Conductivity

Claimed by Patrick Todd (Spring 2017)

Definition

Conductivity is the degree to which a specified material conducts electricity, calculated as the ratio of the current density in the material to the electric field that causes the flow of current. (It is the reciprocal of the resistivity.)

In other words, Conductivity is the measure of the ease at which an electric charge or heat can pass through a material. Electrical conductivity tells us how well a material will allow electricity to travel through it. Thermal conductivity tells us the ease upon which thermal energy (heat for most purposes) can move through a material.

Symbols

Electrical Conductivity is measured in siemens per meter and is often represented using the Greek letters σ (lowercase sigma), κ (kappa), or γ (lowercase gamma).

SI Units

Conductivity's SI units is the siemens per metre, [math]\displaystyle{ A^{2} s^{3} m^{−3} kg^{−1} }[/math](named after Werner von Siemens) or, more simply, [math]\displaystyle{ S m^{−1} }[/math].

Classification of Materials by Conductivity

Conductors, Semiconductors, and Insulators are the main three classifications of a material when talking about its electrical conductivity. Conductors are materials with high conductivity. Semiconductors have an in between level of conductivity, while insulators have low conductivity. Meaning if you want to pass a lot of electricity to something use a conductor, if you want to pass some electricity but also lower the original amount use a semiconductor, and if you want to cut the flow of electricity use an insulator. Provided below is a list of materials that fit into each category.

         Conductors: Gold, Iron, Silver, Copper, Aluminum, Tin
         Semiconductors: Silicon,  Germanium
         Insulators: Glass, Porcelain, Rubber, Cloth, Paper, Air

Semiconductors

Semiconductors are materials that have a conductivity in-between that of an insulator and a conductor. Their electrical resistance are much higher than ordinary conductors but still much lower than most insulators. Interestingly enough, their resistance decreases as their temperature increases, which is behavior opposite to that of a metal (insulator).

Temperature Dependence

Conductivity of a material is determined by two factors: the concentration of free carriers available to conduct current and their mobility (or freedom to move). In a semiconductor, both mobility and carrier concentration are temperature dependent. 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

Maxwell's Equation for Electric Conductivity

J=σE

          J= Electric Current Density
          E= Electric Field
          σ= Conductivity

Electric current density can be thought of as the electric current per cross sectional area of a specific material. Therefore this formula relates to each material differently. Every material has a specific conductivity associated with it, and this conductivity can help describe the electric field in each material. For example, materials such as copper and silver have extremely high electric conductivity and therefore in order to not have an almost infinite electric current density we can approximate the electric field inside the metals to be zero. This equation is essentially the proof for all metals having a zero electric field on the inside. The relationship between these three variables is known as Ohm's Law.

Poulliet's Law of Resistivity

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. The SI unit for this law is Ohm*meter.

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.

https://www.youtube.com/watch?v=ODbgKXFED5o

Mathematical Problems

Simple

Find the Conductivity of a material with an electrical field of [math]\displaystyle{ 5*10^{12} (E = 5*10^{12}) }[/math] and a current density of [math]\displaystyle{ 5*10^2 (J = 5*10^2) }[/math].

Answer
[math]\displaystyle{ =10^{10} }[/math]

Medium

Find the Resistivity of a wire with the resistance of [math]\displaystyle{ 0.69Ω*m (R=0.69Ω*m) }[/math], length of [math]\displaystyle{ 10m (ℓ=10m) }[/math], and cross-sectional area of [math]\displaystyle{ 100m^{2} (A=100m^{2}) }[/math].

Answer
690 = 10ρ
ρ = 69

History

Stephen Gray, Father of Conduction

Born 1666 in Canterbury, England. Died 1736 in London, England. Gray was an innovative thinker who performed many a experiment including work with the transmission of electricity. One day while performing one of his experiments, unbeknownst to him he discovered the difference between insulators and conductors. He was working with transmitting electricity and he changed the transmission wire from silk to brass wire when he noticed that electricity passes completely different in brass than it does in silk. After said discovery, Gray spend the next 3 years with the help of friends and family doing more research in similar topics, and with this research some might say solidified his name as the father of conduction.

Claude Pouillet, Pouillet's Law

Born February 16, 1720 in Cusance, France. Died June 14, 1868 in Paris, France. Claude was one of the earliest scientists to examine the Sun's influence on Earth's atmosphere, beyond simple radiation. After approximating the solar constant to be 1228 [math]\displaystyle{ W/m^{2} }[/math], which turned out to be extremely close to the now recognized constant of 1367 [math]\displaystyle{ W/m^{2} }[/math]. This success earned him a chair in the Physics department at the École Normale Supérieure. From there he went on to design and create early, operational versions of sine and tangent galvanometers which measure current (more commonly known as an ammeter).

Further reading

Georgia Tech Research and Information regarding conduction in School of Materials Science and Engineering http://www.mse.gatech.edu/research/equipment-facilities/electrical-properties-materials-and-devices

External links

Beginner Explanation

Thermal Conductivity

Brittany Spears explains semiconductors