Question

The drift speed of free electrons in a conductor depends upon
A. the material of the conductor
B. the temperature of the conductor
C. the potential difference applied across the ends of the conductor
D. the area of cross section of the conductor

Answer 1

Hint: As a first step, you could give a brief explanation about the drift speed. Then you could check whether this quantity depends on which among the given factors. You could make use of the known expressions to determine the same. The fact that a quantity is seen in the expression doesn’t actually show the dependency.

Complete answer:
In the question, we are asked to find which among the given factors affect the drift speed of free electrons. In order to answer this question, we have to understand what exactly drift velocity is. You may be familiar with the fact that the movement of subatomic particles is in random directions. On applying electric fields there happens to be a drift in their movement to one direction. The net velocity of the electric particles during this drift is called drift velocity, that is, it is the average velocity attained by charged particles as the result of an applied electric field.
The drift velocity is known to be primarily dependent on the applied voltage and another property on which it depends is the molecular structure of the wire and hence the material of the conductor. Slight temperature dependence is also observed.
But this velocity doesn’t depend on the cross sectional area as the ratio $\dfrac{I}{A}$ is constant when applied electric field remains constant. This ratio is what we call the current density and drift velocity is directly proportional to this quantity.

Therefore, we found that options A, B and C are the factors on which the drift velocity depends.

Note:
The temperature dependence of this quantity can be explained like this. Increasing the temperature increases the vibration of the atoms and hence the number of collisions is also
increased and as the result of all these drift velocity is decreased. The only known temperature dependent quantity of a conductor is the change in drift velocity.