Find the effective resistance (resistance between(adsbygoogle = window.adsbygoogle || []).push({}); aandb) of an infinitely long ladder of resistors, as shown in the figure, each having resistanceR.

http://people.tamu.edu/~malindenmoyer/fig.jpg [Broken]

The point is that the input resistance which we do not yet know--call itR--will not be changed by adding a new set of resistors to the front end of the chain to make it one unit longer. But now, adding this section, we see that this new input resistance is justRin series with the parallel combination of_{1}Rand_{2}R. We get immediately an equation that can be solved forR.

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# Effective Resistance of an Infinitely Long Ladder of Resistors

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