Resistance of a metal wire of length 1m is 26 ohm at room temperature. If diameter of wire is 0.3 mm, find the resistivity of the wire

If diameter of wire is 0.3 mm, the resistivity of the wire is 1.8356 × 10⁻⁶ Ωm at room temperature.

Step 1, It is given that resistance , R = 26Ω

Diameter of circular part of wire, d = 0.3 mm = 0.3 × 10⁻³m

Length of wire, L = 1 m

Step 2, now we have to determine the resistivity

Base area of wire, A = πr² = πd²/4 [ ∵d = 2r]

Substituting the values in above eqaution

Area = [3.14 x (0.3 x 10⁻³)²]/4

On simplifying we get

Area = 7.06 × 10⁻⁸ m²

Using the formula,

R = ρL/A

Here, R = resistance, ρ = resistivity, The wire’s base area is A, and its length is L.

So, ρ = RA/L

Substituting the values in above equation

ρ = 26Ω x 7.06 × 10⁻⁸ m²/1

On simplifying we get

ρ = 26Ω x 7.06 × 10⁻⁸ m²

ρ = 1.8356 × 10⁻⁶ Ωm

Therefore, resistivity is 1.8356 × 10⁻⁶ Ωm at room temperature.