J
John S
That seems a bit silly. You could easily choose to use only those
configurations that will handle close to maximum power and end up with
something a lot more useful and a heck of a lot easier to build.
eg. 1R = 3 x R||R||R (gets you 9x25W of dissipation)
Yes, it is silly for the moment. However, I am trying to simplify the
problem so as to come up with the answer for resistances before I look
at the power situation. Once I have a complete solution somewhere, I can
go back and do the power thing, I hope.
It is also incorrect. The parallel resistor can go to any node in the
chain of series resistors and different numbers of resistors already in
series can be placed in parallel. I couldn't convince myself that the
construction I suggested above would get every possible network but
according to Wolfram MathWorld my p(m) = 2^(m-1) is complete.
http://mathworld.wolfram.com/ResistorNetwork.html
(they do it for 1 ohm resistors)
Thanks to your link, I now see that the answer to my OP is 1023
different resistance values. Now, if I can figure out how to continue
your sequence above, I'll put it into a spreadsheet that will tell me
the resistance of the combinations.
Many thanks.