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

If $C, R, L$ and $I$ denote capacity, resistance, inductance and electric current respectively, the quantities having the same dimensions of time are :
$(1)$ $C R$
$(2)$ $\frac{L}{R}$
$(3)$ $\sqrt{L C}$
$(4)$ $L I^2$

Given below are two statements $:$ one is labelled as Assertion $(A)$ and the other is labelled as Reason $(R).$
Assertion $(A) :$ Choke coil is simply a coil having a large inductance but a small resistance. Choke coils are used with fluorescent mercury-tube fittings. If household electric power is directly connected to a mercury tube,the tube will be damaged.
Reason $(R):$ By using the choke coil,the voltage across the tube is reduced by a factor $\left(R / \sqrt{R^2+\omega^2 L^2}\right)$,where $\omega$ is the angular frequency of the supply,$R$ is the resistance,and $L$ is the inductance. If the choke coil were not used,the voltage across the tube would be the same as the applied voltage. In the light of the above statements,choose the most appropriate answer from the options given below $:$

An $AC$ source of $20\,V$ (assuming standard frequency $f = 50\,Hz$ for calculation) is connected to an inductance of $100\,mH$,a capacitance of $100\,\mu F$,and a resistance of $120\,\Omega$ as shown in the figure. The time in which the resistance,having a thermal capacity of $2\,J/^{\circ}C$,will get heated by $16^{\circ}C$ is ..........$s$.

In an electrical circuit,$R, L, C$ and an $a.c.$ voltage source are all connected in series. When $L$ is removed from the circuit,the phase difference between the voltage and the current in the circuit is $\pi /3$. If instead,$C$ is removed from the circuit,the phase difference is again $\pi /3$. The power factor of the circuit is

$A$ direct current of $4\,A$ and an alternating current of peak value $4\,A$ flow through resistances of $3\,\Omega$ and $2\,\Omega$ respectively. The ratio of heat produced in the two resistances in the same interval of time will be.