Ladder Circuit Paradox: Equivalent Resistance Analysis

[GPhab]

We find the equivalent resistance(let us denote it by R) of an infinitely long ladder circuit by considering that it is equal to the same resistance in combination with one segment of the circuit. But when we equate "R" to "R" combined with two segments, will we get the previous result for all possible ladder circuits(I got it for two models. Are these the only possible?)?

 

[psholtz]

It's hard to talk specifics w/o looking at a circuit diagram, but in general ladder networks are modeled as an (infinite) series of circuit elements, each consisting of (a) a resistor R1 in series and (B) a resistor R2 in parallel w/ the "existing" ladder.

Call the (effective) resistance of the "existing" ladder R.

Now add another "link" to the ladder.

This link will consist of R1 in series + (R2 in parallel w/ R).

Set this equal to R, the effective resistence of the ladder.

You can now solve for R in terms of R1 and R2.

 

[Shooting Star]

Hi GPhab,

Provide us with the diagram of at least one model.

 

[PhDorBust]

Good explanation... but what if there is an additional resistor connecting them directly. I understand the process but not the logic behind it; how would this addition change the resistance?