KevinB
Posts: 525
Joined: April 2013
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| Quote (Quack @ Mar. 20 2014,09:29) | | Quote (KevinB @ Mar. 19 2014,13:17) | Is niwrad going to change his "handle" to "notwen", since his mathematics is just as backwards as his biology?
Neil Rickert has alluded to the use of complex numbers in electrical engineering, and noted that in impedance calculations both resistance and reactance are measured in ohms, and "work" together when combined as complex numbers. "Joe" has jumped in and pointed out that | Quote | | Resistance and IMPEDENCE are measured in ohms. |
which is true (when spelt right) but he has missed the salient point that all three quantities are measured in the same units.
What is deeper (and which has obviously escaped niwrad) is that the mapping of complex numbers onto the cartesian plane is a consequence of how complex numbers are defined, and that using complex numbers for impedance calculation is merely a convenient fiddle because the definition of complex arithmetic happens to right for the purpose.
I also note that niwrad has put "convection" instead of "convention" throughout a comment. Perhaps he's trying to boost circulation. :) |
I don't think impedance is synonymous with resistance. |
Blame Oliver Heaviside, who also came up with admittance, permittance and reluctance.
If you apply a sinusoidally-varying voltage (let's say, proportional to sin(wt)) the current flowing in the resistor is also proportional to sin(wt). If you do the same for a capacitor or an inductor is proportional to cos(wt) (I'm avoiding minus signs here.) Electrical engineers divide the peak voltage by the peak current and call the ratio reactance.
If you have a network containing resistors, capacitors and inductors, you can work out what the voltages and currents in the network are by treating the resistances and reactances as vectors perpendicular to each other, and combining them using the mathematics of vectors. The resultants are vectors which point in arbitrary directions on the plane (not necessarily the perpendiculars) and these quantities are "impedances".
Electrical engineers use complex numbers for these calculations because complex arithmetic is (sort of) the same as vector arithmetic.
niwrad is graphing two (potentially) independent variables on orthogonal axes - this is perfectly legitimate, and reveals possible dependence. What is not meaningful is trying to combine the vectors joining each of two points on the graph to the origin.
This is effectively what niwrad is doing when he describes his points on his graph as complex numbers rather than just as Cartesian co-ordinates. It is mathematical nonsense, and his whole discussion about Euler, etc, is merely bafflegab to obfuscate the point that his natural/artificial division is based on numbers plucked out of the air, (or possibly some part of his anatomy.)
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