Problem $2$: $(16\backslash \%$ of Assignment Value$)$

Energy stored in an inductor: An RL circuit includes a basic switch. In position $"$a$",$ the battery, resistor, and inductor are connected in series. In position $"$ b $",$ the battery is replaced with a short. Two voltmeters and an ammeter have been added to the circuit.

Bradford, Luca $-$ lab$6594$@Cpsus.edu

Part $($a$)$

Enter an expression for the voltage across the inductor when the switch is moved to position $"$a$".$

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V$\_\{$L$\}=-\backslash$mathrm$\{$V$\}\_\{0\}$

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Submissions Attempt$(3)$ Remaining: $52$ Free Attempt$($s$),$ then $4\backslash \%$ Deduction per Attempt detailed view

Feedback: $\backslash (2\backslash \%\backslash )$ deduction per feedback.

Hints: $\backslash (2\backslash \%\backslash )$ deduction per hint. Hints remaining: $\backslash (\backslash$underline$\{1\}\backslash )$

Part $($b$)$

Enter an expression for the power in the inductor.

Part $($c$)$

Assume that the current is zero at the instant the switch is closed to position $"$a$",$ and a short time later the current has increased to a value $\backslash ($ I $\backslash ).$ Perform an integral of th power to determine how much energy has been transfered to the inductor during this time interval.

Part $($d$)$

A current$-$carrying inductor does not dissipate energy like a resistor does. It stores the energy similar to the way that a charged capacitor stores energy. $($While the capacitor stores energy in an electric field, the inductor stores energy in a magnetic field.$)$ Modify the expression you obtained in the previous step to express the energy stored in an inductor.