The capacitor is charged by connecting switch S to contact a, so the current after connecting switch to contact b (t = 0) must start with I = V/R.
Only plot A and B are right.
The current can not be the same all the time and since the voltage of a capacitor follows an exponential decay:
V(t) = V0e−t/RC
I(t) = V(t)/R = V0e−t/RC/ R
Only plot B is right.