In an $RL$ circuit,the reactance of the coil is $\sqrt{3}$ times the resistance. The phase difference between the voltage and the current is:

$20\,V$ $AC$ is applied to a circuit consisting of a resistance and a coil with negligible resistance. If the voltage across the resistance is $12\,V$,the voltage across the coil is.....$V$.

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 a.c. source of $15 \, V, 50 \, Hz$ is connected across an inductor $(L)$ and resistance $(R)$ in series. The $R.M.S.$ current of $0.5 \, A$ flows in the circuit. The phase difference between the applied voltage and current is $\left(\frac{\pi}{3}\right)$ radian. The value of resistance $(R)$ is $\left(\tan 60^{\circ}=\sqrt{3}\right)$. (in $\Omega$)

For the $AC$ circuit shown below,the phase difference between emf and current is $\frac{\pi}{4}$ radian as shown in the graph. If the impedance of the circuit is $1414 \Omega$,then the values of $P$ and $Q$ are

$A$ student connects a long air-cored coil of manganin wire to a $100\,V$ $D.C.$ supply and records a current of $25\,A$. When the same coil is connected across a $100\,V$,$50\,Hz$ $A.C.$ supply,the current reduces to $20\,A$. The reactance of the coil is....$\Omega $