A physically unrealizable problem

Electricity and Magnetism Level 4

Let us define a hexaresistor (depicted below)

as a hexagonal resistive network which can be described as below:

with all the resistors having a value of R.

Then, let us define a second order hexaresistor (depicted below)

as a network which can be described as a hexagonal resistive network of hexaresistors as shown below:

If we construct an identical hexagonal resistive network of second order hexaresistors, we will be able to create a third order hexaresistor , and so on, such that an n-order hexaresistor, depicted below

is a network of


If R= 1000 ohms, determine the resistance from points A to B, where B extends to infinity.

Note: This is physically unrealizable, but theoretically, a particular value is approached.


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