# A physically unrealizable problem

**Electricity and Magnetism**Level 4

*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.