The figure shows a circuit containing an electromotive force, a capacitor with a capacitance of C farads (F), and a resistor with a resistance of R ohms (Ω). The voltage drop across the capacitor is Q/C, where Q is the charge (in coulombs, C), so in this case Kirchhoff’s Law gives RI + = E (1)But I = dQldt, so we haveR + ¿Q = E (1)dtSuppose the resistance is 5 2, the capacitance is 0.05 F, and a batterygives a constant voltage of 60 V.(a) Draw a direction field for this differential equation.(b) What is the limiting value of the charge?(c) Is there an equilibrium solution?(d) If the initial charge is Q (0) = 0 C, use the direction field to sketch thesolution curve.(e) If the initial charge is Q (0) = 0 C, use Euler's method with step size0.1 to estimate the charge after half a second. CER

Explanation of Solution Using graphing device draw the direction field of this differential…

Answered: RI + = E (1) But I = dQldt, so we have…

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

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The figure shows a circuit containing an electromotive force, a capacitor with a capacitance of C farads (F), and a resistor with a resistance of R ohms (Ω). The voltage drop across the capacitor is Q/C, where Q is the charge (in coulombs, C), so in this case Kirchhoff’s Law gives

RI + = E (1)
But I = dQldt, so we have
R + ¿Q = E (1)
dt
Suppose the resistance is 5 2, the capacitance is 0.05 F, and a battery
gives a constant voltage of 60 V.
(a) Draw a direction field for this differential equation.
(b) What is the limiting value of the charge?
(c) Is there an equilibrium solution?
(d) If the initial charge is Q (0) = 0 C, use the direction field to sketch the
solution curve.
(e) If the initial charge is Q (0) = 0 C, use Euler's method with step size
0.1 to estimate the charge after half a second.

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