# Z-parameters. Is Z12*Z21 always greater or equal zero if a circuit has only resistors? [duplicate]

Since my last question was probably badly formed and misunderstood this is a new one.

I was trying to find a lower bound solution for an equivalent resistance of an infinite resistor network. In order to do that I connected some nodes and found the equivalent resistance.

How can we mathematically prove that equivalent resistance between any 2 nodes is always lower if we connect any other 2 nodes in a network with a resistor.

Note that this is not example of a parallel circuit, this is example of a 2 port network where we connect a load on one port and measure resistance on another.

tl;dr: 2 port network. Prove that connecting a load will reduce input resistance. In terms of z-parameters we need a prof that $Z_{12} \cdot Z_{21} > 0$.

• Why do you post two same questions? I think you should go and clarify the original question instead of creating a new one. Dec 14, 2012 at 0:02
• I think that I already made the damage so the question is cluttered with non related answers and many edits and it is now hard to follow. I would rather like to delete my old question. Everyone has my sincere apologizes for posting the question again. Dec 14, 2012 at 0:21
• I've closed this question as duplicate, you should consider editing the old question and then accepting the answer that fits the most. Then we may clean it from irrelevant answers, if needed. Dec 14, 2012 at 10:08