The value of the alternating emf in the given series $LCR$ circuit is: (in $V$)

$A$ $220 \; V, 50 \; Hz$ $AC$ source is connected to a $25 \; V, 5 \; W$ lamp and an additional resistance $R$ in series (as shown in the figure) to run the lamp at its rated power. The value of $R$ (in $\Omega$) will be:

An inductance of $\left(\frac{200}{\pi}\right) \text{mH}$,a capacitance of $\left(\frac{10^{-3}}{\pi}\right) \text{F}$,and a resistance of $10 \, \Omega$ are connected in series with an $AC$ source of $220 \, \text{V}, 50 \, \text{Hz}$. The phase angle of the circuit is:

$A$ series $LCR$ circuit consists of an inductor $L$,a capacitor $C$,and a resistor $R$ connected across a source of emf $\varepsilon = \varepsilon_0 \sin \omega t$. When $\omega L = \frac{1}{\omega C}$,the current in the circuit is $I_0$. If the angular frequency of the source is changed to $\omega^{\prime}$,the current in the circuit becomes $\frac{I_0}{2}$. Then,the value of $\left|\omega^{\prime} L - \frac{1}{\omega^{\prime} C}\right|$ is

In a series $L-C-R$ circuit,the inductive reactance is twice the resistance and the capacitive reactance is $1/3$ rd of the inductive reactance. The power factor of the circuit is

For the circuit shown in the figure,the current through the inductor is $0.9\,A$ while the current through the capacitor is $0.4\,A$. Then