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:
“The resistance we make to our passions is due to their weakness, not our strength.”
—François, Duc De La Rochefoucauld (1613–1680)
“High treason, when it is resistance to tyranny here below, has its origin in, and is first committed by, the power that makes and forever re-creates man.”
—Henry David Thoreau (1817–1862)
“The free man is a warrior.—How is freedom measured among individuals, among peoples? According to the resistance that must be overcome, according to the trouble it takes to stay on top. The highest type of free man must be sought where the highest resistance is constantly overcome: five steps away from tyranny, close to the threshold of the danger of servitude.”
—Friedrich Nietzsche (1844–1900)