An AC voltage source is connected to an inductor with inductance $0\mathrm{.}041$ H$.$ The voltage source provides a time$-$dependent voltage V across the inductor as described by V$($t$)=$ v$0$ sin$($t$),$ where v$0=256$ V and $=988$ rad$/$s$.$

Part $($a$)$

Find the current through the inductor, in amperes with its sign, at time t $=2\mathrm{.}3$ s$.$

Part $($b$)$

Calculate the instantaneous power, in watts with its sign, that the inductor is absorbing at time t $=2\mathrm{.}3$ s$.$