In a series $LCR$ circuit, the voltages across $L, C$, and $R$ are $50 \,V, 20 \,V$, and $40 \,V$ respectively. The $A.C.$ voltage applied across the combination of $LCR$ is: (in $\,V$)

In the circuit diagram shown,$X_C = 100 \, \Omega$,$X_L = 200 \, \Omega$,and $R = 100 \, \Omega$. The source voltage is $V = 200 \sin(\omega t) \, \text{V}$. The effective $(RMS)$ current through the source is:

An alternating voltage $\varepsilon = 30 \sin 200 t$ (in volts) is applied to the circuit shown below. The amplitude of the current through the circuit is (in $\text{ A}$)

$A$ 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:

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 . . . . . . .

In a circuit,$L$,$C$,and $R$ are connected in series with an alternating voltage source of frequency $f$. When the current in the circuit leads the voltage by $45^{\circ}$,the value of $C$ is