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

Question

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

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Solution

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 1.68×10−8 Ω⋅m1.68 \times 10^{-8} \, \Omega \cdot m.

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

    • RR is the resistance,
    • ρ\rho is the resistivity,
    • LL is the length of the conductor,
    • AA is the cross-sectional area.

  3. Substitute the given values:

    • ρ=1.68×10−8 Ω⋅m\rho = 1.68 \times 10^{-8} \, \Omega \cdot m,
    • L=1 mL = 1 \, m (since we are calculating per metre length),
    • A=10 mm2=10×10−6 m2A = 10 \, mm^2 = 10 \times 10^{-6} \, m^2 (converting mm² to m²).

  4. Calculate the resistance: R=1.68×10−8 Ω⋅m×1 m10×10−6 m2 R = \frac{1.68 \times 10^{-8} \, \Omega \cdot m \times 1 \, m}{10 \times 10^{-6} \, m^2}

  5. Simplify the expression: R=1.68×10−810×10−6 R = \frac{1.68 \times 10^{-8}}{10 \times 10^{-6}}

  6. Perform the division: R=1.68×10−810−5=1.68×10−3 Ω 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 1.68×10−3 Ω1.68 \times 10^{-3} \, \Omega or 1.68 milliohms.

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