In a circuit made up of a resistance $4\,\Omega$ and an inductance $0.01\,H$,an alternating $emf$ of $200\,V$ at $50\,Hz$ is connected. The phase difference between the current and the $emf$ in the circuit is:

$A$ circuit containing an $80 \, mH$ inductor and a $60 \, \mu F$ capacitor in series is connected to a $230 \, V, 50 \, Hz$ supply. The resistance of the circuit is negligible.
$(a)$ Obtain the current amplitude and $rms$ values.
$(b)$ Obtain the $rms$ values of potential drops across each element.
$(c)$ What is the average power transferred to the inductor?
$(d)$ What is the average power transferred to the capacitor?
$(e)$ What is the total average power absorbed by the circuit? ('Average' implies 'averaged over one cycle'.)

$A$ current of $4 \, A$ flows in a coil when connected to a $12 \, V$ d.c. source. If the same coil is connected to a $12 \, V, (25/\pi) \, Hz$ a.c. source, a current of $2.4 \, A$ flows in the circuit. The inductance of the coil is: (in $ \, mH$)

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

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

$A$ virtual current of $4 \, A$ and $50 \, Hz$ flows in an $AC$ circuit containing a coil. The power consumed in the coil is $240 \, W$. If the virtual voltage across the coil is $100 \, V$,its inductance will be: