current direction when the switch is connected
The right answer is neither a nor b. When the switches close the voltage across the capacitor happens to be 0V, so the capacitor is actually discharged, despite it's been connected to the source for half a period. So technically, in that point no current flows anywhere.

The next instant in time which is when the negative half cycle starts, the capacitor starts charging (in reverse polarity) and the branch with the inductor and resistor also gets current from the source, as in my picture.