$A$ coil of resistance $450 \Omega$ and self-inductance $1.5 \text{ H}$ is connected to an $A$.$C$. source of frequency $\frac{150}{\pi} \text{ Hz}$. The phase difference between voltage and current is

When a $DC$ voltage of $200\, V$ is applied to a coil of self-inductance $\frac{2\sqrt{3}}{\pi}\,H$,a current of $1\, A$ flows through it. When the $DC$ source is replaced by an $AC$ source of $200\, V$,the current in the coil is reduced to $0.5\, A$. The frequency of the $AC$ supply is......$Hz$.

For a series $LCR$ circuit,which one of the following is a $CORRECT$ statement?

An electric bulb and a capacitor are connected in series with an $AC$ source. On increasing the frequency of the source,the brightness of the bulb

In an $LC$ circuit,the inductance $L = 40 \; mH$ and capacitance $C = 100 \; \mu F$. If a voltage $V(t) = 10 \sin (314 t)$ is applied to the circuit,the current in the circuit is given by:

$A$ series $L, R$ circuit connected with an ac source $E = (25 \sin 1000 t) \ V$ has a power factor of $\frac{1}{\sqrt{2}}$. If the source of emf is changed to $E = (20 \sin 2000 t) \ V$,the new power factor of the circuit will be: