Problem $14$: An AC current source is connected to an inductor with an inductance L $=2$ H$.$ At time t $=0,$ the current through the inductor is i$0=0$ A$.$ The power supply provides a time$-$dependent current i through the inductor as described by the following equation: i$($t$)=10$cos$($t$),$ where $=500$ rad$/$s$.$ The current is measured in units of Amps.

Part $($a$)$ Determine the current through the inductor, in amperes, at time t $=3\mathrm{.}5$ sec$.$

i $=-9\mathrm{.}91$

i $=9\mathrm{.}910$

$$ Correct!$$

Part $($b$)$ Determine the voltage across the inductor, in volts, at time t $=3\mathrm{.}5$ sec$.$

Part $($c$)$Determine the magnitude of the maximum voltage, in volts, across the inductor.