$A$ resistor of resistance $R$, an inductor of inductive reactance $2R$, and a capacitor of capacitive reactance $X_C$ are connected in series to an $A.C.$ source. If the series $LCR$ circuit is in resonance, then the power factor of the circuit and the value $X_C$ are respectively:

An $LCR$ circuit is at resonance for a capacitor $C$,inductance $L$,and resistance $R$. If the value of the resistance is halved while keeping all other parameters the same,the current amplitude at resonance will be:

$A$ series $LCR$ circuit with $R = 20 \ \Omega$, $L = 1.6 \ \text{H}$ and $C = 40 \ \mu\text{F}$ is connected to a variable frequency a.c. source. The inductive reactance at resonant frequency is . . . . . . $\Omega$.

$A$ resistor $R$,an inductor $L$,and a capacitor $C$ are connected in series to an oscillator of frequency $N$. If the resonance frequency is $N_R$,then the current lags behind the voltage when:

In the given circuit,the voltmeter reads $75 \ V$. The value of $C$ is $.... \mu F$. (Given: $\pi^2 = 10$)

Figure $(a)$ shows a plot of voltage across the capacitor as a function of the driving frequency for a sinusoidally driven electromagnetic $LCR$ circuit. Figure $(b)$ shows the phase angle $\phi$ (phase difference between voltage and current) vs $\omega / \omega_0$ graph for the same circuit,for three different quality factors corresponding to graphs $1, 2, 3$ of figure $(a)$. Each graph in figure $(a)$ can be matched by one of the graphs $a, b, c$ in figure $(b)$. Which of the following statements is correct?