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 $m m s$ 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 ($2$)

In the circuit shown here, the voltage across $L$ and $C$ are respectively $300\, V$ and $400\, V$. The voltage $E$ of the ac source is……$Volt$

In an $AC$ circuit the potential differences across an inductance and resistance joined in series are respectively $16\,V$ and $20\,V$. The total potential difference of the source is……….$V$

What is phase difference between $V $ and $I$ in a circuit containing only a resistor ? 

The value of the current through an inductance of $1H$ and of negligible resistance, when connected through an $ac$ source of $200 \,V$ and $50 \,Hz$ is