$2.$

$($a$)$ Plot the selectivity curve for the series RLC circuit. $[$Understand$]$

$($b$)$ A series circuit comprising R$,$ L and C is supplied at $\backslash (110\backslash$mathrm$\{$~V$\},50\backslash$mathrm$\{$~Hz$\}\backslash ).$ At resonance, the voltage across the capacitor is $50$ V $.$ The current at resonance is $5$ A $.$ Solve for the circuit parameters $\backslash (\backslash$mathrm$\{$R$\},\backslash$mathrm$\{$L$\}\backslash )$ and C$.[$Apply$]$

$($c$)$ Analyze the circuit to derive the expression for the frequency at which maximum voltage occurs across the capacitance in series resonance circuit in terms of the Q$-$factor and resonance frequency. $[$Analyze$]$