$1.$

$($a$)$ A certain series resonant circuit has a bandwidth of $1000$ Hz$.$ If the existing coil is replaced

by a coil with a lower Q$,$ what happens to the bandwidth? $($Explain$)[$Understand$][3$M$]$

$($b$)$A series RLC circuit consists of resistance R$=10\backslash$Omega $,$ inductance L$=0\mathrm{.}07$ H and capacitance

C$=0\mathrm{.}05\backslash$mu F$.$ Solve the circuit to find out the frequency at resonance. If a $100$ volts of signal

having frequency equal to the frequency of resonance is applied to this circuit, select the

values of VC and VL across C and L respectively. Choose the value of frequencies at which

these voltages VC and VL are maximum? $[$Apply$][4$M$]$

$($c$)$ Analyze the above circuit for the value of impedance at resonant frequency, $20$ Hz above

resonant frequency, and $20$ Hz below resonant frequency. $[$Analyze$]$