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)

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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