Question

13. A circuit consist of a batter with an EMF of 25 V, a capacitor with C= 60e-6 F, and a resistor with R = 70 ohms. The capacitor is initially uncharged and the switch in the circuit it open. What is the current in the circuit 2 ms (milliseconds) after the switch has been closed?

A) 0.135 A

B) 0.429 A

C) 0.490 A

D) 0.533 A

E) 0.222 A

Answer is E. Not sure why. Please help!

Answer 1

Time constant of circuit is

$\tau=RC=70\times60\times10^{-6}=4.2$ ms$$

When the circuit is closed, then capacitor get charged. Charging of capacitor will be given as

$Q=CV\left [ 1-\exp{-\frac{t}{RC}} \right ]\Rightarrow I=\frac{dQ}{dt}=CV\left [ \frac{1}{RC}\exp{-\frac{t}{RC}} \right ]\\$

Hence current will be

$I= \frac{V}{R}\exp{(-\frac{t}{RC})} =\frac{25}{70}\times\exp{-\frac{2}{4.2}}=0.222\\$