When a coil is connected to an $AC$ supply of frequency $50 \, Hz$, a current of $4 \, A$ flows in it and it consumes $240 \, W$ power. If the potential difference across the coil is $100 \, V$, then the inductance value of the coil is

For a series $LCR$ circuit,$R = X_L = 2X_C$. The impedance of the circuit and the phase difference between $V$ and $i$ will be:

$A$ resistor and a capacitor are connected in series with an $AC$ source. If the potential drop across the capacitor is $5 \,V$ and that across the resistor is $12 \,V$, then the applied voltage is (in $\,V$)

In a circuit,$L, C$ and $R$ are connected in series with an alternating voltage source of frequency $f$. The current leads the voltage by $45^o$. The value of $C$ is

$A$ light bulb and an open coil inductor are connected to an $AC$ source through a key as shown in the figure. The switch is closed and after some time,an iron rod is inserted into the interior of the inductor. Does the glow of the light bulb $(a)$ increase,$(b)$ decrease,or $(c)$ remain unchanged? Give your answer with reasons.

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$)