Physics 2021 JAMB Past Questions - Question 17: A wire A is half the length and half the diameter of a wire B of similar material. What is the ratio of the resistance of B to that of A?

Correct Answer

B

Explanation

The resistance of a wire is directly proportional to its length and inversely proportional to its cross-sectional area.

Let's denote the length of wire A as L and its diameter as D. The length of wire B is 2L and its diameter is 2D.

The resistance of a wire is given by the formula: R = ρ * (L/A), where ρ is the resistivity of the material, L is the length, and A is the cross-sectional area.

The cross-sectional area of wire A is π*(D/2)^2, and the cross-sectional area of wire B is π*D^2.

So, the ratio of the resistance of B to that of A is:

R(B)/R(A) = (ρ * 2L) / (π * D^2) / (ρ * L) / (π * (D/2)^2)
          = 2 * (D/2)^2 / D^2
          = 1/2

Therefore, the ratio of the resistance of B to that of A is 1:2.