How to calculate copper conductor AC and DC Resistance?

Copper is a widely used conductor in electrical engineering due to its high electrical conductivity and relatively low cost. The resistance of copper conductors is affected by various factors, including the dimensions of the conductor, the temperature, and the frequency of the current.

The DC resistance of a copper conductor can be calculated using the formula:

R = ρ * l / A

where R is the resistance, ρ is the resistivity of copper, l is the length of the conductor, and A is the cross-sectional area of the conductor. The resistivity of copper is a temperature-dependent property, and its value at 20°C is about 1.68 x 10^-8 Ωm. The resistance will increase as the temperature increases.

The AC resistance of a copper conductor, also known as impedance, is a complex quantity that is affected by the frequency of the current. The AC resistance is given by the formula:

Z = R + jX

where Z is the AC resistance, R is the DC resistance, X is the reactance, and j is the imaginary unit (j^2 = -1). Reactance is the opposition to the current due to the inductive or capacitive nature of the circuit.

The AC resistance of a copper conductor can be broken down into two components: the resistance component (R) and the reactance component (X). The resistance component is equal to the DC resistance of the conductor and is determined by the resistivity of the copper and the dimensions of the conductor. The reactance component is determined by the frequency of the current and the skin effect. The skin effect is the phenomenon that causes the AC current to flow mostly on the surface of the conductor, reducing the effective cross-sectional area of the conductor and increasing the reactance. The skin depth is given by the formula:

δ = (2 / π) * √(ρ / μ_0 * f)

where δ is the skin depth, ρ is the resistivity of copper, μ_0 is the permeability of free space and f is the frequency of the current.

In summary, the resistance of a copper conductor is affected by various factors, including dimensions, temperature and frequency of the current. The DC resistance of a copper conductor can be calculated using the formula R = ρ * l / A and the AC resistance of a copper conductor is a complex quantity given by Z = R + jX and is affected by the frequency of the current and skin effect.

Example Calculation for AC Resistance:

For a frequency of 60 Hz,
K
is typically around 1.02 to 1.05 for copper:

Rac=0.0548×1.05
≈
0.0575Ω

This simplified approach provides a practical estimation of AC resistance without involving complex calculations of skin depth.