Resistors On A Dodecahedron
Electricity and Magnetism
Level
3
Each edge of a regular dodecahedron is a \(1 \Omega\) resistor. If the effective resistance between two adjacent vertices can be represented as \(\dfrac {a}{b} \Omega\) where \(a\) and \(b\) are co-prime positive integers, find \(a + b\).
A dodecahedron has 20 vertices and 30 edges with 3 edges meeting at each vertex.
Image credit: Wikipedia.
by
Akshat Sharda