Two resistors $R_1=15\mathrm{.}0,$ and $R_2=10\mathrm{.}5$ are connected with a $300$ mH inductor, a $12\mathrm{.}0$ V battery and a two$-$way switch as shown in the diagram below. At $t=0,$ the switch ab is closed.

$($a$)$ Determine the time constant for this circuit.

Review the definition of time constant. What is the resistance of the circuit when the switch ab is closed? s

$($b$)$ Calculate the current in the two resistors and the inductor a long time after the switch is closed.

$I_{R1}=$

$I_{R2}=$

$I_L=$

$A$

$($c$)$ What is the voltage across the two resistors and the inductor a long time after the switch is closed?

$V_{R1}=$

$V_{R2}=$

$V_L=$

Now the switch ab is opened and ac is closed.

$($d$)$ Determine the time constant for this circuit. $($Enter your answer to at least four decimal places.$)$

$q,$

$($e$)$ What is the current in the inductor at $t=0\mathrm{.}008s?$

$q,$

$($f$)$ What is the voltage across the two resistors and the inductor at $t=0\mathrm{.}008s?$

$V_{R1}=$

$V_{R2}=$

$V_L=$

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