Question

A capacitor discharges through a resistance. The stored energy $U_0$ in one capacitive time constant falls to

• A. $\frac{U_0}{e^2}$
• B. $e{U}_0$
• C. $\frac{U_0}{e}$
• D. None of these

Answer 1

The correct option is A $\frac{U_0}{e^2}$

Let us consider charge stored in the capacitor at time (t = 0) be $Q_0$ and energy stored in the capacitor be $U_0$.

In case of discharging of capacitor, we know
$Q=Q_0{e}^{\frac{-t}{\tau }}$.......(i)
For 1 capacitive time (i.e t = $\tau$)
$Q=\frac{Q_0}{e}$.....(ii)
We know that $U_0=\frac{Q_0^2}{2C}$.....(iii)
$⟹U=\frac{Q^2}{2C}$......(iv)
Using equation (iii) and (iv) in (ii) we get
$U=\frac{U_0}{e^2}$