An inductor having inductance $\backslash ($ L $\backslash )$ and a capacitor having capacitance $\backslash ($ C $\backslash )$ are connected in series. The current in the circuit increases linearly in time as described by $\backslash ($ I$=$K t $\backslash ).$ The capacitor is initially uncharged. $($Use the following as necessary: $\backslash ($ L$,$ C$,$ K $\backslash ),$ and $\backslash ($ t $\backslash ).)$

$($a$)$ Determine the voltage across the inductor as a function of time.

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$\backslash$varepsilon$\_\{\backslash$mathrm$\{$L$\}\}=$

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$($b$)$ Determine the voltage across the capacitor as a function of time.

$\backslash [$

$\backslash$Delta V$\_\{\backslash$mathrm$\{$C$\}\}=$

$\backslash ]$

$($c$)$ Determine the time when the energy stored in the capacitor first exceeds that in the inductor.

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t$=$

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