An AC current source is connected to an inductor with an inductance L $=5$ 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 $($b$)$

Determine the voltage across the inductor, in volts, at time t $=2\mathrm{.}5$ sec$.$ Part $($c$)$

Determine the magnitude of the maximum voltage, in volts, across the inductor.