A resistive wire of resistance 10 Ω is stretched to increase its length by 100%. Due to the consequent decrease in diameter, the resistance of the stretched wire will be _.

Question

Accepted Answer

(1) 40 Ω. Given: R = 10 Ω; the length increases by 100%, so ℓ' = 2ℓ. Idea: stretching keeps the volume Aℓ fixed, so doubling the length halves the area: A' = A/2. R' = ρ (ℓ')/(A') = ρ (2ℓ)/(A/2) = 4 ρ ℓ/A = 4R. R' = 4×10 = 40 Ω.

A resistive wire of resistance 10 Ω is stretched to increase its length by 100%. Due to the consequent decrease in diameter, the resistance of the stretched wire will be _______.

Step-by-step solution

Why the other options are wrong