For a series $LCR$ circuit, inductive reactance $X_L$ is equal to resistance $R$ and also equal to twice the capacitive reactance $X_C$. The impedance of the circuit and the phase difference between voltage $V$ and current $i$ are respectively

$A$ coil has an inductance of $0.7 \, H$ and is joined in series with a resistance of $220 \, \Omega$. When an alternating $emf$ of $220 \, V$ at $50 \, Hz$ is applied to it,the phase angle by which the current lags behind the applied $emf$ and the wattless component of the current in the circuit are respectively:

$A$ capacitor of capacitance $100 \mu F$ and a coil of resistance $20 \Omega$ and inductance $12.5 mH$ are connected in series with a $220 V, \frac{200}{\pi} Hz$ $AC$ source. The maximum value of instantaneous current in the circuit is (in $A$)

The diagram shows a capacitor $C$ and a resistor $R$ connected in series to an $ac$ source. $V_1$ and $V_2$ are voltmeters and $A$ is an ammeter. Consider the following statements:
$I$. Readings in $A$ and $V_2$ are always in phase.
$II$. Reading in $V_1$ lags behind the reading in $V_2$ by $\frac{\pi}{2}$.
$III$. Readings in $A$ and $V_1$ are always in phase.
Which of these statements is/are correct?

When a $DC$ voltage of $200\, V$ is applied to a coil of self-inductance $\frac{2\sqrt{3}}{\pi}\,H$,a current of $1\, A$ flows through it. When the $DC$ source is replaced by an $AC$ source of $200\, V$,the current in the coil is reduced to $0.5\, A$. The frequency of the $AC$ supply is......$Hz$.

An induction coil has an impedance of $10 \Omega$. When an $AC$ signal of frequency $1000 \ Hz$ is applied to the coil,the voltage leads the current by $45^\circ$. The inductance of the coil is