⇒ How is the intrinsic 'resistance' of different materials compared? How do ou decide which material would be best for the internal connections of a mains plug, or for using as an insulator on a high-voltage line?

• The resistance of a metal wire, for example, depends on the length and area of the wire, as well as the material that the wire is made from

⇒ Consider the following, which shows a metal conductor:

⇒ The resistance of the conductor, R, increases with increasing length, l (there are more positive ion cores in the way of the gas of electrons moving through the conductor)

• In fact, if the length doubles, then the resistance doubles - this means that R is proportional to l

⇒ The resistance of the conductor decreases with increasing cros-sectional area (there are more conducting pathways through the conductor for the electrons to move through)

• In this case, if the cross-sectional area doubles, then the resistance halves - this means that resistivity is proportional to 1/cross-sectional area

⇒ Combining both of these proprtionality statements together:

⇒ Where ρ ('rho') is called the electrical resistivity of the material

⇒ Resistivity is the property that gives the intrinsic resistance of the material independent of its physical dimensions, such as length and cross-sectional area

⇒ Resistivity has the units of ohm metres, Ωm, and is defined by the rearranged form of the equation:

• Where R is the resistance (measured in ohms, Ω), A is the cross-sectional area (measured in metres squared, m²) and l is the length (measured in metres, m)

⇒ The resistivity of a material depends on some intrinsic properties of the material

• In particular, it relates directly to the number of free, conducting electrons that can flow through the structure and the mobility of these electrons to flow through the structure
• The arrangement of the atoms in the conductor and any distribution of impunities affects this mobility, as does the temperature of the material

⇒ At room temperature (20 degrees centigrade), good insulating materials, such as ABS plastic (the material that most mains plugs are now made from), have extremely high resistivity (ABS have an electrical resistivity of 1 x 10¹⁵ &ohms; at 20 degrees)

⇒ Good metallic conductors have very low resistivity

• The resistivity of copper, for example, is 1.68 x 10^-8 Ωm at 20 degrees centigrade
• Superconductor have zero resistivity below their critical temperature

⇒ We can use a water analogy to help understand resistivity

• A hose pipe full of sand is like a high resistivity conductor, as water trickles through slowly when pressure is applied
• However, that same pressure pushes water quickly through an empty hose pipe, which is like a low resistivity conductor
• Remember, though, that the ability of the water to pass through the hosepipe also depends on the length of the hosepipe and its cross-sectional area

⇒ Resistivity is also dependent on temperature

• The resistivity of metals increases with increasing temperature, and the resistivity of many semi-conductors, such as silicon and germanium, decreases with increasing temperature
• The resistivity of a superconductor drops to zero below its critical temperature

⇒ Also see our notes on:

• Moving Charge and Electric Current
• Potential Difference and Electromotive Force
• Resistance
• Current/Potential Difference characteristics and Ohm's Law
• Thermistors