Question

When a capacitor discharges through a resistance $R$, the time constant is $\tau$ and the maximum current in the circuit is $i_0$. Then,

• A. The initial charge on the capacitor was $i_0\tau$
• B. The initial charge on the capacitor was $\frac{1}{2}{i}_0\tau$
• C. The initial energy stored in the capacitor was $i_0^{2}R\tau$
• D. The initial energy stored in the capacitor was $\frac{1}{2}{i}_0^{2}R\tau$

Answer 1

Answer: (A), (D)

The correct options are
A The initial charge on the capacitor was $i_0\tau$
D The initial energy stored in the capacitor was $\frac{1}{2}{i}_0^{2}R\tau$

$q=q_0{e}^{-t/\tau },i=\frac{q_0{e}^{-t/\tau }}{\tau }$
Where, $\tau =RC$
$i_0=q_0/\tau$
where $q_0$ is the maximum charge and $i_0$ is the maximum current.
$E=q_0^2/2C=\frac{i_0^2{\tau }^2}{\frac{2\tau }{R}}$