An inductive circuit contains a resistance of $10 \, \Omega$ and an inductance of $2.0 \, H$. If an $AC$ voltage of $120 \, V$ and frequency $60 \, Hz$ is applied to this circuit,the current would be nearly: ..... $A$

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 electric bulb has a rated power of $50 \, W$ at $100 \, V$. If it is used on an $AC$ source of $200 \, V, 50 \, Hz$, a choke has to be used in series with it. This choke should have an inductance of (in $ \, H$)

In a simple $L-R$ circuit with an $A.C.$ source,the potential difference at any instant across the inductor and the resistor are $V_L$ and $V_R$ respectively,and the $A.C.$ source has a potential difference $V_{AC}$ at the same instant. Then:

When an inductor $L$ and a resistor $R$ in series are connected across a $15 \, V, 50 \, Hz$ a.c. supply, a current of $0.3 \, A$ flows in the circuit. The current differs in phase from the applied voltage by $(\frac{\pi}{3})^c$. The value of $R$ is:
$(\sin \frac{\pi}{6} = \cos \frac{\pi}{3} = \frac{1}{2}, \sin \frac{\pi}{3} = \cos \frac{\pi}{6} = \frac{\sqrt{3}}{2})$

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 . . . . . . .