# Factors affecting the resistance of a wire at constant temperature

Factors affecting the resistance of a wire at constant temperature

When resistors are being made, short lengths of thick wire are used for the low resistances and long lengths of thin wire for the high resistances. Besides length and thickness the material of which the wire is composed is another important factor to be considered when deciding the length and gauge of wire for a particular resistance. Suppose, for instance, that the length of a given wire is doubled. This doubles the resistance, since twice the length of wire is equivalent to two equal resistances in series. If the length of wire is increased five times the resistance likewise becomes five times its previous value, and so on. The resistance of a wire is therefore proportional to its length, l, or in symbols, 1 Roc- A . (1)

With regard to the thickness or area of cross-section of the wire, thick wires may be regarded as equivalent to a number of thinner wires of equal area joined in parallel. Doubling the area will therefore halve the resistance and so on. In other words, the resistance of a wire is inversely proportional to its area of cross-section, A, or Roc- A . (2)