Question

A potential difference of V applied at the ends of a copper wire of length l and diameter d. On doubling only d drift velocity.
A. Becomes two times
B. Becomes half
C. Does not change
D. Becomes one fourth

Answer 1

Hint:First try to find the relation between the drift velocity, Length of the given copper wire and the diameter of the copper wire. If we get any relation that means drift velocity depends on these quantities and hence putting the values from the question we get the desired result.

Formula used:
Drift velocity:
${v_d} = \dfrac{V}{{\rho\, l\,n\,e}}$
Where, V is the potential difference applied at the ends of the given copper wire. $\rho $ is the resistivity. $l$ is the length of the given copper wire. $n$ is the number density of free electrons. $e$ is the charge of the electron.

Complete step by step solution:
Given information from the question:
Potential difference applied on the ends of the wire is $V$.
Length of the copper wire is $l$.
Diameter of the given copper wire is $d$.
We know that, the expression of drift velocity is given as follows:
${v_d} = \dfrac{V}{{\rho\, l\,n\,e}}$
Here in the formula for drift velocity length of the wire is present. But there is no diameter quantity in the formula. It means the drift velocity does not depend on the diameter of the given copper wire. So, doubling the diameter d has no effect on the drift velocity. Therefore, the drift velocity does not change on doubling the diameter of the copper wire.

Hence, the correct answer is option C.

Note: Here the diameter is get doubled and as the drift velocity does not depends on the diameter so it causes no change but if the length of the wire will get doubled then there will be change in the drift velocity as it depends on the length of the wire. Or any of the other quantities in the formula will also cause change.