Infinite Radial Resistors

Electricity and Magnetism Level 2

In the image, the black lines are connecting wires and coloured lines are resistors of \(1\ \Omega\) each. The first circle contains 8 resistors, the second one contains 16, the third one contains 32, and so on. There are infinitely many circles of resistors.

A cell is connected between the centre and the outermost circle. The equivalent resistance (in \(\Omega\)) between the terminals of the cell is \(k\). What is \(100k\)?

Assume that the wires (black lines) have negligible resistance.

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