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
Answers
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.
Answer:
Manganin is more thicker
Explanation:
We know R = ρl/A
Let R₁ be the resistance, A₁ be the area of cross section, ρ₁ be the resistivity and l₁ be the length of copper wire
R₁ = ρ₁l₁/A₁ ...................(1)
Let R be the resistance, A₂ be the area of cross section, ρ₂ be the resistivity and l₂ be the length of Manganin wire
R₂ =ρ₂l₂/A₂ .......................(2)
Given R₁ = R₂ and l₁ = l₂
Since R₁ = R₂
ρ₁l₁/A₁ = ρ₂l₂/A₂
⇒ ρ₁/A₁ = ρ₂/A₂ (l₁ =l₂)
⇒ ρ₁/ρ₂ =A₁/A₂
But ρ₂ > ρ₁ ( Alloy has a higher resistivity than metals)
∴ ρ₁/ρ₂ < 1 ( A number divided by a greater number is always less than 1)
⇒ A₁/A₂ < 1
⇒ A₁ < A₂
∴ Manganin wire is more thicker than Copper wire
................Hope it helps you