__Resistance and Resistivity__

__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

**T****oleranc****e **is indicated as follows: