How Do You Calculate the Equivalent Resistance in an Infinite Resistor Network?

[Saitama]

Homework Statement

Calculate the equivalent resistance of the resistor chain shown in the figure between the points a) A and B; b) A and C the resistor chain is infinite in both directions and each resistor has a resistance of R.

Homework Equations

The Attempt at a Solution

I have solved the b) part. It is the part a) which I face trouble with. How do I approach this?

Any help is appreciated. Thanks!

 

[ehild]

You have the equivalent resistance of both the chain to the left from A and the one to the right from B. Replace the chains with their equivalent resistances in the figure.

ehild

 

[voko]

I would add point D just below B and consider the sub-chains to the left of AC and to the right of BD (with the resistor between A and C or B and C). These sub-chains should have equal resistances. Then the entire ABDC loop can be represented as four resistors.

 

[voko]

By the way, if you solved part (b) in some other way, you can obtain the equivalent resistance of each sub-chain from that result, and then solve part (a).

 

[Saitama]

You have the equivalent resistance of both the chain to the left from A and the one to the right from B. Replace the chains with their equivalent resistances in the figure.

ehild

I would add point D just below B and consider the sub-chains to the left of AC and to the right of BD (with the resistor between A and C or B and C). These sub-chains should have equal resistances. Then the entire ABDC loop can be represented as four resistors.

Thanks ehild and voko! That did the trick. :)

I solved the part b) with the same method but couldn't observe that you could do the same with a).