The total impedance of a series $L-C-R$ circuit varies with the angular frequency of the $AC$ source connected to it,as shown in the graph. The quality factor $Q$ of the series $L-C-R$ circuit is:

Power factor is maximum in an $LCR$ circuit when

If the reading of the voltmeter $V$ shown in the figure at resonance is $200 \, V$,then the quality factor of the circuit is:

If the inductance and capacitance are both doubled in an $L-C-R$ circuit,the resonant frequency of the circuit will

For a given series $LCR$ circuit,it is found that maximum current is drawn when the value of the variable capacitance is $2.5 \ nF$. If a resistance of $200 \ \Omega$ and a $100 \ mH$ inductor are being used in the given circuit,the frequency of the $AC$ source is $... \times 10^3 \ Hz$. (Given $\pi^2 = 10$)

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.