$A$ 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 . . . . . . $\Omega$.

The resonant frequency of a series $LCR$ circuit is $f$. The circuit is now connected to a sinusoidally alternating e.m.f. of frequency $2f$. The new reactance $X_{L}^{\prime}$ and $X_{C}^{\prime}$ are related as:

$A$ series $LCR$ circuit is connected across a source of alternating emf of changing frequency and resonates at frequency $f_0$. Keeping capacitance constant,if the inductance $(L)$ is increased by $\sqrt{3}$ times and resistance is increased $(R)$ by $1.4$ times,the resonant frequency now is

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

$A$ series $LCR$ circuit with $L=0.12\, H$,$C=480\, nF$,$R=23\, \Omega$ is connected to a $230\, V$ variable frequency supply.
$(a)$ What is the source frequency for which current amplitude is maximum? Obtain this maximum value.
$(b)$ What is the source frequency for which average power absorbed by the circuit is maximum? Obtain the value of this maximum power.
$(c)$ For which frequencies of the source is the power transferred to the circuit half the power at resonant frequency? What is the current amplitude at these frequencies?
$(d)$ What is the $Q$-factor of the given circuit?

$A$ series $LCR$ circuit is shown in the figure. Where the inductance of $10 \ H$,capacitance $40 \ \mu F$,and resistance $60 \ \Omega$ are connected to a variable frequency $240 \ V$ source. The current at resonating frequency is (in $A$)