Question

Two wires , one of Cu 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

**Manginin wire is thicker.
it is given that copper has less resistivity than manganin. That means copper wire will have less resistance than manganin wire as it is given that they have equal lengths. But it is also given that they have equal resistance. To prove this manganin wire must be thicker than copper wire as RESISTANCE IS INVERSELY PROPORTIONAL TO THE AREA OF CROSS-SECTION which means more the area, less the resistance. THEREFORE MANGANIN WIRE WITH EQUAL RESISTANCE AND EQUAL LENGTH AS A COPPER WIRE WILL BE THICKER THAN THE COPPER WIRE. 

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 thicker.

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