Resistance R = ρl/A, where ρ is the resistivity, l the length and A the area of cross section of the wire.So, resistivity: ρ = RA/l = 10 x π x (0.25 x 10^-3)^2/75 ohm.m = 0.026 x 10^-6 Ω m. = 2.6 x 10^-8 Ω m.

Resistance R = l/A, where rho is the resistivity, l the length and A the area of cross section of the wire.= RA/l = 10 x ? x (0.25 x 10-3)2/75 ohm.m = 0.026 x 10-6 m. = 2.6 x 10-8 ? m.

Calculating the Resistivity of an Aluminium Wire

Given Data:
- Radius of the aluminium wire: 0.25 mm
- Length of the wire: 75 m
- Resistance of the wire: 10 ohms

Formula:
The resistance of a wire can be calculated using the formula:
R = (ρ * L) / A
where:
R is the resistance of the wire,
ρ (rho) is the resistivity of the material,
L is the length of the wire, and
A is the cross-sectional area of the wire.

Step 1: Calculating the Cross-Sectional Area
The cross-sectional area of the wire can be calculated using the formula:
A = π * r^2
where:
A is the cross-sectional area,
π (pi) is a mathematical constant approximately equal to 3.14159, and
r is the radius of the wire.

Plugging in the given values:
A = π * (0.25 mm)^2
A = 3.14159 * (0.25 mm)^2
A = 3.14159 * (0.00025 m)^2
A = 3.14159 * 0.0000000625 m^2
A ≈ 0.00000019635 m^2

Step 2: Calculating the Resistivity
Rearranging the resistance formula:
ρ = (R * A) / L
where:
ρ (rho) is the resistivity of the material.

Plugging in the given values:
ρ = (10 ohms * 0.00000019635 m^2) / 75 m
ρ = 0.0000019635 m^2 * ohms / 75 m
ρ = 0.00000002618 ohm * m

Step 3: Final Result
Therefore, the resistivity of the aluminium wire is approximately 0.00000002618 ohm * m.

Explanation:
- The resistivity of a material is a measure of its inherent resistance to the flow of electric current.
- In the given problem, the radius and length of the wire are provided, along with the resistance.
- To calculate the resistivity, we use the formula R = (ρ * L) / A, which relates resistance, resistivity, length, and cross-sectional area.
- The first step is to calculate the cross-sectional area of the wire using the formula A = π * r^2, where r is the radius of the wire.
- Once the cross-sectional area is known, we can rearrange the resistance formula to solve for resistivity: ρ = (R * A) / L.
- Plugging in the given values into the formulas, we calculate the resistivity to be approximately 0.00000002618 ohm * m.
- The resistivity value tells us how strongly the aluminium wire resists the flow of electric current.