Question

The switch S is closed at $t=0$. The capacitor C is uncharged but $C_o$ has a charge $Q_o=2\mu C$ at $t=0$. If $R=100\Omega ,C=2\mu F,C_o=2\mu F,E=4V$. Calculate i(t) in the circuit

Answer 1

At $t=0$, capacitor $C_o$ is like a battery of

$emf=\frac{Q_o}{C_o}=1V$

Net emf of the circuit $=4-1=3V$

Total resistance is $R=100\Omega$

$\therefore$ Initial current $=\frac{3}{100}=0.03A$

This current will decrease exponentially to zero.

$\therefore i=0.03e^{-t{\tau }_C}$

Here ${\tau }_C=C_{net}\cdot R=(1\times {10}^{-6})\left(100\right)$

$={10}^{-4}s$

$\therefore 9=0.03e^{-{10}^{4}t}$