The plot given below is of the average power delivered to an $LRC$ circuit versus frequency. The quality factor of the circuit is

For the $LCR$ circuit shown here,the current is observed to lead the applied voltage. An additional capacitor $C'$,when joined with the capacitor $C$ present in the circuit,makes the power factor of the circuit unity. The capacitor $C'$ must have been connected in

The figure shows a series $LCR$ circuit connected to a variable frequency $230 \; V$ source. Given $L = 5.0 \; H$,$C = 80 \; \mu F$,and $R = 40 \; \Omega$.
$(a)$ Determine the source frequency which drives the circuit in resonance.
$(b)$ Obtain the impedance of the circuit and the amplitude of current at the resonating frequency.
$(c)$ Determine the $rms$ potential drops across the three elements of the circuit. Show that the potential drop across the $LC$ combination is zero at the resonating frequency.

At resonance frequency,the impedance in a series $LCR$ circuit is

In a series $LCR$ circuit,the capacitance is changed from $C$ to $4C$. To keep the resonance frequency unchanged,the new inductance should be:

An $LCR$ series circuit with $100 \Omega$ resistance is connected to an $AC$ source of $200 V$ and angular frequency $300 \text{ rad/s}$. When only the capacitor is removed,the current lags behind the voltage by $60^{\circ}$. When only the inductor is removed,the current leads the voltage by $60^{\circ}$. The power dissipated in the $LCR$ circuit will be: