Resistance: Definition & Difference Explained

In summary: Reactance is the opposition to current flow. It is measured in ohms and is usually expressed as a ratio of voltage to current.
  • #36
David Lewis said:
The definition for resistance must specify by what mechanism current is impeded (or V/I ratio is affected) in order to distinguish it from reactance.
No, it doesn't. A component with reactance simply has a non constant resistance. There is no need to specify the mechanism.
 
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  • #37
I find it rather amusing that after 2 pages of discussion on this, not once did I see anyone suggesting that the origin of "resistance" or "resistivity" in a material arises out of the concept the Drude model, which is really the microscopic derivation of Ohm's Law. In it, the origin of the presence of "resistance" for an ideal conductor is clearly laid out.

Maybe this is not considered since the level of knowledge appears to be in First-year physics. But considering all that has transpired here, and how things are going around in circles as people tried to figure out what caused what, maybe it is necessary to go to a more fundamental level.

Zz.
 
  • #38
ZapperZ, Would it be fair to say then resistance arises when electrical energy is converted to heat or radiation?
 
  • #39
David Lewis said:
ZapperZ, Would it be fair to say then resistance arises when electrical energy is converted to heat or radiation?

You are mixing the cause and effect. The presence of resistance LEADS to heat (i.e. Ohmic heating), not the other way around, i.e. the conversion of electrical energy into heat leads to resistance.

At the simplest level, resistance is the collision between electrons and (i) other electrons (ii) lattice ions (iii) impurities.

Zz.
 
  • #40
Dale said:
No, it doesn't. A component with reactance simply has a non constant resistance. There is no need to specify the mechanism.
You mean the resistance (R) of a coil which has reactance as well (XL) is not constant? It varies in time? Or you mean some other type of "non-constant"?
Maybe you are trying to simplify thing more they can be. :)
 
  • #41
nasu said:
You mean the resistance (R) of a coil which has reactance as well (XL) is not constant? It varies in time? Or you mean some other type of "non-constant"?
It is not constant wrt time and wrt frequency.
 
  • #42
How does the resistance changes in time?
Or even the reactance component?
 
  • #43
You agree that if one divides the instantaneous voltage drop across the coil by the instantaneous current across the coil, the quotient is not fixed, right?
 
  • #44
Sure. But the the resistance of the coil is not defined as that ratio. Neither the inductive reactance of the coil.
They are both constants, for a given coil and frequency. Saying that resistance is not constant implies a different definition of resistance and may create confussion rather than clarifying the subject.

I think that Introducing reactance in the discussion about resistance is not useful anyway.
 
  • #45
nasu said:
Sure. But the the resistance of the coil is not defined as that ratio.
Then that is the disagreement at hand.
 
  • #46
nasu said:
Sure. But the the resistance of the coil is not defined as that ratio.
Yes, it is. By definition R=V/I. That ratio is the definition of resistance, and it is not constant wrt time for an inductor as jbriggs444 showed above.

If you disagree with that definition, then can you please provide a reference that defines it differently? There may very well be alternative definitions, as happens often.

nasu said:
I think that Introducing reactance in the discussion about resistance is not useful anyway.
I agree. It should not have been introduced.
 
  • #47
Well, you say "by definition". Do you have a reference for that?
I am not just trying to bounce back the question to you. But it is not so easy to find a definition for the resistance for the general case.

Maybe could just specify what will you call the quantity labeled by R in many RLC circuits, and which is given as 4 Ohms, for example.
Do you call this resistance or something else?

Of course, for an inductive coil, the resistance is not a separate component and it may be the question what u do you consider in u/i.
If you take the overall u, over the coil, what you get depends on bot R and L and frequency. The voltage across the resistive part of the coil's impedance cannot be measured directly, I suppose. But we can model the coil as an RL circuit where R is what you measure in a DC (constant current) regime.
 
  • #48
nasu said:
Well, you say "by definition". Do you have a reference for that?
I am not just trying to bounce back the question to you. But it is not so easy to find a definition for the resistance for the general case.
The definition is easy to find. ##R=V/I##. It is not always useful, but it is clearly defined.

