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

2*10⁻⁷ Ωm

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