When a coil is connected across a $20 \ V$ $DC$ supply,it draws a current of $5 \ A$. When it is connected across a $20 \ V, 50 \ Hz$ $AC$ supply,it draws a current of $4 \ A$. The self-inductance of the coil is .............. $mH$. (Take $\pi=3$)

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 an $LCR$ series circuit,if ${X_C} < {X_L}$ and ${X_C} > {X_L}$,determine whether the current in the circuit leads or lags the voltage.

The variation of impedance $Z$ of a series $\text{LCR}$ circuit with the frequency $f$ of the source is shown in the figure. Which of the following statement$(s)$ is/are true?

An $AC$ circuit has an inductor and a resistor of resistance $R$ in series,such that $X_L = 3R$. Now,a capacitor is added in series such that $X_C = 2R$. The ratio of the new power factor to the old power factor of the circuit is $\sqrt{5} : x$. The value of $x$ is ...... .

Which one of the following curves represents the variation of impedance $(Z)$ with frequency $(f)$ in a series $L-C-R$ circuit,when connected to an $AC$ source?