Question

A 537 × 10-6 F capacitor is discharged through a resistor, whereby its potential difference decreases from its initial value of 84.5 V to 28.7 V in 4.57 s. Find the resistance of the resistor.

Answer 1

Given

C = 537*10^-6 F ,

R = ?

V0 = 84.5 V

v(4.57) = 28.7 V

t = 4.57 s

we know the time constant in RC circuit id T=R*C

nwo the dicharging of a capacitor through the resistor in time t is

V(t) = V0(e^-t/RC)

28.7 = 84.5(e^(-4.57/(R*537*10^-6)))

solving for R

R = 7880.92 ohm

the resistance in the circuit is R = 7880.92 ohm