Resistance of a metal wire of length 1 m is 26 Ω at 20°C. If the diameter of the wire is 0.3 mm, what will be the resistivity of the metal at that temperature?

To find the resistivity of the metal, we can use the formula:

R = ρ * (L / A)

Where:
R = Resistance of the wire = 26 Ω
L = Length of the wire = 1 m
A = Cross-sectional area of the wire
ρ = Resistivity of the material (to be calculated)

Step 1: Calculate the cross-sectional area of the wire
The wire is circular in cross-section. The formula for the area of a circle is:
A = π * (d/2)^2

Here,
d = Diameter of the wire = 0.3 mm = 0.3 × 10^-3 m

Substituting the value of d:
A = π * (0.3 × 10^-3 / 2)^2
A = π * (0.15 × 10^-3)^2
A = π * (0.15^2 × 10^-6)
A = 3.1416 * 0.0225 × 10^-6
A = 7.0686 × 10^-8 m²

Step 2: Rearrange the formula for resistivity
From R = ρ * (L / A), rearranging for ρ:
ρ = R * (A / L)

Substitute the known values:
R = 26 Ω, A = 7.0686 × 10^-8 m², L = 1 m

ρ = 26 * (7.0686 × 10^-8 / 1)
ρ = 26 * 7.0686 × 10^-8
ρ = 1.838 × 10^-6 Ω·m

Final Answer:
The resistivity of the metal at 20°C is 1.838 × 10^-6 Ω·m.