$(10)$ In this circuit, the battery has a voltage of $12V$ between terminals $($and a negligible internal resistance$).$ We are told that the resistor $R$ in the middle branch of the circuit would dissipate $1\mathrm{.}5W$ of power if it was connected all by itself to the battery. How much electric energy per second is converted into heat by the middle resistor $R($a$)$ when switch $S$ is open; $($b$)$ when switch $S$ is closed.