Question

A 4900 Ω resistor is connected across a charged 0.780 nF capacitor. The initial current through the resistor, just after the connection is made, is measured to be 0.265 A .

a.What magnitude of charge was initially on each plate of this capacitor?

b. How long after the connection is made will it take before the charge is reduced to 1e of its maximum value?

Answer 1

a)

Voltage across capacitor

V_C=IR=4900*0.265=1298.5 Volts

Initial charge on the capacitor is

Q_o=CV=(0.78*10^-9)(1298.5)

Q_o=1.01283*10^-6 C=1.01283 uC

b)

Charge as a function in a RC circuit for discharging is given by

Q=Q_oe^-t/T

Given

Q=Q_o/e

=>Q_o/e =Q_oe^-t/T

e^-1 =e^-t/T

t/T=1

t=T

since time constant T=RC

t=RC=4900*0.78*10^-9

t=3.822*10^-6 s =3.822 us