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Home Electricity Poggendorff's Method for the Comparison of Electromotive Forces  
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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 Wheatstonebridge 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 P_{1} be a point on this conductor, E_{1} the difference of potential between A and P_{1}. If A and P_{1} be connected by a second wire AG_{1}P_{1}, including a galvanometer G_{1} in its circuit, a current will flow from A to P_{1} 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 P_{1}, G_{1}, A_{1}) the current actually flowing through the galvanometer G_{1} will depend on the difference between E_{1} and the E.M.F. of this battery. By varying the position of P_{1} along the wire AB, we can adjust matters so that no current flows through the galvanometer G_{1}; when this is the case it is clear that the E.M.F. E_{1} of the battery is equal to the difference of potential between A and P_{1} produced by the first battery. Let the resistance AP_{1} be R_{1} 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 E_{1}/E; for R and R_{1} 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 E_{1}/E = R_{1}/R. This is Poggendorff's method of comparing the E.M.F. of two batteries. The following arrangement, suggested by LatimerClark, obviates the necessity for knowing ρ.


Home Electricity Poggendorff's Method for the Comparison of Electromotive Forces 