In an $L-R$ circuit,the inductive reactance is equal to $\sqrt{3}$ times the resistance $R$ of the circuit. An e.m.f. $E = E_0 \sin(\omega t)$ is applied to the circuit. The power consumed in the circuit is:

In a series $LCR$ circuit, the $rms$ voltage across the resistor and the capacitor are $30 \ V$ and $90 \ V$ respectively. If the applied voltage is $V = 50 \sqrt{2} \sin \omega t$, then the peak voltage across the inductor is

$A$ circuit contains an inductance of $\frac{1}{6 \pi} \text{ H}$ and a resistance of $15 \text{ } \Omega$ in series. If an $AC$ voltage of $100 \text{ V}$ and $60 \text{ Hz}$ is applied to the circuit,then the current in the circuit and the phase difference between voltage and current are,respectively:

An inductance coil has a reactance of $100\, \Omega$. When an $AC$ signal of frequency $1000\, Hz$ is applied to the coil,the applied voltage leads the current by $45^{\circ}$. The self-inductance of the coil is

An inductance coil has a resistance of $80 \Omega$. When an $AC$ signal of frequency $480 \text{ Hz}$ is applied to the coil,the voltage leads the current by $45^{\circ}$. The inductance of the coil in henry is $\left[\sin 45^{\circ}=\cos 45^{\circ}=1 / \sqrt{2}\right]$

In an $L-R$ circuit,the inductive reactance is equal to the resistance $R$ in the circuit. An emf $E = E_0 \cos \omega t$ is applied to the circuit. The power consumed in the circuit is