$A$ bulb and a capacitor are in series with an $ac$ source. On increasing the frequency,how will the glow of the bulb change?

In an $AC$ circuit,a resistance of $R$ $\Omega$ is connected in series with an inductor of self-inductance $L$. If the phase angle between voltage and current is $45^{\circ}$,the value of inductive reactance $(X_{L})$ will be equal to . . . . . . .

For the $AC$ circuit shown below,the phase difference between emf and current is $\frac{\pi}{4}$ radian as shown in the graph. If the impedance of the circuit is $1414 \Omega$,then the values of $P$ and $Q$ are

An ideal inductor of $\left(\frac{1}{\pi}\right) H$ is connected in series with a $300 \Omega$ resistor. If a $20 \ V, 200 \ Hz$ alternating source is connected across the combination,the phase difference between the voltage and current is

In a circuit made up of a resistance $4\,\Omega$ and an inductance $0.01\,H$,an alternating $emf$ of $200\,V$ at $50\,Hz$ is connected. The phase difference between the current and the $emf$ in the circuit is:

An arc lamp requires a direct current of $10\ A$ at $80\ V$ to function. If it is connected to a $220\ V$ (rms),$50\ Hz$ $AC$ supply,the series inductor needed for it to work is close to: (in $H$)