A sinusoidal voltage $$v $=37\mathrm{.}5$ sin$(100$t$),$ where $$v is in volts and t is in seconds, is applied to a series RLC circuit with L $=170$ mH$,$ C $=99\mathrm{.}0$F$,$ and R $=71\mathrm{.}0.$

$($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 $=$ Imax sin$($t $).$

rad$/$s

$($d$)$

Determine the numerical value for $($in rad$)$ in the equation i $=$ Imax 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$)?$

H

$($f$)$

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

A