Wikipedia uses that definition as does my old introductory physics text (Serway, Physics for Scientists and Engineers, P 759, 3ed, 1990). A lot of texts introduce Ohm's law without explicitly defining resistance.
 
  • #49
I was talking a bout a general definition, one that can be applied to AC circuits, including the resistance of an inductive coil.
What is the meaning of these symbols (V,I) for circuits with non-constant voltage and current?
In my books capital letters are usually used for either constant values (DC circuits) or RMS values (AC circuits). In both cases their ratio is constant in time.
 
  • #50
nasu said:
I was talking a bout a general definition, one that can be applied to AC circuits, including the resistance of an inductive coil.
The definition certainly can be applied to AC circuits and inductive coils.

When you apply the definition for certain elements or circuits the result is not constant. So what? Why should the result of all definitions be preordained to be constant?
 
  • #51
By what definition is not constant? R=V/I gives a constant for both AC and DC circuits, as V and I are constants even for AC circuits. (with notations used in Serway in the chapter about AC circuits).

You did not say what would you call the R quantity in an RLC (or just RL) circuit. As used in the Serway text which you mentioned, for example. Is that dependent of time?
 
  • #52
The definition of resistance, more precisely than R = V/I is R = dV(I)/dI. As the others have pointed out, resistance is really the instantaneous slope (derivative) of the V vs. I curve. The resistance is not constant for materials that are not ohmic. It varies with current...meaning the V vs. I curve is not a straight line. It is not even constant for resistors. It's just an approximation we use. Resistors have increased resistance at higher currents because the temperature increases as current increases.

There can be negative differential resistance as well with some devices.
 
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  • #53
Also, make sure to be clear with terminology. Resistance is generally frequency independent but impedance is frequency dependent. For inductors the magnitude of the impedance increases as frequency increases whereas for capacitors the magnitude of the impedance decreases as frequency increases.

Also, resistance is purely a real number, whereas impedance is a complex number, consisting of both a resistance (real) and a reactance (imaginary). Resistors are generally only resistive (real) and inductors/capacitors are generally only reactive (imaginary). When you combine resistors with inductors or capacitors then you get a combination of real and imaginary components of impedance. But to say a capacitor or inductor exhibits a resistance (other than parasitic effects) is incorrect, I'd say.
 
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  • #54
nasu said:
Well, you say "by definition". Do you have a reference for that?
I am not just trying to bounce back the question to you. But it is not so easy to find a definition for the resistance for the general case.

The relationship between voltage and current for a circuit may be extremely complicated. To me, it is only useful to talk about "resistance" in the case where the voltage is (approximately) linearly proportional to the current.

We can define an ideal resistor to be a linear circuit element such that the voltage drop across the element is proportional to the current through the element. If a circuit element is a resistor, then we can define the resistance to be [itex]R = V/I[/itex].

We can define an ideal capacitor to be a linear circuit element such that the voltage drop across the element is proportional to the charge on the element (the charge being the time integral of the current flowing into the element). If a circuit element is a capacitor, then we can define the capacitance to be [itex]C = Q/V[/itex].

We can define an ideal inductor to be a linear circuit element such that the voltage drop across the element is proportional to the time derivative of the current. If an element is an inductor, then we can define the inductance by: [itex]L = V/\frac{dI}{dt}[/itex].

For non-ideal circuit elements (which means any actual circuit element), we can often approximately describe them as a combination of ideal elements, where [itex]R[/itex], [itex]C[/itex] and [itex]L[/itex] may be nonconstant. But this is only a heuristic description---there is nothing fundamental about it. There is no absolute answer to the question: "What is the resistance of this actual, nonideal, circuit element?" You can model the circuit element as a combination of time-dependent, or current-dependent, or frequency-dependent resisters, inductors or capacitors, but I don't think that the question "What is the element's resistance?" makes any sense outside of the particular way you've chosen to model it.
 
  • #55
nasu said:
By what definition is not constant? R=V/I gives a constant for both AC and DC circuits, as V and I are constants even for AC circuit
Please provide a reference for this claim as well as for any alternative definition of resistance that you would like to use.
 
