Calculate the electrical resistance per metre length at 20°C of a copper conductor of a
10 mm? cross-sectional area.

To calculate the electrical resistance per metre length of a copper conductor at 20°C with a 10 mm² cross-sectional area, follow these steps:

1. Identify the resistivity of copper at 20°C: The resistivity (ρ) of copper at 20°C is approximately $1.68 \times 10^{-8} \, \Omega \cdot m$.

2. Use the formula for resistance: The resistance (R) of a conductor is given by the formula: $R = \frac{\rho \cdot L}{A}$ where:

   • $R$ is the resistance,
   • $\rho$ is the resistivity,
   • $L$ is the length of the conductor,
   • $A$ is the cross-sectional area.

3. Substitute the given values:

   • $\rho = 1.68 \times 10^{-8} \, \Omega \cdot m$,
   • $L = 1 \, m$ (since we are calculating per metre length),
   • $A = 10 \, mm^2 = 10 \times 10^{-6} \, m^2$ (converting mm² to m²).

4. Calculate the resistance: $R = \frac{1.68 \times 10^{-8} \, \Omega \cdot m \times 1 \, m}{10 \times 10^{-6} \, m^2}$

5. Simplify the expression: $R = \frac{1.68 \times 10^{-8}}{10 \times 10^{-6}}$

6. Perform the division: $R = \frac{1.68 \times 10^{-8}}{10^{-5}} = 1.68 \times 10^{-3} \, \Omega$

Therefore, the electrical resistance per metre length of the copper conductor at 20°C with a 10 mm² cross-sectional area is $1.68 \times 10^{-3} \, \Omega$ or 1.68 milliohms.