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. $2 \, μF$ capacitor losses $50\%$ charge sooner than $1 \, μF$ 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 $=RCln\left(\right.2\left.\right)$
As $1^{s t}$ capacitance is 50% less than that of $2^{n d}$ capacitance,
hence $1 \, \mu F$ will take less time compared to $2 \, \mu F$