Note.—The standard resistance will have to be arranged to suit each particular case to make the calculations even approximately correct. (See [Exp. 129], Note.) The standard resistance may be increased by adding the various coils and rheostat wires, their values being known.
349. Summary of Laws of Resistance. 1. The resistance of a wire is directly proportional to its length, provided its cross-section, material, etc., are uniform.
EXAMPLE. If 39.1 ft. of No. 24 copper wire has a resistance of 1 ohm, 78.2 ft. will have a resistance of 2 ohms, because 78.2 is twice 39.1; 70.38 ft. will have a resistance of 1.8 ohms, as (70.38 ÷ 39.1 = 1.8) it is 1.8 times 39.1.
2. The resistance of a wire is inversely proportional to its area of cross-section. The areas of cross-section of round wires vary as the squares of their diameters; so the resistance of a wire is also inversely proportional to the square of its diameter, other things being equal.
EXAMPLE. A No. 30 wire has a diameter of about .01 inch, while the diameter of a No. 24 wire is about .02 in.; that is, the No. 24 has twice the diam. that the No. 30 has. The area of cross-section of the No. 24, however, is four times that of the No. 30, so its resistance is but ¼ that of the No. 30, the lengths, etc., being the same. (See [Wire Tables].)
3. The resistance of a wire depends upon its material, as well as upon its length, size, etc.
4. The resistance of a wire depends upon its temperature. (See Elementary Electrical Examples.)