An electric bulb of $100 \,W -300 \,V$ is connected with an $AC$ supply of $500 \,V$ and $\frac{150}{\pi} \,Hz$. The required inductance to save the electric bulb is ……….$H$

In an $LC$ circuit, the capacitor has maximum charge $q_0$. The value of is ${\left. {\frac{{di}}{{dt}}} \right|_{\max }}$

Discuss the power in $AC$ circuit containing only an inductor. 

A coil of inductance $0.50\;H$ and resistance $100 \;\Omega$ is connected to a high frequency supply $(240\; V, 10 \;k\,Hz)$

$(a)$ What is the maximum current in the coil?

$(b)$ What is the time lag between the voltage maximum and the current maximum?

Hence, explain the statement that at very high frequency, an inductor in a circuit nearly amounts to an open circuit. How does an inductor behave in a $dc$ circuit after the steady state?

A circuit connected to an $ac$ source of $emf$ $e = e_0\, sin\, (1000t)$ with $t$ in seconds, gives a phase difference of $\frac{\pi }{4}$ between the $emf$ $e$ and current $i$. Which of the following circuits will exhibit this?