Resistance and Resistivity

The resistance of an electrical conductor depends on 4 factors, namely:

1. The length of the conductor
2. The cross-sectional area of the conductor
3. The type of material
4. The temperature of the material

The resistance, R, is directly proportional to length L of a conductor.

Resistance, R, is inversely proportional to cross-sectional area a, of a conductor.

Because R is proportional to L and, R is proportional to

By inserting a constant of proportionality into this relationship, we can take care of the material used. This constant of proportional is known as the resistivity of the material and represented by the symbol ρ.

Hence,

Therefore, ρ is measured in ohm meters (𝝮m). The value of the resistivity is the resistance of a unit cube of the material measured between opposite faces of the cube.

Resistivity varies with temperature. Good conductors of electricity have low value of resistivity and good insulators have a high value of resistivity.

The Temperature Coefficient of Resistance

Generally, as the temperature of a material increase, most conductors increase in resistance, insulators decrease in resistance, while the resistance of some special alloys remains almost constant.

The temperature coefficient of resistance can be defined as the increase in the resistance of a 1 𝝮 resistor of that material when it is subjected to a rise of temperature of 1 °C. The symbol for temperature coefficient is α. For example if say a copper wire of resistance 1 𝝮 is heated through 1 °C and its resistance is then measured as 1.0043 then α = 0.0043 𝝮/𝝮°C for copper. The units are normally expressed as per °C

So, α = 0.0043/°C

If the 1 𝝮 resistor of copper is heated through 10 °C then the resistance at 10 °C will be 1 + 10×0.0043 = 1.043 𝝮.

If the resistance of a material at 0 °C is known, then the resistance at any other temperature can be determined from:

R_ϴ = R₀(1 + α₀ϴ)

Where, R₀ = resistance at 0°C

R_ϴ = resistance at temperature ϴ °C

α₀ = temperature coefficient of resistance at 0°C

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