Using a variable-frequency a.c. voltage source, the maximum current measured in the given $LCR$ circuit is $50 \text{ mA}$ for $V = 5 \sin(100t)$. The values of $L$ and $R$ are shown in the figure. The capacitance of the capacitor $(C)$ used is . . . . . . $\mu\text{F}$.

In an $LCR$ series $AC$ circuit at resonance,the value of the power factor will be . . . . . . .

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

In a series $LCR$ circuit,resonance occurs at frequency $f = f_0$. If at this moment the amplitude of current is $I_0$,then calculate the wattless current at the same moment.

$A$ series $LCR$ circuit containing a resistance of $120\,\Omega$ has a resonance frequency of $4 \times 10^5\, rad\, s^{-1}$. The voltages,at resonance,across the resistance and inductance are $60\,V$ and $40\,V$ respectively. The values of $L$ and $C$ respectively are:

$A$ $100 \, \Omega$ resistance,a $0.1 \, \mu \text{F}$ capacitor,and an inductor are connected in series across a $250 \, \text{V}$ supply at variable frequency. Calculate the value of inductance of the inductor at which resonance will occur. Given that the resonant frequency is $60 \, \text{Hz}$. (In $\text{H}$)