Electrical Conductivity/Resistivity
The idea of Electrical Conductivity and Resistivity permeates throughout modern life, from our cell phones, to the internet. All things that rely on electricity, relies on the concepts of Electrical Conductivity and Resistivity.
Definition
Electrical Resistivity is a measure of how a given material opposes current flow. Low resistivity shows a material that allows the flow of current, whereas the opposite is true for high resistivity. Electrical Conductivity is the reciprocal/inverse of Electrical Resistivity, in that it measures the ability of a given material to conduct electric current
Symbols
Electrical Resistivity is mainly represented by the Greek lower-case rho. Electrical Conductivity is mainly represented by the Greek lower-case sigma, but is occasionally represented by a lower-case kappa, or gamma.
SI Units
Electrical Resistivity is measured in Ohm-Metres. Electrical Conductivity is measured in Siemens per Metre
Classification of Materials by Conductivity
Materials with high Conductivity are known as conductors. ex. metals Materials with low Conductivity are known as resistors. ex. vacuums, glass, etc.
Semiconductors
Semiconductors are materials that have a conductivity in-between that of an insulator and a conductor. However, as temperature increases, unlike in most metals, the conductivity of semiconductors increases.
Temperature Dependence
As temperature increases, the electrical resistivity of metals increases. This is a reason why when computers heat up, they tend to slow down. Some materials exhibit superconductivity at extremely low temperatures. Below a certain temperature, resistivity vanishes, such as Pb at 7.20 K.
Equations
Poulliet's Law
R=ρℓ/A
R = Electric Resistance
ρ = Electric Resistivity
ℓ = Length
A = Cross-Sectional Area
Poulliet's Law states that a given materials resistance will increase in length, while it will decrease with an increase in Area.
Conductivity in Real Life
Conductors are used to carry electricity, as well as electrical signals in circuits. Complementary metal–oxide–semiconductors, or CMOS for short, are the foundational building block of gate based logic circuits, that make up the majority of all modern electronics. CMOS circuits are composed of a combination of p-type and n-type semiconductors. These semiconductors will change their conductivity, based on the applied voltage, allowing for logic of 0's and 1's, or low voltage and high voltage, to be transferred through logical circuits. This allows us to apply boolean logic to circuits, such as AND and OR logic, or even create an amalgamation of AND's and OR's to create electronics, such as multiplexors, switches, latches, registers, decoders, encoders, etc.
History
The beginning of the study of electrical conductivity began at the same time that the study of electricity began, with Benjamin Franklin. In the late 18th century, Franklin studied lightning, and realized that lightning would travel along a rod, and created the lightning rod. Alessandro Volta derived electric potential and batteries from his study of static electricity. Once batteries were created, they were utilized in experiments into current. Georg Simon Ohm then found the exact ratio of current to potential difference, which is now our measurement of electrical conductivity