$A$ $10\, V, 60\, W$ bulb is to be connected to a $100\, V, 50\, Hz$ $AC$ source. To operate the bulb at its rated power,an induction coil is connected in series with it. Calculate the required self-inductance of the coil.

$A$ series $R-C$ circuit is connected to an $AC$ voltage source. Consider two cases: $(A)$ when $C$ is without a dielectric medium and $(B)$ when $C$ is filled with a dielectric of constant $K = 4$. The current $I_R$ through the resistor and voltage $V_C$ across the capacitor are compared in the two cases. Which of the following is/are true?

In an $LR$-circuit,the inductive reactance is equal to the resistance $R$ of the circuit. An e.m.f. $E = E_0 \cos(\omega t)$ is applied to the circuit. The power consumed in the circuit is:

An alternating emf is applied across a parallel combination of a resistance $R$,capacitance $C$ and an inductance $L$. If $I_R$,$I_L$,and $I_C$ are the currents through $R$,$L$,and $C$ respectively,then the diagram which correctly represents the phase relationship among $I_R$,$I_L$,$I_C$,and the source emf $E$ is:

$A$ circuit connected to an $ac$ source of $emf$ $e = e_0 \sin(1000t)$,where $t$ is in seconds,exhibits a phase difference of $\frac{\pi}{4}$ between the $emf$ $e$ and current $i$. Which of the following circuits will exhibit this?

In a series $A.C.$ circuit,the current and voltage are given respectively as:
$I = 10 \sin \omega t$; $V = 10 \sin \left( \omega t + \pi / 4 \right)$
Then,which of the following elements may be present in the circuit?
$(a)$ Only $C$
$(b)$ All $L, C$ and $R$
$(c)$ Both $C$ and $R$
$(d)$ Both $L$ and $R$