Thread: Resistors
View Single Post
Old 2021-01-13, 10:10   #1
LaurV
Romulan Interpreter
 
LaurV's Avatar
 
Jun 2011
Thailand

33·347 Posts
Default Resistors

How many ways you can connect a maximum of N resistors, assuming:
a) all resistors are equal ?
b) all resistors are different, and given ?
c) all resistors are different and you can chose such as:
c1) you have the smallest possible number of resulting values ?
c2) you have the largest possible number of resulting values ?

This number grows faster than sequences found in oeis which start with the same or similar numbers (1, 2, 5, 18, ...). I can come with the calculus for any particular N, but a general formula eludes me. The c2 case is the most interesting.

Example, zero resistors you can connect in only one way, and have infinite resistance. One resistor you can connect in two ways and have either R, or infinite. Two resistors you can connect either in series or in parallel, which makes 5 ways totally, with resistance: either infinite, R1, R2, R1*R2/(R1+R2), or R1+R2. If they are equal, you only get 4 ways: infinite, R/2, R, 2R. When N gets larger, the possibilities get ugly very fast.

Last fiddled with by LaurV on 2021-01-13 at 10:10
LaurV is offline   Reply With Quote