Resistance: Definition & Difference Explained

[nasu]

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?

 

[leright]

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.

 

[leright]

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.

 

[stevendaryl]

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 R = V/I.

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 C = Q/V.

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: L = V/\frac{dI}{dt}.

For non-ideal circuit elements (which means any actual circuit element), we can often approximately describe them as a combination of ideal elements, where R, C and L 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.

 

[Dale]

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.

 

[Dale]

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.

 

[David Lewis]

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.

 

[leright]

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.