Question

The drift velocity of electrons in a conducting wire is of the order of $ 1mm/s $ , yet the bulb glows very quickly after the switch is put on because
(A) The random speed of electrons is very high of the order of $ {10^{ - 6}}m/s $
(B) The electrons transfer their energy very quickly through collision.
(C) Electric field is set up in the wire very quickly, producing a current through each cross section almost instantaneously
(D) All the above

Answer 1

Hint: The flow of electrons causes electrons to move at a speed called the drift velocity which is the reason for the bulb to glow. We know that when electrons flow, in a battery or cell, the flow is unidirectional and opposite to the flow of electrons from the battery.

Formulas used : We might be using the formula or the notion from formula $ {v_d} = \dfrac{{ - eE}}{m}\tau $ where $ e $ is the charge on the electrons, and $ E $ is the intensity of electric field, $ m $ is the mass of electrons , while $ \tau $ is called the relaxation time or the time between the collision of electrons with each other, we use this formula to find the value of drift velocity, or the $ {v_d} $ .

Complete Step by Step Solution
We know that a wire is full of electrons and all you need is to pass them through the conducting copper wire to switch the bulb on. Yes, this process seems to be instantaneous but actually is it? So, let us consider the first statement,
It says that the random speed of electrons is very high and thus the movement of those electrons can cause the action to take place so fast. But this would also mean that those are the only electrons that cause the light to turn on. As earlier mentioned, we know that a conductor is filled with free electrons thus we have a contradicting fact. Hence the statement is false.
So, in this case it is said that the electrons transfer their energy through collisions to cause the light bulb to glow. The energy created here would-be electrical energy that will be transferred along with the kinetic energy of each electron. But this means that there is no actual movement of electrons happening and this contradicts the very basic definition of electricity.
Now taking the last statement, we know that when the electrons carrying a charge exert force on each other, it causes an electric field in the space. Thus, causing the movement of electrons. We also know that the drift velocity of electrons can be given by, $ {v_d} = \dfrac{{ - eE}}{m}\tau $ and from here we can see that the $ {v_d} \propto E $ .Thus electric field can cause movement in electrons and thus result in the bulb to glow. Hence this is the true statement.
Hence the correct answer is option C.

Note
The concepts of molecular kinetics will not always hold true in case of electrical energy because charged subatomic particles tend to act differently under a few circumstances. Thus, comparing molecular kinetics concepts like collision with the concepts of electricity and charges.