The power is transmitted from a power house on high voltage $ac$ because

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?

$A$ resistor of resistance $R$ and an inductor of inductive reactance $R$ are connected in series to an $AC$ source. $A$ capacitor of capacitive reactance $2R$ is then connected in series with $L$ and $R$. The ratio of the power factors of the $LR$ and $LCR$ circuits is:

An $AC$ generator consists of a coil of $100$ turns and is of cross-sectional area $3 \ m^2$. It is rotating at a constant angular speed of $60 \ rad \ s^{-1}$ in a uniform magnetic field of $0.04 \ T$. The resistance of the coil is $360 \ \Omega$. What is the maximum power dissipation in the coil (in $W$)?

You are given many resistances,capacitors and inductors. These are connected to a variable $DC$ voltage source (the first two circuits) or an $AC$ voltage source of $50 \ Hz$ frequency (the next three circuits) in different ways as shown in Column $II$. When a current $I$ (steady state for $DC$ or rms for $AC$) flows through the circuit,the corresponding voltage $V_1$ and $V_2$ (indicated in circuits) are related as shown in Column $I$. Match the two.

Statement-$I$: $A$ capacitor can be used in an $a.c.$ circuit in place of a choke coil.
Statement-$II$: $A$ capacitor blocks $d.c.$ and allows $a.c.$ to pass.