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

The phase difference between the alternating current and emf is $\frac{\pi}{2}$. Which of the following cannot be the constituent of the circuit?

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$)

$A$ resistor of $300 \Omega$ and an inductor of $\frac{1}{\pi} \text{ H}$ are connected in series with a $20 \text{ V}$,$200 \text{ Hz}$ $AC$ source. What is the phase difference between the current and the voltage?

In an $LCR$ series $a.c.$ circuit,the voltage across each of the components $L, C$ and $R$ is $60 \,V$. The voltage across the $LC$ combination is

$A$ $100 \;\mu F$ capacitor in series with a $40 \;\Omega$ resistance is connected to a $110 \;V, 12 \;kHz$ supply.
$(a)$ What is the maximum current in the circuit?
$(b)$ What is the time lag between the current maximum and the voltage maximum?
Hence,explain the statement that a capacitor is a conductor at very high frequencies. Compare this behaviour with that of a capacitor in a $dc$ circuit after the steady state.