Why can one assume in “infinite grid of resistors” that in the center there are diagonal nodes that have $-1$ and $+1$ currents?

Why can one assume in "infinite grid of resistors" that in the center there are diagonal nodes that have $-1$ and $+1$ currents?

As in the matrix $P$ in the following picture:

• Were you asked to find the equivalent resistance between those particular nodes? – The Photon Feb 3 '18 at 16:51
• @ThePhoton, further down the line, yes of course. – mavavilj Feb 4 '18 at 7:45

1 Answer

In comments you said you were asked to find the equivalent resistance between these nodes.

Imagine you had a physical resistor network and were asked to measure the equivalent resistance between two nodes of that network. One way to do that would be to apply a test current in one of those nodes and out the other, and measure the voltage developed between the nodes.

What your book is showing is mathematically modeling what would happen if that test were done on the infinite network of resistors.

• This doesn't answer the question. – mavavilj Feb 3 '18 at 18:12
• You asked why you can assume a current going in one node and out the other. My answer says you can assume a current going in one node and out the other because you could test the network by applying such a current. – The Photon Feb 3 '18 at 18:13
• So you say that it doesn't matter which two nodes we measure, for the resistance that is? – mavavilj Feb 3 '18 at 18:15
• It should be the two nodes you were asked to find the equivalent resistance between. – The Photon Feb 3 '18 at 18:41
• why are they -1 and +1 then? – mavavilj Feb 3 '18 at 18:47