A cylindrical metallic wire is stretched to increase its length. If the resistance of the wire is increased by 4 % then the percentage increase in its length is

Step-by-step solution

In the above case the volume and specific resistivity of the wire does not change, it means, V 1 = V 2 ⇒ π r 1 2 l 1 = π r 2 2 l 2 ⇒ r 1 2 r 2 2 = l 2 l 1 Now recall the formula of resistance in terms of specific resistivity, R = ρ × l π r 2 ⇒ R 1 R 2 = l 1 π r 1 2 l 2 π r 1 2 = l 1 l 2 2 ⇒ l 1 l 2 2 = R 1 R 2 ⇒ 2 ∆ l 1 l 2 l 1 l 2 × 100 = ∆ R 1 R 2 R 1 R 2 × 100 = 4 % ⇒ ∆ l 1 l 2 l 1 l 2 × 100 = 2 %