total resistance in parallel circuits

Yes Jamie, It can be confusing. If you can use your algebra ( a must in this field) you may better understand the concept if you consider only two resistances in parallel.

With manipulation you will arrive at the - product over sum - formula. R1 x R2/(R1 + R2) You can do two resistors (resistances), come to a conclusion, use the result to combine the other one in the pair.

Then you will appreciate the - one over, one over formula. Yes they are conductance's. As for you coincidence: is 2+2 the same as 2 squared? Is 4+4 the same as 4 squared?

Review the algebra. Best Regards, Tom

I think so. At least you seem to be getting that an ohm is just another way of saying 1 volt per ampere. Another way to look at the parallel resistance formula is that you convert the resistances to conductances (amperes per volt, as you have figured out, but now you have a word that names that ratio). Then, after adding the conductances together to get a total conductance you convert that conductance back to a resistance by taking the inverse (flipping the amperes in the numerator with the volts in the denominator to get back to volts per ampere.

Exactly. Conductance (a bit different than conductivity, which is a property of a bulk material) is the name for the ratio of amperes per volt.

Not wrong, just sticking to the more fundamental units.

It is the definition of conductance.

Incorrect: the ones do not represent any units, so the only thing you'll get out is what you put in - in this case, ohms. The intermediate step of reciprocal resistance in ohms (which is conductance in mhos) follows from the nature of the circuit.

Aside from the confusion on units ...

Correct.

What you are imagining is equivalent to the mathematical technique of testing a "well-behaved" function at a convienient value like x = 1 and extrapolating or proving other values based on this.

Given nice ohmic devices, the exact same behavior applies, as a matter of fact, so it is true you can test and prove it in this way.

Only as I mentioned above. Gotta watch units in equations. :)

Nope, it's by definition in fact :)

Tim

-- Deep Fryer: a very philosophical monk. Website:

That's not a bad way to interpret what's going on. But, to make the units work out properly, we could multiply the expression by 1V/1V (since that equals 1 and multiplying by 1 is allowed), then manipulate things like this:

1 1V R(tot) = ---------------- x ---- 1 1 1 1V -- + -- + -- R1 R2 R3 1V The Moon is Waxing Crescent (7% of Full)

Hmmmm. Years ago I had DOS version of that program. Is there something available for Windows these days?

Think of it as the sum of conductances. It's simple then.

Graham

I saw this derived from the sum of conductances:

G(tot) = G1 + G2 + G3

Since conductance is the reciprocal of resistance,

G(tot) = 1 / R(tot) G1 = 1 / R1 etc

so

1 / R(tot) = (1 / R1) + (1 / R2) + (1 / R3)

Multiply through by R(tot)

1 = R(tot) * ((1 / R1) + (1 / R2) + (1 / R3))

Divide through by ((1 / R1) + (1 / R2) + (1 / R3))

1 / ((1 / R1) + (1 / R2) + (1 / R3)) = R(tot)

QED. (I've always wanted to be able to say that! :-) )

Cheers! Rich

....

you are measuring conductance if you put 1 volt across a resistor and measure the current it passes.

I would say that both interpretations are equivalent.

Bye. Jasen

it looks like the output from "pom" the bsd "phase of moon" program

The Moon is Waxing Crescent (23% of Full)

C source is available from ftp://ftp.netbsd.org/pub/NetBSD/NetBSD-current/tar_files/src/games.tar.gz

winzip (etc) should be able to open that file, and pretty much any C compiler should be able to produce a working executable from the source. some of the other "games" in the package may not compile for windows as easily.

Bye. Jasen

Today is Sweetmorn, the 62nd day of Bureaucracy in the YOLD 3171