$A$ resistance of $40\, \Omega$ and an inductance of $95.5\, \text{mH}$ are connected in series in a $50\, \text{Hz}$ $AC$ circuit. The impedance of this combination is very nearly.....$\Omega$.

An arc lamp requires a direct current of $10\ A$ at $80\ V$ to function. If it is connected to a $220\ V$ (rms),$50\ Hz$ $AC$ supply,the series inductor needed for it to work is close to: (in $H$)

An e.m.f. $E=E_0 \cos \omega t$ is applied to a circuit containing $L$ and $R$ in series. If $X_L=2 R$,then the power dissipated in the circuit is

An inductor and a resistor are connected in series to an $AC$ source. The current in the circuit is $500 \,mA$, if the applied $AC$ voltage is $8 \sqrt{2} \,V$ at a frequency of $\frac{175}{\pi} \,Hz$, and the current in the circuit is $400 \,mA$, if the same $AC$ voltage at a frequency of $\frac{225}{\pi} \,Hz$ is applied. The values of the inductance and the resistance are respectively:

$A$ sinusoidal voltage $V_0 \sin \omega t$ is applied across a series combination of resistance $R$ and inductance $L$. The amplitude of the current in this circuit is

The following series $L-C-R$ circuit,when driven by an emf source of angular frequency $70 \text{ krad/s}$,behaves effectively as: