 +125) b) Calculate the electric current 1(s) in the frequency domain. c) Using the final value theorem, calculate the limit electric current as t goes to infinity. d) Derive I(t) by inverse Laplace transform. e) Using I(t) calculated in Q3-d, calculate the limit electric current as t goes to infinity. f) Using I(t) calculated in Q3-d, calculate Ve(t).

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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The capacitor voltage of the RC circuit depicted in Fig Q3 is denoted by V.(t). Vin R Vc(s) = 1 (t) Fig. Q3 RC circuit R=4000 2 is the resistance, C = 2 x 106 F is the capacitance, Vin (t) is the input voltage and I(t) is the electric current. The capacitor voltage Ve(t)is given by the solution of the equation RCVc(t) + Vc(t) = Vin(t). The capacitor voltage is related to the current through the equation I(t) = CVc(t). a) It is assumed that the input voltage is Vin(t) = t-e-4t and the initial capacitor voltage and initial current are both zero. By calculating the Laplace Transform of Equation (3.1), show that the capacitor Vc(s) in the frequency domain is Vc (t) -125 (8²-8-4) 8² (8+4)(8 +125) b) Calculate the electric current I(s) in the frequency domain. c) Using the final value theorem, calculate the limit electric current as t goes to infinity. d) Derive I(t) by inverse Laplace transform. e) Using I(t) calculated in Q3-d, calculate the limit electric current as t goes to infinity. f) Using I(t) calculated in Q3-d, calculate Ve(t).
Transcribed Image Text:The capacitor voltage of the RC circuit depicted in Fig Q3 is denoted by V.(t). Vin R Vc(s) = 1 (t) Fig. Q3 RC circuit R=4000 2 is the resistance, C = 2 x 106 F is the capacitance, Vin (t) is the input voltage and I(t) is the electric current. The capacitor voltage Ve(t)is given by the solution of the equation RCVc(t) + Vc(t) = Vin(t). The capacitor voltage is related to the current through the equation I(t) = CVc(t). a) It is assumed that the input voltage is Vin(t) = t-e-4t and the initial capacitor voltage and initial current are both zero. By calculating the Laplace Transform of Equation (3.1), show that the capacitor Vc(s) in the frequency domain is Vc (t) -125 (8²-8-4) 8² (8+4)(8 +125) b) Calculate the electric current I(s) in the frequency domain. c) Using the final value theorem, calculate the limit electric current as t goes to infinity. d) Derive I(t) by inverse Laplace transform. e) Using I(t) calculated in Q3-d, calculate the limit electric current as t goes to infinity. f) Using I(t) calculated in Q3-d, calculate Ve(t).
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