# Traffic hold-ups Gustav Kirchhoff graduated from the University of Konigsberg in 1847 and married his professor’s daughter.  Many people are familiar with his name from studying electrical circuits at school.  His circuit law is an extension of the law of conservation of energy and governs how to combine the effect of multiple electrical resistors.  When resistors are connected in series, i.e. like barges towed by a tug one behind the other, then the value of the resistances can be added together to give a total resistance for the set of resistors.  So, three resistors of 2, 4 and 8 ohms connected in series provide a total resistance of 14 ohms.

However, when resistors are connected in parallel, i.e. like barges strapped alongside the tug, then the calculation of the combined resistance is a little more involved.  The inverse or reciprocal of each resistance must be added together and then the inverse taken of the sum.  So, three resistors of 2, 4 and 8 ohms connected in parallel provide a total resistance of 8/7 ohms [=1/(0.5+0.25+0.125)].

In a parallel circuit, the electrons have a choice about which resistance to flow through.  The same idea can be extend to the resistance to flow in water pipes and to traffic flow.  For traffic flow, the effect of road-works and other hold-ups on multiple routes can be modelled.