Ok, so, this has been bothering me for a while now. I have recently become interested in amp circuits, and higher voltage pedal schematics (18v instead of 9v), and I noticed a lot of schematics use a low ohm resistor on the supply (as part of a supply filter and/or to prevent shorts from frying something), mostly 10R or 100R. For simplicity, I will use the 10R for an example. Let's say our circuit is 100R, with a 10R supply resistor, at 18v. Ok, so my thinking is that the power loss in the 10R is that which the whole circuit draws, which is (18/(100+10))*18=(18/110)=0.16363...*18=2.94534 watts. But then there is the (I^2)*R=P equation, which means that I would do this:

18/100=0.18

18/10=1.8

100*(0.18^2)=3.24 watts

10*(1.8^2)=32.4 watts

So that means that either the resistors drop 2.95ish watts total, which would be split to 1.475 watts each; or 32.4 and 3.24 watts separately, which averages to 17.82 watts, or 35.64 watts for the entire circuit.

2.95W or 35.64W for total draw?

Or could it be (bare with me. I'm still not all that steady calculating voltage dividers):

(10+100)/(10*100)=...

Scratch that equation...

100/(100+10)*V=.9090...*V=16.362 volts

The 100R drops 16.362 volts. That means that the 10R drops 18-16.362=1.638 volts. That then give us:

(1.638/10)*1.638=0.263044

(16.382/100)*16.382=2.68269924

So that gives us a total dissipation of about 2.95 watts, which makes more sense with the total resistance, but that doesn't answer the dissipation of the individual resistances. So to summarize:

2.95W10R+100R or

35.65W10R+100Ror

0.263W10R and 2.683W100R or

1.475W10R+100R or

32.4W10R and 3.24W100R or

17.82W10R+100R

So my question is, how do I know which equation(s) to use to find the total draw and the individual draw?

Man, and I thought doing trig identities was fun...