Question

If a copper wire is stretched to make it 0.1% longer, then what is the percentage change in its resistance? 

(A) 0.2 % 

(B) 0.3 % 

(C) 0.4 % 

(D) 0.1%

Answer 1

The correct option is (A) 0.2 %.

Explanation:

R = (ρℓ / A) = (ρℓ² / ℓA) 

but Aℓ = volume = V 

Hence R = (ρℓ² / V) = constant × ℓ² 

Let constant be K hence 

R = Kℓ² 

∴ (dR / R) = 2(dℓ / ℓ) 

100 × (dR / R) = 200 × (dℓ / ℓ) 

Given (dℓ / ℓ) = 0.1 % 

∴ % change in R = [200 × {0.1 / (100)}]% = 0.2%.