PHYSICS
JAMB 2021 - Question 17
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?
Choose the correct answers from the options given.
A:
B:
C:
D:
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.
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