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Generally speaking resistance is not a function of frequency but specific resistor can be considered as frequency dependent impedance. All depends on parasitics.
If I'm not mistaken, when 'skin effect' happens, the frequency of the current/signal is usually very high. Is there any formula to relate 'resistance to frequency' at high frequency?
Look up "skin depth" in a first year physics or engineering book. The depth and thus resistance is related to the square root of frequency, conductivity, permittivity, and permeability of the wire material.
This skin effect is why cross country mains cables have aluminum on the outside and steel on the inside (for strength).
Real Resistance (reciprocal of conductivity) in itself is not frequency depedent directly. 5ohm is 5ohm , is this the fact we use to make matching broadband. A resistive load or generator looking both ways makes circuit broadband in frequency, hence frequency indipedent.
If you would have talked for temperature (what would happen to temperature in differenct frequencies? to indirectly affect?) I would agree, resistance is temperature depedent.
What is fully frequency depedent is impedance composed by resitance + susceptance... etc.
Hi.
Resistance is not frequency dependent.
Reactance and impedance is.
Reactance is the equivalent to resistance for alternating current.
If a resistor has some reactive effect, will exhibit some dependency.
Capacitive reactance Zc = 1 ÷ 2¶fC where f is frequency. Thus, there is the frequency dependance.
Miguel
When an AC transmission through cable is considered resistance is frequency dependent by virtue of skin effect....When a DC tranmission is considered like HVDC transmission resistance is not frequency dependent as you can find the spectrumof a dc signal just contains an impulse at omega=0.
Look up "skin depth" in a first year physics or engineering book. The depth and thus resistance is related to the square root of frequency, conductivity, permittivity, and permeability of the wire material.
This skin effect is why cross country mains cables have aluminum on the outside and steel on the inside (for strength).
wat i was taught is, as the EM waves at that high frequencies are allowed thro the cable, the impedance at the centre of the cable will be increased to the extent possible and least at the edges... i dont exactly remember the reason i was told for this behaviour.. and since the impdeance is minimum at the edges, it will flow across the boundaries. here, in the explanation everything comes with impedance and no term involves resistance...
but we write the formula for the skin depth as r = 1/2*pi * f * c. where f and c are frequency and capacitances respectively.. so as the frequency increases, the impedance increases at the centrre and decreases at the edges.. which implies the resistance decreases at the edges... (because of the relation of impedance and resistance.. its just an addition)... so, as frequency increases, the resistance of the cable becomes distributed in a more exponential fashion with maximum at the centre and minimum at the boundaries.... this is actually the variation of the resistance of the cable as a function of frequency. in this context, resistance is a function of frequency. and this is to be justified everywhere too... hope i am right. incase there are some discrepencies, let me know that i would rectify my errors....
If we speak in terms of circuits theory, the resistance R (as abstract notion) is not the function of frequency. But if we are speaking about physical world it is.
Effective AC resistance in a conductor is a function of frequency.
The current density (J) in the conductor decreases exponentially with depth δ, as follows: J=e^(-δ/d) where d is a constant called the skin depth which is where the current at a depth d is 1/e times the current at the surface.
d is found from: d=sqrt(2ρ/ωμ) where
ρ = resistivity of conductor and ω = angular frequency of current = 2*pi*f
and μ = absolute magnetic permeability of conductor
As an example, for long, thin conductors, the resistance is approximately that of a hollow tube with wall thickness d carrying direct current. For example, for a round wire, the resistance is approximately:
R=(ρ/d)(L/pi(D-d)))
where L = length of conductor and D = diameter of conductor
a further approximation R=(ρ/d)(L/pi(D))
if D >> d.
In summary R is inversely proportional to d which is inversely proportional to the square root of ω. Therefore as ω goes up, d goes down, and R goes up.
You Did't Clarify You Question? .
Not Resistane But Cap ,Inducatnce and Many Lumped Elements are frequency
Dependent .
But if You are Using Resistane in Frequency In Ranges Less than 450 Mhz
you Can Neglect this effect.
The Skin effect is the Problem if you Use Resistance in High Frequency the
flow of charges in the Cable force each other (F=qE+VxB) and they Go
to outer Parts of Cable (Skin Effect ) So in the Resistance Simple equ
we have R=ρL/A --> which ρ is Coeff that depends on Material (Copper ,Iron...)
L is the Lenght of Material used to be a resistance you can sense this in Potentiometer and A is the Area (you Can see this by two same Parallel resistors).
So , when the charges in the cable force each outher to go to the Outer Areas
the charges see Less Area to go so Resistance will increase (A is Becoming Smaller) this effect is Like Inductance in high freq.
But the Main Question remains here:
It is only Inductive effect ?
No, Let's Remind that Simple Cap is 2 Plates which has A Area and d Distance
and Capacitance Impedance Equ is XC=1/Cω which ω is frequency (ω=2*pi*freq).
So , in High frequency Cap acts like Short Circuit.
But If You twist two wire to each other they acts like Cap.
Ok, if You use Ressitors in you Board in StandUp position the two Part of its wire
LooksLike Cap (This Effect will Happens in Very High frequency ) So,thats why
we should Use (SMT Surface Mount Technology) for High Frequency Devices.
As mentioned in the previous post the resistance is not a function of frequency in the sense that inductance and capacitance are. resistance is always related to the opposition to the flow of electrons in the conductor material. And in high frequencies the current flowing inside the conductor encounters self inductance which opposes the flow and as the number of flux lines/unit area near the centre are more the opposition is more at the core. As the curent flow takes the path of least resistance it shifts itself to the outer radii of the conductor where it encounters least resistance to flow. Hence the actual area utilized for the current flow is reduced due to this skin effect and hence we observe a corresponding increase in resistance.
Alot of comments on this topic. Every component in electronics is having a frequency depending performance. If the frequency increases the resistor which is labled 100 Ohm will slowly change, from inductive into capacitive.
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