Question

A capacitor in an RC circuit is charged by a battery to an initial voltage of 10V. The capacity is then disconnected from the battery and connected, at time t=0, in series with a 1MOhm resistor. At t=300 s the voltage across the capacitor has decreased to .1V. (a) Find the value of the capacitance. (b) Calculate the initial energy of the capacitor. (c) Calculate the final energy of the capacitor. (d) The difference between the answers to (b) and (c) should be relatively large. Where did the energy go? Explain clearly.

Answer 1

V_c = V_s* e^-t/RC

V_c = 10* e^-t/RC

=>0.1 = 10e^{-300/1000000*C}

-300/10⁶*C = ln(0.1/10) = -6.907755579

=> C = 4.342944819 x10^-5 F

=> C = 43.4 micro Farads (approx)

Initial energy , E = 0.5CV² = 0.5*43.4x10^-6 *100

Final energy , E = 0.5CV² = 0.5*43.4x10^-6 *10^-2