An RC circuit has a time constant of 2.10 s.At t = 0,the capacitor is fully charged.At what time will the energy stored in the capacitor be half of its initial value?
A)0.728 s
B)1.35 s
C)1.46 s
D)1.83 s
E)2.58 s

Question

Quizplus · Accepted Answer

The energy stored in a capacitor is given by E = (1/2)CV^2. At t = 0, the capacitor is fully charged, so V = V0. At time t, the voltage across the capacitor is given by V = V0e^(-t/RC). Therefore, the energy stored in the capacitor at time t is given by E = (1/2)CV0^2e^(-2t/RC). At the time when the energy stored in the capacitor is half of its initial value, we have E = (1/2)(1/2)CV0^2 = (1/4)CV0^2. Therefore, we have e^(-2t/RC) = 1/4, which gives t = RCln(4) = 2.10 s ln(4) = 1.46 s.

An RC Circuit Has a Time Constant of 2