Sensitivity of a galvanometer as a function of its resistance
Howard Brooks · Bureau of Standards Journal of Research · 1930
Maxwell derived a theorem which states that for the maximum deflection of a galvanometer connected to a given external circuit containing a given electro- motive force the ratio of galvanometer resistance to external resistance should be equal to the ratio of the diameter of the wire in the galvanometer coil (before insulation) to the diameter including the insulation.Ayrton and Perry later stated that the galvanometer resistance should be equal to the external resistance.This widely quoted statement differs from Maxwell's because Maxwell assumed an unchanging thickness of insulation, Ayrton and Perry a thickness varying directly as the diameter of the bare wire.The present paper demonstrates that while both statements are correct for their respective assumptions, the sensitivity function in each case is very flat in the vicinity of the maximum; that aside from considerations of damping the user has a wide range of choice of galvanometer resistance with relatively small loss of sensitivity, and can in fact sometimes obtain much better sensitivity with moving-coil galvanometers (when critical damping is considered) by departing from the theoretical optimum value of resistance.A general curve of the sensi- tivity function for the Ayrton-Perry assumption is given with a similar curve for a particular case for the Maxwell assumption.The performance of four lines of commercial galvanometers is shown by plotted points.The constructional limitations and those related to damping which must be considered in applying the conclusions of the paper are outlined, and the practical advantages of the facts brought out, to both maker and user, are briefly sum- marized.