Page:A Treatise on Electricity and Magnetism - Volume 1.djvu/436

394 On the Comparison of Resistances.

345.] If $$E$$ is the electromotive force of a battery, and $$R$$ the resistance of the battery and its connexions, including the galvanometer used in measuring the current, and if the strength of the current is $$I$$ when the battery connexions are closed, and $$I_1,\, I_2$$ when additional resistances $$r_1,\, r_2$$ are introduced into the circuit, then, by Ohm's Law,

Eliminating $$E,$$ the electromotive force of the battery, and $$R$$ the resistance of the battery and its connexions, we get Ohm's formula This method requires a measurement of the ratios of $$I,\, I_1$$ and $$I_2,$$ and this implies a galvanometer graduated for absolute measurements.

If the resistances $$r_1$$ and $$r_2$$ are equal, then $$I_1$$ and $$I_2$$ are equal, and we can test the equality of currents by a galvanometer which is not capable of determining their ratios.

But this is rather to be taken as an example of a faulty method than as a practical method of determining resistance. The electromotive force $$E$$ cannot be maintained rigorously constant, and the internal resistance of the battery is also exceedingly variable, so that any methods in which these are assumed to be even for a short time constant are not to be depended on.

346.] The comparison of resistances can be made with extreme accuracy by either of two methods, in which the result is in dependent of variations of $$R$$ and $$E$$.