A sinusoidal voltage $v=37\mathrm{.}5sin(100t),$ where $v$ is in volts and $t$ is in seconds, is applied to a series RLC circuit with $L=180mH,C=99\mathrm{.}0F,$ and $R=54\mathrm{.}0.$

$($a$)$ What is the impedance $($in $)$ of the circuit?

$$

$($b$)$ What is the maximum current $($in A$)?$

$$ A

$($c$)$ Determine the numerical value for $($in rad$/$s$)$ in the equation $i=I_{\text{m}\text{a}\text{x}}sin(t-).$

$$ rad$/$s

$($d$)$ Determine the numerical value for $($in rad$)$ in the equation $i=I_{\text{m}\text{a}\text{x}}sin(t-).$

$$ rad

$($e$)$ What If$?$ For what value of the inductance $($in H $)$ in the circuit would the current lag the voltage by the same angle $$ as that found in part $($d$)?$

$$

$($f$)$ What would be the maximum current $($in A$)$ in the circuit in this case?

$$ A