q5.pdf - Quiz 5 Solutions Question A 10 F capacitor is charged with a battery of 10V After charging this capacitor is disconnected from the battery and

q5.pdf - Quiz 5 Solutions Question A 10 F capacitor is...

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Quiz 5 Solutions Question A 10 F capacitor is charged with a battery of 10V. After charging, this capacitor is discon- nected from the battery and connected to another capacitor of 5 F. a. Find the initial charge on the 10 F capacitor and the potential energy stored in it. b. Find the final potential difference across the capacitors, and the charges on each of the capacitors. c. Find the final potential energy stored in the two capacitors. d. How much is the total final potential energy? Is it same or different than the initial potential energy? e. (Bonus question, no penalty if wrong) Depending on what you find, explain why is the total final potential energy same/different than the initial potential energy? Solution a) Voltage across the 10 μF is 10V. Therefore the charge on it Q intial = CV = 10 × 10 = 100 μC , and energy is U = CV 2 / 2 = 5 × 10 ( - 4) J . Let the charge on this be Q initial . b) After charging the 10 μF (call it capacitor 1) is connected to uncharged 5 μF (capacitor 2). Charge will thus flow from the charged capacitor to the uncharged. In this flow of charge though, the total initial charge will be conserved. Thus, Q initial = Q 1 ,final + Q 2 ,final (1) The charges flow because there is an electric force pushing them. This electric field is coming from the difference in potentials of the two capacitors. Capacitor 1 starts from 10V, and capacitor 2 starts from 0V. As charge is transferred from capacitor 1, Q 1 decreases and Q 2 increases, and because V =
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