$A$ $12\,\Omega$ resistor and a $0.21\,H$ inductor are connected in series to an $ac$ source operating at $20\,V$,$50\,Hz$. The phase angle between the current and the source voltage is.....$^o$

$A$ coil has $L = 0.04 \, H$ and $R = 12 \, \Omega$. When it is connected to a $220 \, V$,$50 \, Hz$ supply,the current flowing through the coil in amperes is: (in $.7$)

Which of the following plots may represent the reactance of a series $LC$ combination?

An electric lamp connected in series with a capacitor and an a.c. source is glowing with certain brightness. On reducing the frequency of the source, the brightness of the lamp

For the given $RL$ circuit,the maximum power loss across the circuit can be $W$.

In a circuit,a metal filament lamp is connected in series with a capacitor of capacitance $C \mu F$ across a $200 V, 50 Hz$ supply. The power consumed by the lamp is $500 W$ while the voltage drop across it is $100 V$. Assume that there is no inductive load in the circuit. Take $rms$ values of the voltages. The magnitude of the phase-angle (in degrees) between the current and the supply voltage is $\varphi$.
Assume,$\pi \sqrt{3} \approx 5$.
$(1)$ The value of $C$ is . . . . . .
$(2)$ The value of $\varphi$ is
Give the answers of the questions $(1)$ and $(2)$: