The voltage drop across a capacitor with capacitance C is given by q(t)/C, where qis the charge on the capacitor. Hence, for the RC series circuit, Kirchhop's secondlaw gives2.1Ri + 79E(t).But current i and charge q are related by i = dq/dt. So, the above equation becomesdąR-1E(t).dt T9Use 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 doesq(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

(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

Power System Analysis and Design (MindTap Course List)

6th Edition

ISBN:9781305632134

Author:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma

Publisher:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma

Chapter6: Power Flows

Section: Chapter Questions

Problem 6.27P

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Question

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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