Question

A piece of silver wire has a resistance of 1Ω. What will be the resistance of manganin wire of one-third the length and one-third the diameter. if the specific resistance of manganin is 30 times that of silver

Answer 1

For silver wire R₁ = l₁/A₁; For manganin wire, R = ρ₂(l₂/A₂)

∴ R₂/R₁ = ρ₂/ρ₁ x l₂/l₁ x A₁/A₂

Now A₁ = πd₁²/4 and A₂ = πd₂²/4

∴ A₁/A₂ = d₁²/d₂²

∴ R₂/R₁ = ρ₂/ρ₁ x l₂/l₁ x (d₁/d₂)²

R₁ = 1Ω; l₂/l₁ = 1/3, (d₁/d₂)² = (3/1)² = 9; ρ₂/ρ₁ = 30

∴ R₂ = 1 x 30 x (1/3) x 9 = 90Ω