Question

A 591 μF capacitor is discharged through a resistor, whereby its potential difference decreases from its initial value of 88.5 V to 11.9 V in 3.09 s. Find the resistance of the resistor in kilohms.

Answer 1

Answer:

2.6 kilo Ohm

Explanation:

Capacitance, C = 591 μF = 591 x 10^-6 F

Vo = 88.5 V

V = 11.9 V

t = 3.09 s

Let the resistance is R.

$V = V_{0}e^{\frac{-t}{RC}}$

$\frac{11.9}{88.5} = e^{\frac{-t}{RC}}$

$0.135 = e^{\frac{-t}{RC}}$

Take natural log on oth the sides

ln 0.135 = - 3.09 / RC

RC = 1.545

R = 1.545 / ( 591 x 10^-6)

R = 2614.2 ohm

R = 2.6 kilo Ohm

Thus the resistance is  2.6 kilo Ohm.