Question

Capacitor $C_1$ of capacitance $1$ $\mu F$ and capacitor $C_2$ of capacitance $2$ $\mu F$ are separately charges fully by a common battery. The two capacitors are then separately allowed to discharged through equal resistors at time $t=0$.

• A. The current in each of the two discharging circuits is zero at $t=0$
• B. The currents in the two discharging circuits at $t=0$ are equal but non-zero
• C. The currents in the two discharging circuits at $t=0$
• D. Capacitor $C_1$ loses $40\%$ of its initial charge sooner than $C_2$ loses $40\%$ of initial charge

Answer 1

Answer: (B)

The currents in the two discharging circuits at $t=0$ are equal but non-zero

Here, $V_0$ and R in the two CR circuits are same, hence the currents in the two discharging circuits at $t=0\left(V_0/R\right)$ will be same.
We know that time constant of a resistance and capacitance circuit is CR. Here, time constant of first circuit (capacity $C_1=1\mu F$) is half of the time constant of second circuit (capacity $C_2=2\mu F$). Hence $C_1$ loses $50\%$ its initial charge sooner.