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(C) When the switch $S$ is closed for a long time,the capacitors reach a steady state. In a $DC$ circuit,capacitors act as open circuits in a steady s

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No current will flow

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(C) When the switch $S$ is closed for a long time,the capacitors reach a steady state. In a $DC$ circuit,capacitors act as open circuits in a steady state. When the switch $S$ is opened,the circuit configuration changes. However,the battery $B$ is connected in series with capacitors $C_2$ and $C_3$. Since capacitors are present in the path of the battery,they will eventually block the $DC$ current once they reach a new steady state. Therefore,no steady current can flow through the battery. Initially,there might be a transient current as the capacitors charge or discharge to reach the new steady state,but the question asks about the current flowing through the battery in the context of the circuit behavior. Since the battery is in series with capacitors,the final steady-state current will be zero.

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