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Re: [Phys-l] Frequency dependence of resistance

Resistance is defined to be the component of the impedance that is due to the component of the current that is in phase with the potential difference. The definition of resistance does not imply that resistance is independent of frequency. At high frequencies, the skin effect increases the resistance of metal wires, for example.

Daniel Crowe
Loudoun County Public Schools
Academy of Science
dan.crowe@loudoun.k12.va.us

John Denker <jsd@av8n.com> 9/18/2008 11:16 AM >>>
On 09/18/2008 12:38 AM, Savinainen Antti wrote:

I was wondering how to explain qualitatively why the resistance of a resistor
stays constant (at least in the first approximation, that is in the HS physics
:-)) when frequency of current increases. The frequency dependence in the case
of reactance of coil or capacitor is quite easy to explain in terms of
self-induction (coil) and charging/discharging (capacitor). These results can
also be derived using simple calculus which is understandable by (good) HS
students.

One possible explanation might use the idea of storing energy: resistor just
dissipates energy to thermal energy which cannot be returned to the power
supply. Capacitor and coil can store energy in electric/magnetic fields and
then give it back to the power supply when the cycle proceeds. Can these
considerations lead to a plausible explanation why the resistance of a resistor
stays constant in an AC-circuit, no matter what frequency? Or is so that energy
has nothing to do with this?

It would also be interesting to hear to what extent resistance is actually
independent of frequency.

Answer #1) I assume the intent was to ask about the _impedance_ of a
resistor. If the impedance is observed to be frequency independent,
that's a nontrivial observation. In contrast, the "resistance" is by
definition the frequency-independent part of the impedance. So asking
about a frequency-independent "resistance" would be circular and
pointless.