$A$ student connects a long air-cored coil of manganin wire to a $100\,V$ $D.C.$ supply and records a current of $25\,A$. When the same coil is connected across a $100\,V$,$50\,Hz$ $A.C.$ supply,the current reduces to $20\,A$. The reactance of the coil is....$\Omega $

In a circuit,a metal filament lamp is connected in series with a capacitor of capacitance $C \mu F$ across a $200 V, 50 Hz$ supply. The power consumed by the lamp is $500 W$ while the voltage drop across it is $100 V$. Assume that there is no inductive load in the circuit. Take $rms$ values of the voltages. The magnitude of the phase-angle (in degrees) between the current and the supply voltage is $\varphi$.
Assume,$\pi \sqrt{3} \approx 5$.
$(1)$ The value of $C$ is . . . . . .
$(2)$ The value of $\varphi$ is
Give the answers of the questions $(1)$ and $(2)$:

$A$ coil of inductance $0.1 H$ and resistance $110 \Omega$ is connected to a source of $110 V$ and $350 Hz$. The phase difference between the voltage maximum and the current maximum is

An e.m.f. $E = 4 \cos(1000t) \, V$ is applied to an $LR$-circuit of inductance $3 \, mH$ and resistance $4 \, \Omega$. The amplitude of current in the circuit is:

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 $R$

In an $AC$ circuit,the potential differences across an inductance and a resistance joined in series are $16 \, V$ and $20 \, V$ respectively. The total potential difference of the source is .......... $V$.