The graphical methods of Sumpner, Drysdale and Marchant: solving the Kelvin equation

Abstract

The paper commences with the equation derived in 1853 by Kelvin, for circuits containing inductance, resistance and capacitance. From this, the history of a graphical analysis is traced from Sumpner in 1888, to Drysdale who in 1910 published details of his planimeter, a manual device to solve LR and CR circuits. Little was added to the method, until Marchant extended it, in 1960, to cover all three circuit parameters, L, R and C, by one graphical solution. The methods are useful in explaining circuit operation and examples of use are given.