Question

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

• A. At $t=0$ the value of current in the circuit containing $1\mu F$ is more than current in the circuit containing $2\mu F$
• B. At $t=0$ the current in $2\mu F$ capacitor circuit is more than current in $1\mu F$ capacitor circuit
• C. $1\mu F$ capacitor losses $50\%$ charge sooner than $2\mu F$ capacitor
• D. $2\mu F$ capacitor losses $50\%$ charge sooner than $1\mu F$ capacitor

Answer 1

Answer: (C)

Total potential difference $E_0$ is given to both of the capacitor.
The two capacitors are then separately allowed to discharge through same resistors.
Since both capacitors are charged to same potential difference hence current at $t=0$ , $I_0=\frac{E_0}{R}$ will be same in both circuits.
Time taken in $50\%$ discharging $=RCln(2)$
As $1^{st}$ capacitance is 50% less than that of $2^{nd}$ capacitance,
hence $1\mu F$ will take less time compared to $2\mu F$