Consider three wires X, Y and Z of the same length such that the ratio of their conductivities is 1 : 2 : 3. Further, the cross-sectional area of wire Z is twice that of Y and the resistance of X is equal to the resistance of Z. What is the ratio of the resistance of Y to that of X?
- A.1 : 1
- B.3 : 1
- C.2 : 1
- D.1 : 2
Correct answer
Explanation
The correct answer is B, 3 : 1. Using R = L/(σA) with equal lengths, the resistance of Y comes out three times that of X.
Resistance falls as conductivity σ and cross-sectional area A rise. Take the area of Y as A. Then Z has area 2A and conductivity 3, so RZ = L/(3 × 2A) = L/6A. Since X has the same resistance as Z, RX = L/6A. Wire Y has conductivity 2 and area A, so RY = L/2A. The ratio RY : RX = (1/2) : (1/6) = 3 : 1. Note that the area of X never has to be found separately; equating X with Z is enough.
A, 1 : 1, would need Y to have the same σA product as Z, but Y's product is 2 against Z's 6.
C, 2 : 1, comes from comparing conductivities alone and forgetting the area of Z.
D, 1 : 2, inverts the relation, treating resistance as rising with conductivity.
Exam tip: R = ρL/A = L/(σA); higher conductivity or a thicker wire means lower resistance.
Practice Questions
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Show answer
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