The graph shows the variation of current $I$ with frequency $f$ for a series $R-L-C$ network. Keeping $L$ and $C$ constant,if resistance $R$ decreases:

$A$ series $LCR$ circuit with $L = \frac{100}{\pi} \text{ mH}$,$C = \frac{10^{-3}}{\pi} \text{ F}$,and $R = 10 \ \Omega$ is connected across an $AC$ source of $220 \text{ V}, 50 \text{ Hz}$ supply. The power factor of the circuit would be . . . . . . .

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:

$A$ circuit containing resistance $R_1$,inductance $L_1$,and capacitance $C_1$ connected in series resonates at the same frequency $f_r$ as another circuit containing $R_2$,$L_2$,and $C_2$ in series. If the two circuits are connected in series,then the new frequency at resonance is

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

The inductance $L$,capacitance $C$,and resistance $R$ are the values of the components connected in series to an $AC$ source of angular frequency $\omega$. The inductive and capacitive reactances are $X_L$ and $X_C$ respectively. If the circuit is purely resistive,then