# Resistors 5

Solution

The effective resistance between points $A$ and $B$ is $\frac{10}{7}\Omega$. To arrive at this result, the easiest method was to label the current passing through each resistor $I_1$ to $I_{18}$ and then create equations by considering each node. The equations are shown in the diagram below. Solution of these equations was then completed using Mathematica (largely because I'm lazy).

Equations A through K come from consideration of the nodes labelled in the diagram (foolishly I've not been consistent with my labelling in relation to the original problem, but hopefully its still easy enough to follow).

The latter equations come from considering the voltage around each of the small triangles (by applying Kirchoff's second law (the potential differences around any closed loop add to zero)).

The solution is over specified, we have 19 equations in 18 variables, so one equation can be legitimately ignored or used as a check of the final answer.