$3.$

$($a$)$ Explain half$-$power frequencies. $[$Understand$][3$M$]$

$($b$)$ A constant voltage at a frequency of $10$ MHz is applied to an inductor in series with a

variable capacitor when the capacitor is set to $400$ PF$,$ the current has the max. value, while

it is reduced to one half when capacitance $500$ PF$,$ solve it to find out $($i$)$ resistance $($ii$)$

inductance $($iii$)$ Q factor of inductor. $[$Apply$][4$M$]$

$($c$)$ In a series RLC circuit if the applied voltage changed to $10$ V$,$ and resonance frequency is

$1$ kHz$,$ and Q factor is $10,$ Calculate the maximum voltage across the inductance. $[$Analyze$]$

$[3$M$]$