Absolute Measurement of Electrical Resistance

Electrical resistance is measured in terms of its proper unit defined by the equation

For let a conductor be such that unit difference of potential between its two ends produces unit current; then in the above equation E and C are both unity; so that R is also unity and the conductor in question has unit resistance.

DEFINITION OF AN ABSOLUTE UNIT RESISTANCE. - The unit of resistance is the resistance of a conductor in which unit electromotive force produces unit current.

This is a definition of the absolute unit. Now it is found⁽¹⁾ that on the C.G.S. system of units the unit of resistance thus defined is far too small to be convenient. Therefore, just as was the case for E.M.F., a practical unit of resistance is adopted, and this contains 10⁹ absolute C.G.S. units, and is called an 'ohm'; so that 1 ohm contains 10⁹ absolute units.

We have already seen that the volt or practical unit of E.M.F. is given by the equation

1 volt = 10⁸ absolute units.

Let us suppose that we have a resistance of 1 ohm and that an E.M.F. of 1 volt is maintained between its ends; then we have for the current in absolute units

Thus an ampere, the practical unit of current, is that produced by a volt when working through an ohm.

But electrical resistance is, as we have seen, a property of material conductors. We can, therefore, construct a coil, of German-silver or copper wire suppose, which shall have a resistance of 1 ohm. The first attempt to do this was made by the Electrical Standards Committee of the British Association, and the standards constructed by them are now at the Cavendish Laboratory at Cambridge.

More recent experiments have shown, however, that these standards have a resistance somewhat less than i ohm. They have for some time past been in use as ohms and numbers of copies have been made and circulated among electricians. The resistances of these standards are now known as British Association Units.

An international congress of electricians, assembled at Paris during the present year (1884), has defined the ohm in terms of the resistance of a certain column of mercury. According to their definition, an ohm is equal to the resistance of a column of mercury 106 centimetres in length, and one square millimetre in section, at a temperature of 0° C. This standard is known as the Legal Ohm. To obtain the relation between the legal ohm and the B.A. unit, the resistance of this column of mercury in B.A. units is required. The value of this quantity has been determined by various experimenters,⁽²⁾ and for the purpose of issuing practical standards the B.A. Committee have decided to take 0.9540 B.A. unit as representing the resistance at 0°C of a column of mercury 100 centimetres in length, one square millimetre in section.

It follows from this that

and

so that to reduce to legal ohms a resistance given in B.A. units, we have to multiply its value by 0.9889.

Most of the resistance coils now in existence in England which are marked as ohms, or multiples of an ohm, are in reality B.A. units, or multiples of a B.A. unit.

(1)	See F. Jenkin, Electricity and Magnetism, chap, x.; Maxwell, Electricity and Magnetism, vol. ii. §629.
(2)	See a paper by Lord Rayleigh and Mrs. Sidgwick, Phil. Trans.9 1883.