# Resistance Variation

### Resistance and Resistivity

The resistance of an electrical conductor depends on four factors, these being:

(a) the length of the conductor, (b) the cross-sectional area of the conductor,

(c) the type of material and (d) the temperature of the material.

Resistance, R, is directly proportional to length, l, of a conductor, i.e. R / l. Thus, for example, if the length of a piece of wire is doubled, then the resistance is doubled.

Resistance, R, is inversely proportional to cross-sectional area, a, of a conductor, i.e. . Thus, for example, if the cross-sectional area of a piece of wire is doubled then the resistance is halved.

Since R / l and then . By inserting a constant of proportionality into this relationship the type of material used may be taken into account.

The constant of proportionality is known as the resistivity of the material and is given the symbol p (Greek rho).

#### Temperature Coefficient of Resistance

In general, as the temperature of a material increases, most conductors increase in resistance, insulators decrease in resistance, whilst the resistance of some special alloys remain almost constant.

If the resistance of a material at room temperature (approximately 20°C), R20, and the temperature coefficient of resistance at 20°C, ˛20, are known, then the resistance Rˇ at temperature ˇ°C is given by:

For example, a coil of copper wire has a resistance of 10 Q at 20°C. If the temperature coefficient of resistance of copper at 20°C is 0.004/° C the resistance of the coil when the temperature rises to 100° C is given by:

If the resistance at 0°C is not known, but is known at some other temperature ˇ1, then the resistance at any temperature can be found as follows:

For example, some copper wire has a resistance of 200 Q at 20°C. A current is passed through the wire and the temperature rises to 90° C. The resistance of the wire at 90°C, assuming that the temperature coefficient of resistance is 0.004/° C at 0°C, is given by:

Resistor Colour Coding and Ohmic Values

##### (a) Colour code for fixed resistors

The colour code for fixed resistors is given in Table 41.1

(i) For a four-band fixed resistor (i.e. resistance values with two significant figures):

yellow-violet-orange-red indicates 47 kQ with a tolerance of š2% (Note that the first band is the one nearest the end of the resistor)

(ii) For a five-band fixed resistor (i.e. resistance values with three significant figures):

red-yellow-white-orange-brown indicates 249 kQ with a tolerance of š1%

(Note that the fifth band is 1.5 to 2 times wider than the other bands)

##### (b) Letter and digit code for resistors

Another way of indicating the value of resistors is the letter and digit code shown in Table 41.2

Tolerance is indicated as follows: