Calculating the Resistance of a Wire

Explanation:

To find the resistance of the 35m length wire that is 3mm in diameter, we can use the formula R = ρ × (L/A), where R is the resistance, ρ is the resistivity of the material, L is the length of the wire, and A is the cross-sectional area of the wire.

Since the 20m length wire with a diameter of 1.5mm has a resistance of 2.5 ohms, we can use this information to calculate the resistivity of the material (ρ). Given that the resistance is inversely proportional to the cross-sectional area (A) and directly proportional to the length (L), we can set up the following equation: R₁ = ρ × (L₁/A₁), where R₁ is the resistance of the 20m length wire, ρ is the resistivity of the material, L₁ is the length of the 20m wire, and A₁ is the cross-sectional area of the 1.5mm wire. Substituting the given values, we get: 2.5 = ρ × (20/((π × (1.5/2)^2)). Solving for ρ, we find that ρ = 0.05 ohm·m.

Now, we can use ρ and the given values of the 35m length wire to calculate its resistance (R₂). Substituting the values into the formula, we have: R₂ = ρ × (35/((π × (3/2)^2))). Solving for R₂, we find that the resistance of the 35m length wire is approximately 7.4 ohms.