What will be the self-inductance of a coil,to be connected in series with a resistance of $\pi \sqrt{3} \, \Omega$,such that the phase difference between the $EMF$ and the current at $50 \, Hz$ frequency is $30^o$ (in $, H$)?

$A$ coil has an inductance of $0.7 \, H$ and is joined in series with a resistance of $220 \, \Omega$. When an alternating $emf$ of $220 \, V$ at $50 \, Hz$ is applied to it,the phase angle by which the current lags behind the applied $emf$ and the wattless component of the current in the circuit are respectively:

When an $AC$ source of $e.m.f.$ $e = E_0 \sin(100t)$ is connected across a circuit,the phase difference between the $e.m.f.$ $e$ and the current $i$ in the circuit is observed to be $\pi/4$,as shown in the diagram. If the circuit consists possibly only of $RC$ or $LC$ in series,find the relationship between the two elements.

Calculate the capacitive reactance of a capacitor in order to run a bulb rated at $10 \, W, 60 \, V$ when connected in series to an $a.c.$ source of $100 \, V$.

In a series $LR$ circuit,$X_L=R$,the power factor is $P_1$. If a capacitor of capacitance $C$ with $X_C=X_L$ is added to the circuit,the power factor becomes $P_2$. The ratio of $P_1$ to $P_2$ will be

$A$ resistance of $400\,\Omega$ is connected in series with an inductor of $(3/\pi)\,H$ and this combination is connected across an $A.C.$ source as shown in the figure,where $e = 400 \sin(100\pi t)$. Which of the following statements is correct?