$A$ capacitor of capacitance $100 \mu F$ and a coil of resistance $20 \Omega$ and inductance $12.5 mH$ are connected in series with a $220 V, \frac{200}{\pi} Hz$ $AC$ source. The maximum value of instantaneous current in the circuit is (in $A$)

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 . . . . . . .

An inductor and a resistor are connected in series to an ac source of variable frequency. When the frequency of the applied ac is $50 \ Hz$,the power factor of the circuit is $\frac{\sqrt{3}}{2}$. If the frequency of the ac is increased by $200 \%$,the power factor of the circuit is . . . . . . .

In the figure,if $A$ and $B$ are identical bulbs,which bulb glows brighter?

When $100 \, V$ $DC$ is applied across a coil,a current of $1 \, A$ flows through it. When $100 \, V$ $AC$ at $50 \, Hz$ is applied to the same coil,only $0.5 \, A$ current flows. The impedance of the coil is ....... $\Omega$.

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