$A$ resistor of $500 \Omega$ and an inductor of $0.5 \ H$ are connected in series with an $AC$ source given by $V = 100 \sqrt{2} \sin(1000 t)$. The power factor of the combination is:

The power factor of a $CR$ circuit is $\frac{1}{\sqrt{2}}$. If the frequency of an $AC$ signal is halved,then the power factor of the circuit will become:

In the given circuit,the $rms$ value of current $(I_{rms})$ through the resistor $R$ is: $..........\,A$

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

An inductance coil has a resistance of $80 \Omega$. When an $AC$ signal of frequency $480 \text{ Hz}$ is applied to the coil,the voltage leads the current by $45^{\circ}$. The inductance of the coil in henry is $\left[\sin 45^{\circ}=\cos 45^{\circ}=1 / \sqrt{2}\right]$

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