Q. Capacitor $C_1 $ of capacitance $1 \mu F $ and capacitor $C_2 $ of capacitance $2 \mu F $ are separately charged fully by a common battery. The two capacitors are then separately allowed to discharge through equal resistors at time $t = 0$.
IIT JEEIIT JEE 1989Electrostatic Potential and Capacitance
Solution:
The discharging current in the circuit is,
$i=i_0e^{-t/CR} $
Here, $i_0$=initial current $= \frac {V}{R} $
Here, $V$ is the potential with which capacitor was charged.
Since, $V$ and $R$ for both the capacitors are same, initial discharging current will be same but non-zero.
$\therefore $ Correct option is (b).
Further, $\tau_c=CR $
$C_1< C_2$ or $\tau_{C_1} < \tau_{C_2} $
or $C_1 $ loses its $ 50 \% $ of initial charge sooner than $C_2. $
