A student builds a series circuit using a $1\mathrm{.}30$ mH inductor and an initially uncharged $1\mathrm{.}45$F capacitor. The current in the circuit increases linearly in time as

i $=18\mathrm{.}0$t$,$

where i is in amperes and t is in seconds. $($Note: For parts $($a$)$ and $($b$),$ if the voltage is in the same direction as the emf of the battery that supplies the current, express it as a positive voltage. If the voltage opposes the emf of the battery, express it as a negative voltage.$)$

$($a$)$

Determine the voltage across the inductor as a function of time. $($Use the following as necessary: t$.$ Assume L is in mV and t is in seconds. Do not include units in your answer.$)$

L $=$

$($b$)$

Determine the voltage across the capacitor as a function of time. $($Use the following as necessary: t$.$ Assume $$VC is in MV and t is in seconds. Do not include units in your answer.$)$

$$VC $=$

$($c$)$

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

$$s