A wire of length l has a resistance R . If half of the length is stretched to make the radius half of its original value, then the final resistance of the wire is

Step-by-step solution

R = ρ l A = ρ l π r 2 π r 2 l 2 = π ( r 2 ) 2 l ′ l ′ = 2 l R ' = ρ l ' A ' = ρ 2 l π r 2 2 = 8 R R '' = ρ l 2 π r 2 = R 2 R eq = R ' + R '' = 17 R 2