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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)
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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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 by i = dq/dt. So, the above equation becomes 1 dt T9 = 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 10-4 farad. Find the charge q(t) on the capacitor if q(0) = 0. Find the current i(t). Ans(t) = rOu (1 – e-50(); i(t) = }e=50t 100 (b) Let R = 10 ohms and C = 0.1 farad. Let E(t) be exponentially decaying, say, E(t) = 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-t-e-3); q'(t) = 0 gives tm = 0.549; qm = 0.577 coulomb
Transcribed Image Text: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 by i = dq/dt. So, the above equation becomes 1 dt T9 = 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 10-4 farad. Find the charge q(t) on the capacitor if q(0) = 0. Find the current i(t). Ans(t) = rOu (1 – e-50(); i(t) = }e=50t 100 (b) Let R = 10 ohms and C = 0.1 farad. Let E(t) be exponentially decaying, say, E(t) = 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-t-e-3); q'(t) = 0 gives tm = 0.549; qm = 0.577 coulomb
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