physics
posted by john on .
A 20.0 \mu F capacitor initially charged to 20.0 \mu C is discharged through a 1.90 k\Omega resistor. How long does it take to reduce the capacitor's charge to 5.00 \mu C?

The charge of the discharging capacitor, as a function of t, is:
Q(t) = Qo* e^(t/RC)
Qo is the initial charge, RC is the time constant, which in this case is 1900*20*10^6 = 0.038 seconds
So, solve
5*10^6 = 20*10^6*e^(t/0.038)
ln(1/4) = t/0.038
t = ?