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# Poggendorff's Method for the Comparison of Electromotive Forces

The method given in §76 for the comparison of electromotive forces is subject to a defect similar to that mentioned in §77, on the measurement of resistance; that is, it depends upon measuring the deflexion of a galvanometer needle, and assumes that the E.M.F. of the batteries employed remain constant throughout the experiment.

The following method, first suggested by Poggendorff, resembles the Wheatstone-bridge method for measuring resistances, in being a null method; it depends, that is to say, on determining when no current passes through a galvanometer, not on measuring the deflexion. We have seen (p. 422) that if a current C be flowing through a conductor, the E.M.F. or difference of potential between any two points, separated by a resistance R, is CR.

Let AB (fig. 75) be a conductor of considerable resistance, through which a current is flowing from A to B; let P1 be a point on this conductor, E1 the difference of potential between A and P1. If A and P1 be connected by a second wire AG1P1, including a galvanometer G1 in its circuit, a current will flow from A to P1 through this wire also. Let a second battery be placed in this circuit in such a way as to tend to produce a current in the direction P1, G1, A1) the current actually flowing through the galvanometer G1 will depend on the difference between E1 and the E.M.F. of this battery. By varying the position of P1 along the wire AB, we can adjust matters so that no current flows through the galvanometer G1; when this is the case it is clear that the E.M.F. E1 of the battery is equal to the difference of potential between A and P1 produced by the first battery. Let the resistance AP1 be R1 and let R be the resistance of AB, and ρ that of the battery which is producing the current through AB, including, of course, any connecting wires, E being the E.M.F. of this battery. Then, if C be the current in AB, we have

or,

This equation gives us, if we know ρ, the ratio E1/E; for R and R1 can be observed.

This method will be satisfactory in practice if R is very great compared with ρ, for then an approximate value of ρ will be sufficient; or if R is sufficiently large, ρ may be entirely neglected, and we may write E1/E = R1/R.

This is Poggendorff's method of comparing the E.M.F. of two batteries. The following arrangement, suggested by Latimer-Clark, obviates the necessity for knowing ρ.

Last Update: 2011-03-19