A$3.$ The elements have the following values for the circuit shown below: $10VR=200$ and $L=50H.($a$)$ Find the time constant of the circuit. $($b$)$ If switch $S_z$ is at position $\text{'}a\text{'}$ and switch $S_l$ is thrown closed at $1=0,$ calculate the time it takes the current in the circuit to reach $40\%$ of maximum current. $($c$)$ Calculate the energy stored in the inductor at this time.