  • #56
leright said:
The definition of resistance, more precisely than R = V/I is R = dV(I)/dI. As the others have pointed out, resistance is really the instantaneous slope (derivative) of the V vs. I curve. The resistance is not constant for materials that are not ohmic. It varies with current...meaning the V vs. I curve is not a straight line.
That is another suitable definition for resistance. A circuit textbook of mine did not explicitly define resistance in the text, but when it introduced Ohm's law it drew a picture of the V/I curve for a resistor with a little graphic indicating that the slope was R. I actually prefer that definition since it is easier to apply to things like voltage and current sources.

The Wikipedia article calls it "differential resistance" to distinguish it from "chordal resistance". I am not sure where that terminology came from so I am not sure I trust it.
 
  • #57
R=V/I is a perfectly good definition for resistance, with two caveats:

1. Since reactance also equals V/I, the definition only applies when electrical energy is converted to heat or radiation.

2. V/I defines resistance in the particular sense (how much you have, or would have, in particular cases). Whenever a physical quantity is defined in the particular sense, it's conveyed as a formula, with physical quantities represented by algebraic variables.

In the general sense, resistance is the property of a circuit or circuit element that opposes current in the process of converting electrical energy to heat or electromagnetic radiation. Whenever a physical quantity is defined in the general sense (what it is) it's expressed rhetorically, i.e. numbers are not put to it.
 
  • #58
stevendaryl said:
The relationship between voltage and current for a circuit may be extremely complicated. To me, it is only useful to talk about "resistance" in the case where the voltage is (approximately) linearly proportional to the current.

Not unless you use the more general definition of resistance, R = dV/dI, which reduces to R = V/I for devices with linear V vs. I characteristics.
 
<h2>What is resistance?</h2><p>Resistance is the measure of how difficult it is for electricity to flow through a material. It is represented by the symbol "R" and is measured in ohms (Ω).</p><h2>What factors affect resistance?</h2><p>Resistance is affected by the type of material, its length, its cross-sectional area, and its temperature. Materials with high resistance include rubber, glass, and plastic, while materials with low resistance include copper, aluminum, and gold.</p><h2>What is the difference between resistance and resistivity?</h2><p>Resistance is a measure of how difficult it is for electricity to flow through a specific object, while resistivity is a measure of a material's inherent resistance to the flow of electricity. Resistivity is a property of the material itself, while resistance is dependent on the material's dimensions and temperature.</p><h2>How does resistance affect electrical circuits?</h2><p>Resistance affects the flow of electricity in a circuit. In series circuits, resistance reduces the amount of current flowing through the circuit, while in parallel circuits, resistance affects the distribution of current among the branches.</p><h2>What are some real-life examples of resistance?</h2><p>Some common examples of resistance in everyday life include the resistance of a light bulb filament, the resistance of a wire in an electrical appliance, and the resistance of a heating element in a stove. Resistance is also used in electronic devices such as resistors and potentiometers to control the flow of electricity.</p>

What is resistance?

Resistance is the measure of how difficult it is for electricity to flow through a material. It is represented by the symbol "R" and is measured in ohms (Ω).

What factors affect resistance?

Resistance is affected by the type of material, its length, its cross-sectional area, and its temperature. Materials with high resistance include rubber, glass, and plastic, while materials with low resistance include copper, aluminum, and gold.

What is the difference between resistance and resistivity?

Resistance is a measure of how difficult it is for electricity to flow through a specific object, while resistivity is a measure of a material's inherent resistance to the flow of electricity. Resistivity is a property of the material itself, while resistance is dependent on the material's dimensions and temperature.

How does resistance affect electrical circuits?

Resistance affects the flow of electricity in a circuit. In series circuits, resistance reduces the amount of current flowing through the circuit, while in parallel circuits, resistance affects the distribution of current among the branches.

What are some real-life examples of resistance?

Some common examples of resistance in everyday life include the resistance of a light bulb filament, the resistance of a wire in an electrical appliance, and the resistance of a heating element in a stove. Resistance is also used in electronic devices such as resistors and potentiometers to control the flow of electricity.

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