An engineer has a $12$ mH inductor, a $0\mathrm{.}01$ micro$-$Farad capacitor, and a $75-$ohm resistor. By drawing a circuit, show how the engineer should arrange these elements to obtain a first$-$order series resonant passive band pass filter. The winding resistance is $10$ ohms. For this filter, determine the following:

$($a$)$ Determine its center frequency.

$($b$)$ Calculate its band width.

$($c$)$ Determine the critical frequencies.

$($d$)$ Draw a fully labeled Bode Plot for this filter.