An inductor is connected to an AC source. If the inductance of the inductor is $0\mathrm{.}420$ H and the output voltage of the source is given by $v=(120V)sin[(27\mathrm{.}5s^{-1})t],$ determine the following.

$($a$)$ the frequency of the source $($in Hz $)$

$$ Hz

$($b$)$ the rms voltage across the inductor $($in V$)$

$$

$($c$)$ the inductive reactance of the circuit $($in $)$

$$

$($d$)$ the rms current in the inductor $($in A$)$

$$ A

$($e$)$ the maximum current in the inductor $($in A$)$

$$