$[1\mathrm{.}34/2$ Points$]$

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 $).$

rad $\frac{?}{s}$

$($d$)$ Determine the numerical value for $($in rad$)$ in the equation $).$

Does the current lead or lag the voltage in this circuit? 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?

$A$

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