When the capacitor is charged, the voltage across it is equal to the voltage across the battery (

). The voltage across a capacitor cannote change discontinuously, therefore the voltage across the capacitor immediately after the switch is thrown to contact

is still

. We can apply Kirchhoff's voltage loop around the right loop to find that

where

is the voltage difference between the top and the bottom of the capacitor, and

is the clockwise current. This equation must be true for all

. In particular, at

,

. Since it was already argued that

, the voltage of the battery, we must have that

. This means that curves A and B are the only ones that could be correct. We can distinguish between them be solving for the current as a function of time. The current through a capacitor is given by

Because of the way we have defined the current

and the voltage

, the right equation is actually

in this case.
So, if we differentiate equation (1) and use this relation, we find that

The solution to this differential equation is (with the initial condition

)

So, the current is

at

and then it decays exponentially to

. Thus, answer (B) is the correct.