Calculate the resistance of a piece of copper wire that is 1m long and has a diameter of 1mm. Take resistivity of copper as 1,68×10-⁸ ohm metre.
To calculate the resistance of the copper wire, we can use the formula:
Resistance (R) = resistivity (ρ) * length (L) / cross-sectional area (A)
First, we need to calculate the cross-sectional area of the copper wire using its diameter:
Radius (r) = diameter / 2 = 1 mm / 2 = 0.5 mm = 0.5 × 10^-3 m
Area (A) = π * r^2 = π * (0.5 × 10^-3 m)^2
Now, we can substitute the values into the formula to calculate the resistance:
R = (1.68 × 10^-8 ohm·m) * (1 m) / (π * (0.5 × 10^-3 m)^2)
R = (1.68 × 10^-8 ohm·m) * (1 m) / (3.14159 * (0.5 × 10^-3 m)^2)
R = (1.68 × 10^-8 ohm·m) * (1 m) / (3.14159 * (0.25 × 10^-6 m^2))
R = (1.68 × 10^-8 ohm·m) * (1 m) / (7.854 × 10^-7 m^2)
R ≈ 2.138 ohms
Therefore, the resistance of the copper wire is approximately 2.138 ohms.