$2.$

$($a$)$ Plot the selectivity curve for the series RLC circuit. $[$Understand$][3$M$]$

$($b$)$ A series circuit comprising R$,$ L and C is supplied at $110$ V$,50$ Hz$.$ At resonance, the voltage

across the capacitor is $50$ V$.$ The current at resonance is $5$A$.$ Solve for the circuit parameters

R$,$ L and C$.[$Apply$][4$M$]$

$($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$]$