Question

Consider the series RC-circuit shown below for which R = 41.0 k?, C = 41.0 µF, and [e m f] = 26.5 V. Find the following.
(a) the time constant of the circuit
1 s

(b) the charge on the capacitor one time constant after the switch is closed
2 C

Answer 1

part a )

time constant = t = RC

R = 41 x 10^3 ohm , C = 41 x 10^-6 F

t = 1.681 s

part b )

Qmax = CV

Qmax = 41 x 10^-6 x 26.5 = 1.0865 x 10^-3 C

Q = Qmax(1-e^-T/t)

hete T = t

Q = Qmax(1-e^-1)

Q = Qmax(1-1/e)

Q = 6.87 x 10^-4 C