Question

The resistivity of iron is 1 x 10 -7 Ωm. The resistance of a iron wire of particular length and thickness is 1 ohm. If the length and the diameter of wire both are doubled, then the resistivity in Ωm will be

Answer 1

2×10⁻⁷ Ωm

Step-by-step explanation:

From the question,

R = 4ρL/πd².................... Equation 1

Where R = Resistance of the wire, ρ = resistivity of the wire, L = length of the wire, d = diameter of the wire.

Therefore,

ρ = Rπd²/4L............. Equation 2

Given: R = 1 ohm, ρ = 1×10⁻⁷Ωm

1×10⁻⁷ = πd²/4L.................... Equation 3

If the length and the diameter are doubled, and the resistance remaining constant

ρ' = π(2d)²/4(2L)

Where ρ' = new resistivity

ρ' = 4πd²/8L

ρ' = 2πd²/4L = 2ρ

ρ' = 2(1×10⁻⁷)

ρ' = 2×10⁻⁷ Ωm