Question

Length of a wire of resistance RΩ is increased to 10 times, so its resistance becomes 1000Ω, therefore R = .... (The volume of the wire remains same during increase in length) 

(A) 0.01Ω 

(B) 0.1Ω 

(C) 1Ω 

(D) 10Ω

Answer 1

 The correct option (D) 10Ω

Explanation:

R = (ρℓ/A)  (1)

after increasing length to 10 times, R¹ = 1000Ω

ℓ' = 10ℓ.

volume = area × length = constant

∴ Aℓ = A'ℓ'

∴ (A'/A) = (ℓ/ℓ')

Now    R¹ = {(ρℓ')/A'} (2)

from (1) & (2)

∴ (R/R') = (ℓ/A) × (A'/ℓ') = (ℓ/ℓ') × (ℓ/ℓ')

∴ R = 1000 (ℓ/ℓ')² = 1000 × (1/10)² = 10Ω