Calculate the capacitive reactance of a capacitor in order to run a bulb rated at $10 \, W, 60 \, V$ when connected in series to an $a.c.$ source of $100 \, V$.

$A$ circuit when connected to an $A.C.$ source of $12 \; V$ gives a current of $0.2 \; A$. The same circuit when connected to a $D.C.$ source of $12 \; V$,gives a current of $0.4 \; A$. The circuit is

For a series $LCR$ circuit with $R=100\,\Omega$,$L=0.5\,mH$ and $C=0.1\,pF$ connected across $220\,V-50\,Hz$ $AC$ supply,the phase angle between current and supplied voltage and the nature of the circuit is:

An induction coil has an impedance of $10\,\Omega$. When an $AC$ signal of frequency $1000\,Hz$ is applied to the coil,the voltage leads the current by $45^o$. The inductance of the coil is

$A$ current of $\frac{25}{\pi} \text{ Hz}$ frequency is passing through an $AC$ circuit having a series combination of $R=100 \ \Omega$ and $L=2 \text{ H}$. The phase difference between voltage and current is . . . . . . . (in $^{\circ}$)

$A$ 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.