$A$ 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 $A$)?

$A$ 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'.)

The impedance of an $LR$ circuit with $L=\frac{60}{\pi} \text{ mH}$,$R=8 \Omega$ and frequency $f=50 \text{ Hz}$ is (in $\Omega$)

In an $ac$ circuit,the current lags behind the voltage by $\pi /3$. The components in the circuit are

An inductor and a resistor are connected in series to an ac source of variable frequency. When the frequency of the applied ac is $50 \ Hz$,the power factor of the circuit is $\frac{\sqrt{3}}{2}$. If the frequency of the ac is increased by $200 \%$,the power factor of the circuit is . . . . . . .

If a dielectric slab is inserted in the capacitor of the given $RC$ circuit,then the brightness of the bulb will: