# A capacitor $C_1$ of capacitance $1 \mu F$ and $C_2$ of capacitance $2 \mu F$ are separately charged by a common battery for a long time. The two capacitors are then separately discharged through equal resistors. Both the discharge circuits are connected at $t=0$. One or more of the following happen.

(1) The currents in both the circuits are zero at $t = 0$

(2) The currents in the two circuits are equal at $t = 0$, but not zero.

(3) The currents in both the circuits at $t = 0$ are unequal.

(4) $C_1$ loses 50% of its charge sooner than C2 loses 50% of its charge.

Which of the following are true:

$\begin {array} {1 1} (A)\;1\:and \: 4 \: only & \quad (B\;2\:and \: 4 \: only \\ (C)\;3\:and \: 4 \: only & \quad (D)\;1 \: only \end {array}$

The currents will be equal and non-zero due to same driving potential in the circuits.
$C_1$ has a smaller time constant and hence loses charge faster than $C_2.$
Ans : (B)
edited Mar 14, 2014