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

$A$ current of $4 \, A$ flows in a coil when connected to a $12 \, V$ d.c. source. If the same coil is connected to a $12 \, V, (25/\pi) \, Hz$ a.c. source, a current of $2.4 \, A$ flows in the circuit. The inductance of the coil is: (in $ \, mH$)

$A$ resistance of $40\, \Omega$ and an inductance of $95.5\, \text{mH}$ are connected in series in a $50\, \text{Hz}$ $AC$ circuit. The impedance of this combination is very nearly.....$\Omega$.

When a $60 \text{ mH}$ inductor and a resistor are connected in series with an $AC$ voltage source,the voltage leads the current by $60^{\circ}$. If the inductor is replaced by a $0.5 \text{ } \mu\text{F}$ capacitor,the voltage lags behind the current by $30^{\circ}$. What is the frequency of the $AC$ supply?

$A$ 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 inductor and a resistor are connected in series to an $AC$ source of voltage $V = 144 \sin \left(100 \pi t + \frac{\pi}{2}\right) \text{ V}$. If the current in the circuit is $I = 6 \sin \left(100 \pi t + \frac{\pi}{6}\right) \text{ A}$,then the resistance of the resistor is: (in $Omega$)