What is the AC and DC resistance of a conductor in simple terms?

In electrical engineering, the resistance of a conductor is a measure of its opposition to the flow of an electric current. The resistance is measured in units of ohms (Ω) and is given by the formula:

R = V / I

where R is the resistance, V is the voltage across the conductor, and I is the current flowing through the conductor.

or

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

R = ρ * l / A

where R is the resistance, ρ is the resistivity, l is the length of the conductor, and A is the cross-sectional area of the conductor.


There are two types of resistance that are commonly discussed in electrical engineering: AC resistance and DC resistance.

AC resistance, also known as impedance, is the resistance to the flow of alternating current (AC). The AC resistance is a complex quantity, which is the vector sum of resistance and reactance. The AC resistance is given by the formula:

Z = ( R ^2+ jX^2 )^0,5

jX = X_L- X_C

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. Inductive reactance is given by the formula:

X_L = 2πfL

where X_L is the inductive reactance, f is the frequency of the current, and L is the inductance of the circuit. Capacitive reactance is given by the formula:

X_C = 1 / (2πfC)

where X_C is the capacitive reactance, f is the frequency of the current, and C is the capacitance of the circuit.

For copper ,

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.

DC resistance is not affected by the frequency of the current and is usually measured in ohms. It is a scalar quantity and is independent of the phase of the current.

In summary, AC resistance, also known as impedance, is the resistance to the flow of alternating current and is a complex quantity that is affected by frequency, material, and dimensions of the conductor. DC resistance is the resistance to the flow of direct current and is measured in ohms. It is not affected by frequency and is a scalar quantity.

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