Question

When no current pass through the conductor
A) The free electron do not move
B) The average speed of a free electron over a large period of time is zero
C) The average velocity of free electron over a large period of time is zero
D) The average velocities of free electrons at an instant is zero

Answer 1

Hint
Even when no current passes through the conductor the electrons are in the random motions caused by thermal excitation. So the random motion makes their net velocity to be 0.

Complete step-by-step answer:
For option (A):
The free electrons do not move even when no current is passing through them because the conductor possesses the thermal energy which excites the electron.
So the option is wrong.
For option (B):
As the speed is a scalar quantity so the average speed of the electron will not be 0. So even after all random motion it does not cancel out.
So this is also a wrong option.
For option (C):
When no electric field is applied the electrons are in the random motion. So the net displacement of electrons is zero. So, the sum of the velocities which the electrons get in the motion is also zero. Over a larger period the average velocity of one electron will also be zero.
This option is correct.
For option (D):
As one free electron has the average velocity is zero, the sum of average velocities will add up and also be zero. So the average velocities of all electrons will also be zero. In another way we can say that as the net current in the conductor is zero it implies that the displacement for all electrons will also be zero. This means they have zero drift velocity. So the average velocities at any instant of free electrons is a zero.
This option is also correct.
Hence, C and D options are correct.

Note
When an electric field is applied across the conductor the electrons drift in the opposite direction of the field and move towards the higher potential. This average velocity over a period of time is termed as the drift velocity which is zero in the static state.