Resistance
The effective resistance due to a current confined near the surface of a large conductor (much thicker than δ) can be solved as if the current flowed uniformly through a layer of thickness δ based on the DC resistivity of that material. We can therefore assume a cross-sectional area approximately equal to δ times the conductor's circumference. Thus a long cylindrical conductor such as a wire, having a diameter D large compared to δ, has a resistance approximately that of a hollow tube with wall thickness δ carrying direct current. Using a material of resistivity we then find the AC resistance of a wire of length L to be:
The final approximation above assumes .
A convenient formula (attributed to F.E. Terman) for the diameter DW of a wire of circular cross-section whose resistance will increase by 10% at frequency f is:
The increase in AC resistance described above is accurate only for an isolated wire. For a wire close to other wires, e.g. in a cable or a coil, the ac resistance is also affected by proximity effect, which often causes a much more severe increase in ac resistance.
Read more about this topic: Skin Effect
Famous quotes containing the word resistance:
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—Edgar Allan Poe (1809–1849)
“The aim of every political association is the preservation of the natural and imprescriptible rights of man. These rights are liberty, property, security and resistance to oppression.”
—French National Assembly. Declaration of the Rights of Man (drafted and discussed August 1789, published September 1791)
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—Sun Tzu (6–5th century B.C.)