In an $L-C-R$ series $AC$ circuit,the voltage across each of the components $L, C$,and $R$ is $50\,V$. The voltage across the $L-R$ combination will be

An a.c. source of angular frequency $\omega$ is connected across a resistor $R$ and a capacitor $C$ in series. The current is observed as $I$. Now the frequency of the source is changed to $\omega/4$,(keeping the voltage unchanged) the current is found to be $I/3$. The ratio of resistance to reactance at frequency $\omega$ is

$A$ sinusoidal voltage of peak value $283 \, V$ and angular frequency $320 \, rad/s$ is applied to a series $LCR$ circuit. Given that $R = 5 \, \Omega$,$L = 25 \, mH$,and $C = 1000 \, \mu F$. The total impedance and the phase difference between the voltage across the source and the current will respectively be:

The power factor of an $R-L$ circuit is $\frac{1}{\sqrt{2}}$. If the frequency of $AC$ is doubled,the power factor will now be

In the given figure,the current amplitude is

When a $DC$ voltage of $100 \, V$ is applied to an inductor, a $DC$ current of $5 \, A$ flows through it. When an $AC$ voltage of $200 \, V$ peak value is connected to the inductor, its inductive reactance is found to be $20\sqrt{3} \, \Omega$. The power dissipated in the circuit is . . . . . . $W$.