Question

Two wires, one of copper and other of manganin, have equal lengths and equal
resistances. Which wire is thicker ? Given that resistivity of copper is lower than that
of manganin.

Answer 1

Manganin is an alloy of Cu with manganese and nickel. Since the latter two metals have resistivity greater than copper, the pure copper has lower resistivity and the manganin thus has to be thicker to have the same resistance.

Answer 2

We know that resistance of a wire is given as,

R = ρL/A

let the resistivity and area of copper wire is ρ₁ and A₁

and let the resistivity and area of manganin wire is ρ₂ and A₂

since resistance and length of both the wires are equal,

=> ρ₁/A₁ = ρ₂/A₂

=> A₁/A₂ = ρ₁/ρ₂

since ρ₁<ρ₂

=> A₁<A₂

hence manganin wire will be more thick.

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