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(b) Let R = 10 ohms and C = 0.1 farad. Let E(t) be exponentially decaying, say, E(t) = 30e q(t) reach a maximum? What is that maximum charge? volts. Assuming q(0) = 0, find and graph q(t). At what time does Ans: q(t) = 1.5(e--e-*); d'(t) = 0 gives tm 0.549; qm = 0.577 coulomb

(b) Let R = 10 ohms and C = 0.1 farad. Let E(t) be exponentially decaying, say, E(t) = 30e q(t) reach a maximum? What is that maximum charge? volts. Assuming q(0) = 0, find and graph q(t). At what time does Ans: q(t) = 1.5(e--e-*); d'(t) = 0 gives tm 0.549; qm = 0.577 coulomb

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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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 2. 1 Ri + 79 E(t). But current i and charge q are related by i = dq/dt. So, the above equation becomes dą R- 1 E(t). dt T9 Use this differential equation to solve the following: (b) Let R = 10 ohms and C = 0.1 farad. Let E(t) be exponentially decaying, say, E(t) = 30e * 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(et -e-3t); q'(t) = 0 gives tm = 0.549; qm = 0.577 coulomb
Transcribed Image Text: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 2. 1 Ri + 79 E(t). But current i and charge q are related by i = dq/dt. So, the above equation becomes dą R- 1 E(t). dt T9 Use this differential equation to solve the following: (b) Let R = 10 ohms and C = 0.1 farad. Let E(t) be exponentially decaying, say, E(t) = 30e * 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(et -e-3t); q'(t) = 0 gives tm = 0.549; qm = 0.577 coulomb
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