Question

How long will it take the voltage across the capacitor in an RC circuit to discharge 75% of its initial charged voltage if the resistor has a resistance of 450 kilo-Ohms and the capacitor has a capacitance of 49 micro-farads?

How do I solve this problem?

Thanks!

Answer 1

C = q/V
q = C V
i = -dq/dt = -C dV/dt
so
dV/dt = -i/C


V = i R = 4.5 * 10^5 i
so
i = .222 * 10^-5 V = 2.22*10^-6 V

then combine
dV/dt = -(1/c)(2.22*10^-6 V)

dV/V = -(2.22/49) dt

ln V = -.0453 t + constant

V = Vi e^-.0453 t

. 75 = e^-.0453 t
ln .75 = - .288 = - .0453 t
t = 6.35 s
CHECK ARITHMETIC !!!

Answer 2

R = 450k Ohms.
C = 49 uF

100%-75%=25% of the voltage remaining.

x = t/RC = t/(450*49) = 4.54*10^-5t

1/e^x = 0.25
e^x = 4
x*Ln e = Ln 4
X = 1.386

x = 4.54*10^-5t = 1.386
t = 1.386/4.54*10^-5=30535 Milliseconds = 30.54 Seconds.