An intuitive understanding of conductance

Hi,

I don’t like understanding things “by formulas”. I am totally understanding, from an intuitive perspective, ohm’s law. What I am struggling with is the intuitive understanding of conductance.

Conductance is seen as 1/R. It’s me mathematical “reciprocal”. But… what happens when you actually see them?

Here:

http://fooplot.com/#W3sidHlwZSI6MCwiZXEiOiJ4IiwiY29sb3IiOiIjMDAwMDAwIn0seyJ0eXBlIjowLCJlcSI6IjEveCIsImNvbG9yIjoiIzAwMDAwMCJ9LHsidHlwZSI6MTAwMCwid2luZG93IjpbIi0xMi42OTUzMTI0OTk5OTk5OTEiLCIxMi42OTUzMTI0OTk5OTk5OTEiLCItNy44MTI0OTk5OTk5OTk5OTQiLCI3LjgxMjQ5OTk5OTk5OTk5NCJdfV0-

(also, see attached image)l

While it’s true, “the lower the resistance, the bigger the conductance”, while resistance is linear (y=x), conductance is not: you can see how the conductance curve is in fact anything but linear.

How do you see this in an “intuitive” way? From an intuitive point of view, conductance would be linear just like resistance – that is, intuitively speaking, as resistance goes up, conductance would go down proportionally.

So, what’s the intuitive way of explaining the “curve”?

Merc.

conructance.png

You just have to realise that many parameters used in maths, electronics etc are 'constructs'. Many parameters are used to make calculations more convenient, or more efficient. Or some calculations or formulas look more compact and neat when particular parameters are used. It just depends on situation.

Also.... your comment about 'linear'. Linear is a definition. If one variable has a linear relationship with the other, then it is like y = k.x

The relation applies to parameters 'y' and 'x'. If you apply a nonlinear operation like g = 1/x, then parameter 'y' isn't going to have a linear relationship with 'g'.... because a nonlinear operation was carried out.

Now, even though G is 1/R ..... some calculations can be convenient when working with G. And, in the end, as long as you know the link between G and R, then what you do to something (ie. take inverse or reciprocals etc), you can often undo. So if you end up getting some value of 'G', you can usually get the counterpart value of it... ie. 1/G = R.

When thinking about conductance, resistance is the reciprocal, and thus non-linear,
just like when thinking about resistance conductance is reciprocal and non-linear.

You might find it easier to think about heat conduction, where its much more normal to
think in the conductance way. Heat conductance is measured in W/K, though you do sometimes
use thermal resistance, K/W, in particular with heatsinks. When thinking about heat loss from
a building you naturally think about conductance though.

Back to electronics when putting resistors in parallel you can just sum the conductances
to get the conductance of the combined parallel circuit, which is the converse of adding
resistances in a series circuit.

If V = IR is your nice, linear voltage vs current relationship, than I = VC is an equally valid and still linear relationship involving the conductance instead of the resistance. Your problem trying to understand the Resistance vs Conductance graph is that they have a purely mathematical relationship, rather than a physical one.

The symbol for conductance is G, not C. C is the coulomb!

I = VG

[ yes G is also the gravitational constant, but its deemed not to be so common in the world of electronics as the unit of electric charge! ]

From an intuitive point of view conductance is just resistance stood on its head.

It doesn't look any different from the physical point of view, it is just a different way of writing down its value.

mercmobily:
Conductance is seen as 1/R. It's me mathematical "reciprocal". But... what happens when you actually see them?

If you can literally see resistance and conductance you're a better man than I.

While it's true, "the lower the resistance, the bigger the conductance", while resistance is linear (y=x), conductance is not: you can see how the conductance curve is in fact anything but linear.

What nonsense are you on about? Conductance is perfectly linear. G + G = 2G after all, just like R + R = 2R.

Using your graph, I could just as easily say that resistance is nonlinear by plotting G against 1/R. Now conductance is straight and resistance is curved. That's not what the graph actually says though, because you are misinterpreting it quite badly.

The resistance curve means nothing. Any quantity plotted against itself is going to result in a straight, unity-slope line (y=x). The resistance of a substance plotted as a function of its resistance is a tautological function that has literally no value. The only functions that have any meaning are when one value is plotted against a different value to show the relationship between them.

So plot R on the x axis and G on the y axis, and you get that 1/x function.

Now plot G on the x axis and R on the y axis. Anything change? How is one any more or less linear than the other?

How do you see this in an "intuitive" way? From an intuitive point of view, conductance would be linear just like resistance -- that is, intuitively speaking, as resistance goes up, conductance would go down proportionally.

Conductance does go down proportionally. If resistance is doubled, conductance is halved. Conversely, twice as much conductance works out to half as much resistance.

Do you have the same trouble with period and frequency? They have a reciprocal relationship too. The unit for period is seconds per cycle, and the unit for frequency is cycles per second. t=1/f, and f=1/t.

Similarly, ohms can be expressed as a derived unit of volts per amp, and conductance is amps per volt.

MarkT:
The symbol for conductance is G, not C. C is the coulomb!

I = VG

[ yes G is also the gravitational constant, but its deemed not to be so common in the world of electronics as the unit of electric charge! ]

Actually, the symbol for charge is Q, just like I is for current. C is the unit abbreviation for coloumb, like A is the abbreviation for ampere.

C is the symbol for capacitance.