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:
“Even the most subjected person has moments of rage and resentment so intense that they respond, they act against. There is an inner uprising that leads to rebellion, however short- lived. It may be only momentary but it takes place. That space within oneself where resistance is possible remains.”
—bell hooks (b. c. 1955)
“Hence to fight and conquer in all your battles is not supreme excellence; supreme excellence consists in breaking the enemys resistance without fighting.”
—Sun Tzu (65th century B.C.)
“The greatest, or rather the most prominent, part of this city was constructed with the design to offer the deadest resistance to leaden and iron missiles that might be cast against it. But it is a remarkable meteorological and psychological fact, that it is rarely known to rain lead with much violence, except on places so constructed.”
—Henry David Thoreau (18171862)