Question

In an RC circuit, with 50-μF capacitor and a 80Ω resistor, what fraction of the final energy is stored in an initially uncharged capacitor after it has been charging for 2 ms?

Answer 1

For a charging RC circuit with resistance R, capacitance C and voltage V, the charge as a function of time is given by

Since the energy stored in a capacitor with charge q and capacitance C is

The energy stored in the capacitor as function of time can be written as

So, final ( ) energy stored is given by,

The ratio of energy at any time t to the final energy can be calculated as,

Given,

the resistance R = 80Ω

the capacitance C = 50μF= 50 x 10^-6 F

the time t = 2 ms = 2 x 10^-3 s.

So the ratio is,

Therefore, the fraction of energy stored in the capacitor at t = 2ms compared to the final energy is 0.155.