$A$ series $LCR$ circuit containing a resistance of $120 \, \Omega$ has an angular resonance frequency of $4 \times 10^3 \, rad \, s^{-1}.$ At resonance, the voltages across the resistance and the inductance are $60 \, V$ and $40 \, V$ respectively. The values of $L$ and $C$ are respectively:

In the $LCR$ circuit shown in the figure,what will be the readings of the voltmeter across the resistor $(V_R)$ and the ammeter $(A)$ if an a.c. source of $220 \ V$ and $100 \ Hz$ is connected to it?

In a series $LCR$ circuit,the inductance,capacitance,and resistance are $L = 100 \, mH$,$C = 100 \, \mu F$,and $R = 10 \, \Omega$ respectively. They are connected to an $AC$ source of voltage $220 \, V$ and frequency $50 \, Hz$. The approximate value of current in the circuit will be.....$A$.

Obtain the relation for the voltage applied to a series $LCR$ circuit.

In the following circuit,the emf of the source is $E_0 = 200 \, V$,$R = 20 \, \Omega$,$L = 0.1 \, H$,and $C = 10.6 \, F$. If the frequency is variable,then the current at frequency $f = 0$ and $f = \infty$ is:

An inductor of $10 \text{ mH}$, capacitor of $0.1 \text{ } \mu\text{F}$ and a resistor of $100 \text{ } \Omega$ are connected in series across an $a.c.$ power supply of $220 \text{ V}$, $70 \text{ Hz}$. The power factor of the given circuit is $0.5$. The difference between the inductive reactance and capacitive reactance is $\sqrt{3}\alpha \text{ } \Omega$. The value of $\alpha$ is . . . . . . .