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An electric circuit, consisting of a capacitor, resistor, and an electromotive force can be modeled by the differential equation bp dt 1 + R = E(t), where R and C are constants (resistance and capacitance) and = b q(t) is the amount of charge on the capacitor at time t. For simplicity in the following analysis, let R = C = 1, forming the differential equation dq/dt + q = E(t). In Exer- cises 17–20, an electromotive force is given in piecewise form, a favorite among engineers. Assume that the initial charge on the capacitor is zero [q(0) = 0]. (i) Use a numerical solver to draw a graph of the charge on the capacitor during the time interval [0, 4]. (ii) Hind an explicit solution and use the formula to determine the charge on the capacitor at the end of the four-second time period. 2t, if 0 < t < 2, 19. Е(() — 0, if t > 2

An electric circuit, consisting of a capacitor, resistor, and an electromotive force can be modeled by the differential equation bp dt 1 + R = E(t), where R and C are constants (resistance and capacitance) and = b q(t) is the amount of charge on the capacitor at time t. For simplicity in the following analysis, let R = C = 1, forming the differential equation dq/dt + q = E(t). In Exer- cises 17–20, an electromotive force is given in piecewise form, a favorite among engineers. Assume that the initial charge on the capacitor is zero [q(0) = 0]. (i) Use a numerical solver to draw a graph of the charge on the capacitor during the time interval [0, 4]. (ii) Hind an explicit solution and use the formula to determine the charge on the capacitor at the end of the four-second time period. 2t, if 0 < t < 2, 19. Е(() — 0, if t > 2

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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Please answer 19 part ii showing the steps to arrive at the solution also attached in a pic.

An electric circuit, consisting of a capacitor, resistor, and an electromotive force can be modeled by the differential equation bp R- 1 T9 = E(t), %3| dt where R and C are constants (resistance and capacitance) and q(t) is the amount of charge on the capacitor at time t. For simplicity in the following analysis, let R = C = 1, forming the differential equation dq/dt +q = E(t). In Exer- cises 17–20, an electromotive force is given in piecewise form, a favorite among engineers. Assume that the initial charge on the capacitor is zero [q(0) = 0]. (i) Use a numerical solver to draw a graph of the charge on the capacitor during the time interval [0, 4]. (ii) Hind an explicit solution and use the formula to determine the charge on the capacitor at the end of the four-second time period. || 2t, if 0 < t < 2, 19. Е((). | 0, if t > 2
Transcribed Image Text:An electric circuit, consisting of a capacitor, resistor, and an electromotive force can be modeled by the differential equation bp R- 1 T9 = E(t), %3| dt where R and C are constants (resistance and capacitance) and q(t) is the amount of charge on the capacitor at time t. For simplicity in the following analysis, let R = C = 1, forming the differential equation dq/dt +q = E(t). In Exer- cises 17–20, an electromotive force is given in piecewise form, a favorite among engineers. Assume that the initial charge on the capacitor is zero [q(0) = 0]. (i) Use a numerical solver to draw a graph of the charge on the capacitor during the time interval [0, 4]. (ii) Hind an explicit solution and use the formula to determine the charge on the capacitor at the end of the four-second time period. || 2t, if 0 < t < 2, 19. Е((). | 0, if t > 2
The exact solution is | 2(t – 1+e¬t), if 0 < t < 2, 2(1+e-2)e²-1, if t > 2 q(t) = Hence q(4) = 2(1+e-2)e-2 ~ 0.3073.
Transcribed Image Text:The exact solution is | 2(t – 1+e¬t), if 0 < t < 2, 2(1+e-2)e²-1, if t > 2 q(t) = Hence q(4) = 2(1+e-2)e-2 ~ 0.3073.
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