Question
A 5 µF capacitor is charged by being connected to a 3 V battery. The battery is then disconnected. If the resistance of the dielectric material between the capacitor plates is 109 Ω, what is the charge remaining on the capacitor 1 h after it has been disconnected ?
1.5 × 10-5 C
7.4 × 10-6 C
5.4 × 10-6 C
8.4 × 10-5 C
Solution
B.
7.4 × 10-6 C
T = R C
= ( 109 Ω ) ( 5 × 10-6 F )
= 5 × 103 s
=
T =
T = 1.4 h
The initial charge on the capacitor is
Q0 = C V
= ( 5 × 10-6 F ) ( 3V )
Q0 = 1.5 × 10-5 C
After t = 1h
= 0.71
and Q = Q0 e-t/T
= (1.5 × 10-5 C ) ( e-0.71 )
= ( 1.5 × 10-5 C ) ( 0.49 )
Q = 7.4 × 10-6 C
