$A$ resistor and a pure inductor are connected to an $AC$ supply of $120\,V$ and $50\,Hz$. The current in the circuit is $3\,A$. If the power consumed in the circuit is $108\,W$,then the resistance in the circuit is.....$\Omega $

$A$ 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:

$A$ coil has self-inductance $L = 0.04 \ H$ and resistance $R = 12 \ \Omega$. When it is connected to a $220 \ V, 50 \ Hz$ supply,what will be the current flowing through the coil (in $A$)?

An a.c. voltage source $V=V_0 \sin \omega t$ is connected across resistance $R$ and capacitance $C$ in series. It is given that $R=\frac{1}{\omega C}$ and the peak current is $I_0$. If the angular frequency of the voltage source is changed to $\frac{\omega}{\sqrt{3}}$,then the new peak current in the circuit is

An induction coil has an impedance of $10 \Omega$. When an $AC$ signal of frequency $1000 \ Hz$ is applied to the coil,the voltage leads the current by $45^\circ$. The inductance of the coil is

An inductor and a resistor in series are connected to an $A.C.$ supply of variable frequency. As the frequency of the source is increased,the phase angle between current and the potential difference across $L$ will