$A$ $50 \,W$ bulb connected in series with a heater coil is put to an $AC$ mains. Now the bulb is replaced by a $100 \,W$ bulb. The heater output will ...........

$A$ 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,$R = 18 \ \Omega$ and the impedance $Z = 33 \ \Omega$. An $r.m.s.$ voltage of $V_{rms} = 220 \ V$ is applied across the circuit. The true power consumed in the $a.c.$ circuit is: (in $W$)

An oscillating circuit consists of a capacitor with capacitance $C = 10 \, \mu F$, a coil with inductance $L = 6.0 \, \mu H$, and active resistance $R = 10 \, \Omega$. The mean power that should be fed to the circuit to maintain undamped harmonic oscillations with an external driving source of frequency $f = 50 \, Hz$ and peak voltage $V_m = 280 \, V$ is:

An a.c. source is applied to a series $LR$ circuit with $X_L = 3R$ and the power factor is $X_1$. Now,a capacitor with $X_C = R$ is added in series to the $LR$ circuit and the power factor is $X_2$. The ratio $X_1$ to $X_2$ is

In a series $LCR$ circuit,the voltages across $R, L$ and $C$ are shown in the figure. The voltage of the applied source is ........ $V$. (in $, V$)