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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 ohms (^). The voltage drop across the capacitor is Q/C, where Q is the charge (in coulombs), so in this case we use the Kirchhoff's Law. RI + = E (t) But I = dQ/dt, so we have the formula below. R +e = E() dt Suppose the resistance is 20 N, the capacitance is 0.01 F, and a battery gives a constant voltage of 100 V. (a) Draw a direction field for this differential equation. (Do this on paper. Your instructor may ask you to turn in this sketch.) (b) What is the limiting value, Q of the charge? Q = 1 (c) What is an equilibrium solution? Q = 1

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 ohms (^). The voltage drop across the capacitor is Q/C, where Q is the charge (in coulombs), so in this case we use the Kirchhoff's Law. RI + = E (t) But I = dQ/dt, so we have the formula below. R +e = E() dt Suppose the resistance is 20 N, the capacitance is 0.01 F, and a battery gives a constant voltage of 100 V. (a) Draw a direction field for this differential equation. (Do this on paper. Your instructor may ask you to turn in this sketch.) (b) What is the limiting value, Q of the charge? Q = 1 (c) What is an equilibrium solution? Q = 1

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 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 (2). The voltage drop across the capacitor is Q/C, where Q is the charge (in coulombs), so in this case we use the Kirchhoff's Law. RI + := E (t) But I = dQ/dt, so we have the formula below. ' = E (t) dt Suppose the resistance is 20 n, the capacitance is 0.01 F, and a battery gives a constant voltage of 100 V. (a) Draw a direction field for this differential equation. (Do this on paper. Your instructor may ask you to turn in this sketch.) (b) What is the limiting value, Q of the charge? Q = 1 (c) What is an equilibrium solution? Q = 1 (d) If the initial charge is Q(0) = 0 C, use the direction field to sketch the solution curve. (Do this on paper. Your instructor may ask you to turn in this sketch.) (e) If the initial charge is Q(0) = 0 C, use Euler's method with step size 0.1 to estimate the charge, Q after half a second, Q(0.5). (Round your answer to the nearest hundredth.) Q(0.5) = C
Transcribed Image Text: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 (2). The voltage drop across the capacitor is Q/C, where Q is the charge (in coulombs), so in this case we use the Kirchhoff's Law. RI + := E (t) But I = dQ/dt, so we have the formula below. ' = E (t) dt Suppose the resistance is 20 n, the capacitance is 0.01 F, and a battery gives a constant voltage of 100 V. (a) Draw a direction field for this differential equation. (Do this on paper. Your instructor may ask you to turn in this sketch.) (b) What is the limiting value, Q of the charge? Q = 1 (c) What is an equilibrium solution? Q = 1 (d) If the initial charge is Q(0) = 0 C, use the direction field to sketch the solution curve. (Do this on paper. Your instructor may ask you to turn in this sketch.) (e) If the initial charge is Q(0) = 0 C, use Euler's method with step size 0.1 to estimate the charge, Q after half a second, Q(0.5). (Round your answer to the nearest hundredth.) Q(0.5) = C
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