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Problem 7.2 A capacitor C has been charged up to potential Vo; at time t = 0, it is connected to a resistor R, and begins to discharge (Fig. 7.5a). +Q -Q (a) ww R +Q C Vo Te R FIGURE 7.5 (b) (a) Determine the charge on the capacitor as a function of time, Q(t). What is the current through the resistor, I (t)? (b) What was the original energy stored in the capacitor (Eq. 2.55)? By integrating Eq. 7.7, confirm that the heat delivered to the resistor is equal to the energy lost by the capacitor. Now imagine charging up the capacitor, by connecting it (and the resistor) to a battery of voltage Vo, at time t = 0 (Fig. 7.5b). (c) Again, determine Q(t) and I(t). (d) Find the total energy output of the battery (f VoI dt). Determine the heat de- livered to the resistor. What is the final energy stored in the capacitor? What fraction of the work done by the battery shows up as energy in the capacitor? [Notice that the answer is independent of R!]

Problem 7.2 A capacitor C has been charged up to potential Vo; at time t = 0, it is connected to a resistor R, and begins to discharge (Fig. 7.5a). +Q -Q (a) ww R +Q C Vo Te R FIGURE 7.5 (b) (a) Determine the charge on the capacitor as a function of time, Q(t). What is the current through the resistor, I (t)? (b) What was the original energy stored in the capacitor (Eq. 2.55)? By integrating Eq. 7.7, confirm that the heat delivered to the resistor is equal to the energy lost by the capacitor. Now imagine charging up the capacitor, by connecting it (and the resistor) to a battery of voltage Vo, at time t = 0 (Fig. 7.5b). (c) Again, determine Q(t) and I(t). (d) Find the total energy output of the battery (f VoI dt). Determine the heat de- livered to the resistor. What is the final energy stored in the capacitor? What fraction of the work done by the battery shows up as energy in the capacitor? [Notice that the answer is independent of R!]

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Problem 7.2 A capacitor C has been charged up to potential Vo; at time t = 0, it is connected to a resistor R, and begins to discharge (Fig. 7.5a). +Q -Q (a) ww R +Q C Vo Te R FIGURE 7.5 (b) (a) Determine the charge on the capacitor as a function of time, Q(t). What is the current through the resistor, I (t)? (b) What was the original energy stored in the capacitor (Eq. 2.55)? By integrating Eq. 7.7, confirm that the heat delivered to the resistor is equal to the energy lost by the capacitor. Now imagine charging up the capacitor, by connecting it (and the resistor) to a battery of voltage Vo, at time t = 0 (Fig. 7.5b). (c) Again, determine Q(t) and I(t). (d) Find the total energy output of the battery (f VoI dt). Determine the heat de- livered to the resistor. What is the final energy stored in the capacitor? What fraction of the work done by the battery shows up as energy in the capacitor? [Notice that the answer is independent of R!]
Transcribed Image Text:Problem 7.2 A capacitor C has been charged up to potential Vo; at time t = 0, it is connected to a resistor R, and begins to discharge (Fig. 7.5a). +Q -Q (a) ww R +Q C Vo Te R FIGURE 7.5 (b) (a) Determine the charge on the capacitor as a function of time, Q(t). What is the current through the resistor, I (t)? (b) What was the original energy stored in the capacitor (Eq. 2.55)? By integrating Eq. 7.7, confirm that the heat delivered to the resistor is equal to the energy lost by the capacitor. Now imagine charging up the capacitor, by connecting it (and the resistor) to a battery of voltage Vo, at time t = 0 (Fig. 7.5b). (c) Again, determine Q(t) and I(t). (d) Find the total energy output of the battery (f VoI dt). Determine the heat de- livered to the resistor. What is the final energy stored in the capacitor? What fraction of the work done by the battery shows up as energy in the capacitor? [Notice that the answer is independent of R!]
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