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55. Figure 8 shows a circuit consisting of a resistor of R ohms, a capacitor of C farads, and a battery of voltage V. When the circuit is completed, the amount of charge q(t) (in coulombs) on the plates of the capacitor varies according to the differential equation (t in seconds) dq R= dt where R, C, and V are constants. (a) Solve for q(t), assuming that q (0) = 0. (b) Sketch the graph of q. (c) Show that lim q(t) = CV. t-00 (d) Show that the capacitor charges to approximately 63% of its final value CV after a time period of length t is called the time constant of the capacitor). RC (t FIGURE 8 An RC circuit.

55. Figure 8 shows a circuit consisting of a resistor of R ohms, a capacitor of C farads, and a battery of voltage V. When the circuit is completed, the amount of charge q(t) (in coulombs) on the plates of the capacitor varies according to the differential equation (t in seconds) dq R= dt where R, C, and V are constants. (a) Solve for q(t), assuming that q (0) = 0. (b) Sketch the graph of q. (c) Show that lim q(t) = CV. t-00 (d) Show that the capacitor charges to approximately 63% of its final value CV after a time period of length t is called the time constant of the capacitor). RC (t FIGURE 8 An RC circuit.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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55. Figure 8 shows a circuit consisting of a resistor of R ohms, a capacitor of C farads, and a battery of voltage V. When the circuit is completed, the amount of charge q(t) (in coulombs) on the plates of the capacitor varies according to the differential equation (t in seconds) dq R= dt where R, C, and V are constants. (a) Solve for q(t), assuming that q (0) = 0. (b) Sketch the graph of q. (c) Show that lim q(t) = CV. t-00 (d) Show that the capacitor charges to approximately 63% of its final value CV after a time period of length t is called the time constant of the capacitor). RC (t FIGURE 8 An RC circuit.
Transcribed Image Text:55. Figure 8 shows a circuit consisting of a resistor of R ohms, a capacitor of C farads, and a battery of voltage V. When the circuit is completed, the amount of charge q(t) (in coulombs) on the plates of the capacitor varies according to the differential equation (t in seconds) dq R= dt where R, C, and V are constants. (a) Solve for q(t), assuming that q (0) = 0. (b) Sketch the graph of q. (c) Show that lim q(t) = CV. t-00 (d) Show that the capacitor charges to approximately 63% of its final value CV after a time period of length t is called the time constant of the capacitor). RC (t FIGURE 8 An RC circuit.
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