2. The voltage drop across a capacitor with capacitance C is given by q(t)/C, where q is the charge on the capacitor. Hence, for the RC series circuit, Kirchhop's second law gives Ri + a = E(t) But current i and charge q are related byi= dq/dt. So, the above equation becomes dq 1 R dt 9 = E(t) Use this differential equation to solve the following: (a) A 100 volt electromotive force is applied an RC series circuit in which the resistance is 200 ohms and the capacitance is 10-+ farad. Find the charge q(t) on the capacitor if q(0) = 0. Find the current i(f). Ans(t) = r (1 – e-50*); i(t) = ļe¬50t (b) Let R = 10 ohms and C = 0.1 farad. Let E(t) be exponentially decaying, say, E(E) = 30e-3t volts. Assuming q(0) = 0, find and graph q(t). At what time does q(t) reach a maximum? What is that maximum charge? Ans: q(t) = 1.5(e-- e-3); q'(f) = 0 gives tm= 0.549; qm= 0.577 coulomb %3D

2. The voltage drop across a capacitor with capacitance C is given by q(t)/C, where q is the charge on the capacitor. Hence, for the RC series circuit, Kirchhop's second law gives Ri + a = E(t) But current i and charge q are related byi= dq/dt. So, the above equation becomes dq 1 R dt 9 = E(t) Use this differential equation to solve the following: (a) A 100 volt electromotive force is applied an RC series circuit in which the resistance is 200 ohms and the capacitance is 10-+ farad. Find the charge q(t) on the capacitor if q(0) = 0. Find the current i(f). Ans(t) = r (1 – e-50*); i(t) = ļe¬50t (b) Let R = 10 ohms and C = 0.1 farad. Let E(t) be exponentially decaying, say, E(E) = 30e-3t volts. Assuming q(0) = 0, find and graph q(t). At what time does q(t) reach a maximum? What is that maximum charge? Ans: q(t) = 1.5(e-- e-3); q'(f) = 0 gives tm= 0.549; qm= 0.577 coulomb %3D

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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An inductance of 1 H, a resistance of 8 Ω and capacitance of 0.04 F are connected in series with a variable voltage E = 50 sin 3t. Find the current and charge in the system, given the initial conditions q = 0 and l = 0 when t = 0, using method of solution of higher order linear ordinary differential equation.
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