At very high frequencies, the current $(i)$ in the given circuit is (in $A$)

Is the current distribution shown in the figure possible?

Answer the following questions:
$(a)$ In any $ac$ circuit, is the applied instantaneous voltage equal to the algebraic sum of the instantaneous voltages across the series elements of the circuit? Is the same true for $rms$ voltage?
$(b)$ Why is a capacitor used in the primary circuit of an induction coil?
$(c)$ An applied voltage signal consists of a superposition of a $dc$ voltage and an $ac$ voltage of high frequency. The circuit consists of an inductor and a capacitor in series. Show that the $dc$ signal will appear across $C$ and the $ac$ signal across $L$.
$(d)$ $A$ choke coil in series with a lamp is connected to a $dc$ line. The lamp is seen to shine brightly. Insertion of an iron core in the choke causes no change in the lamp's brightness. Predict the corresponding observations if the connection is to an $ac$ line.
$(e)$ Why is a choke coil needed in the use of fluorescent tubes with $ac$ mains? Why can we not use an ordinary resistor instead of the choke coil?

What is the reason we prefer $A.C.$ voltage over $D.C.$ voltage for power transmission?

The self-inductance of a choke coil is $10\, mH$. When it is connected to a $10\, V$ $dc$ source,the power loss is $20\, W$. When it is connected to a $10\, V$ $ac$ source,the power loss is $10\, W$. The frequency of the $ac$ source is......$Hz$.

$A$ coil of self-inductance $L$ is connected in series with a bulb $B$ and an $AC$ source. The brightness of the bulb decreases when: