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 = Ï Ã (L/A), where R is the resistance, Ï 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 (Ï). 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: Râ = Ï Ã (Lâ/Aâ), where Râ is the resistance of the 20m length wire, Ï is the resistivity of the material, Lâ is the length of the 20m wire, and Aâ is the cross-sectional area of the 1.5mm wire. Substituting the given values, we get: 2.5 = Ï Ã (20/((Ï Ã (1.5/2)^2)). Solving for Ï, we find that Ï = 0.05 ohm·m.
Now, we can use Ï and the given values of the 35m length wire to calculate its resistance (Râ). Substituting the values into the formula, we have: Râ = Ï Ã (35/((Ï Ã (3/2)^2))). Solving for Râ, we find that the resistance of the 35m length wire is approximately 7.4 ohms.