$A$ $220 \; V, 50 \; Hz$ $AC$ 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:

In the circuit shown,$C = \frac{\sqrt{3}}{2} \times 10^{-3} \, F$,$R_2 = 20 \, \Omega$,$L = \frac{\sqrt{3}}{10} \, H$,and $R_1 = 10 \, \Omega$. The current in the $L-R_1$ branch is $I_1$ and in the $C-R_2$ branch is $I_2$. The voltage of the $A.C.$ source is given by $V = 200\sqrt{2} \sin(100t) \, V$. The phase difference between $I_1$ and $I_2$ is:

In an $AC$ circuit,an inductor,a capacitor,and a resistor are connected in series with $X_{L} = R = X_{C}$. The impedance of this circuit is:

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

$A$ capacitance of $\left(\frac{10^{-3}}{2 \pi}\right) F$,an inductance of $\left(\frac{100}{\pi}\right) mH$,and a resistance of $10 \Omega$ are connected in series with an $AC$ voltage source of $220 V, 50 Hz$. The phase angle of the circuit is (in $^{\circ}$)

In an $LCR$ series circuit, if the potential differences across the inductor, capacitor, and resistor are $60 \,V$, $30 \,V$, and $40 \,V$ respectively, then the $AC$ voltage applied to the circuit is: (in $\,V$)