In an $AC$ circuit,a resistance of $R \, \Omega$ is connected in series with an inductance $L$. If the phase angle between voltage and current is $45^o$,the value of inductive reactance will be:

The phase difference between the alternating current and emf is $\frac{\pi}{2}$. Which of the following cannot be the constituent of the circuit?

When an inductor $L$ and a resistor $R$ in series are connected across a $15 \, V, 50 \, Hz$ a.c. supply, a current of $0.3 \, A$ flows in the circuit. The current differs in phase from the applied voltage by $(\frac{\pi}{3})^c$. The value of $R$ is:
$(\sin \frac{\pi}{6} = \cos \frac{\pi}{3} = \frac{1}{2}, \sin \frac{\pi}{3} = \cos \frac{\pi}{6} = \frac{\sqrt{3}}{2})$

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

$A$ series $R-C$ circuit is connected to an alternating voltage source. Consider two situations:
$(a)$ When the capacitor is air-filled.
$(b)$ When the capacitor is mica-filled.
If the current through the resistor is $i$ and the voltage across the capacitor is $V$,then:

An $AC$ voltage source of variable angular frequency $\omega$ and fixed amplitude $V_0$ is connected in series with a capacitance $C$ and an electric bulb of resistance $R$ (inductance zero). When $\omega$ is increased,