Question

1. A capacitor C has been charged up to potential Vo. At timet0, it is connected to a resistor R, and begins to discharge [see figure (a) below] +0 (a) i Determine the charge Q(t) on the capacitor as a function of time. ii. What is the current I(t) through the resistor? iii. Sketch Q(t) and I(t) as a function oft iv. Wha v. By integrating P VI, where P is the power delivered to the circuit and V the volt t was the original energy stored in the capacitor age, confirm that the heat delivered to the resistor is balanced by the energy lost by the capacitor. (b) Now imagine charging up the capacitor, by connecting it and the resistor to a battery of voltage Vo at time t0 [see figure (b) above] i. Again, determine Q(t) and I(t) ii. Sketch Q and I as a function of t ii Find the total energy output of the battery Vo I dt iv. Determine the heat delivered to the resistor v. What is the final energy stored in the capacitor? vi. What fraction of the work done by the battery shows up as energy in the capacitor? [1]

Answer 1

Pont(o) Initia Patondial Vo Given Initial change- C.o_C½ bscoune change fo tina de RC

ui) Cunant I through the Rarintov tRC d & olVa 30 2.

fhs o riginal enangy Storeo ud d 2 Po P- Te