# Electrical Conductivity and Its Derivation

The first person experimented with electrical conductivity is Stephen Gray. He is an English dyer & astronomer. He was born in England in December 1666 and died in London on 7th February 1736. Benjamin Franklin, Alessandro Volta, Georg Simon Ohm, Andre Marine Ampere, Joseph John Thomson are other scientists who observed the electrical conductivity process by using different types of metals in their experiments. In earlier day’s people used coal to produce electricity in industries, homes, ships, engines, iron boxes, etc. This article discusses an overview of electrical conductivity.

## What is Electrical Conductivity?

Electrical conductivity is defined as one type of conductivity that has an ability of substance or materials to conduct electricity over a defined area; we can also call it as conductivity or Electrolyte conductivity or conductivity or EC. The symbol of the electrical conductivity is represented by sigma (σ).

When ions are present in the solution then only the substances transmit electricity. Ions are defined as a particle that carries positive (+) or negative (-) charges in the solution. It is measured by the EC meter. Conductivity Unit: SI unit of conductivity is Siemen’s per meter (s/m), which is invented by Werner Von Siemens and Johann Georg Halske.

### Overview of Electrical Conductivity

Electrical Conductivity is the process that conducts electricity using different metals. The devices which are electrical converts electrical energy into other energies. Electrical devices consume more power for conduction of current and it works on only high voltage. Some of the electrical devices are water heaters, televisions, microwave oven, hairdryers, grinders, vacuum cleaners, fans, fridge, etc.

Present we are getting electricity using different types of metals like silver, aluminum, gold, water, brass, tin, lead, mercury, graphite, copper, steel, iron, seawater, lemon juice, concrete, etc are the good conductors that conduct electricity. Some of the bad conductors are Glass, paper, wood, honey, plastic, rubber, air, Sulphur, gases, oils, diamonds, etc which don’t conduct electricity.

Materials are of two types they are metals and non – metals. Metals are good conductors that conduct electricity and non – metals are bad conductors that don’t conduct electricity.

### EC Meter

EC meter is used to measure the electrical conductivity of water to check the purity of water. It consists of a 24 kHz square wave generator, platinum probe sensor, I–V converter, rectifier, filter, IoT module, Atmega 328 microcontroller, and temperature sensor. The block diagram of EC meter is shown below:

**Square Wave Generator:**The square wave generator generates only digital signals in a square waveform because the amplitude levels are finite.**Platinum Probe Sensor:**The output of the square wave generator is given as input to the sensor probe, which is made up of platinum. It is a device, which is used to detect changes in the environment.**I – V Converter:**It is used to produce a voltage (v) which is proportional to the given current (i).**Rectifier:**Rectifier is an electrical device that converts ac (alternating current) to dc (direct current).**Filter:**It is a device that is used to remove impurities in liquids or gases.**IoT Module:**It is a small electronic device embedded in machines and things. It is used to send and receive data through a wireless network.**Atmega328 Microcontroller:**It is an IC (Integrated Circuit) embedded in electronic devices and its size is very small.**Temperature Sensor:**It is one type of sensor which is used to detect or sense the temperature in the environment and electronic devices.

### Electrical Conductivity of Water

The electrical conductivity of water passes the current when we add salt, sugar or any other solvents which dissolve in water can break into ions. Ions are two types they are positively charged ions and negatively charged ions. Chemicals or solvents which dissolve into ions are also known as electrolytes. Water ability is increased by ions to conduct electricity. The conductivity of water is high when more ions are present and the Conductivity of water is low when fewer ions are present.

**Examples**

To test the conductivity of water dissolved in water, we need a battery(9v), distilled water, beaker, wire, sugar, baking soda.

**Example 1:** Connect the wires to the battery properly and take 50 ml of distilled water in a beaker and insert the wires of the battery into the beaker, no gas bubbles are formed in the beaker because distilled water doesn’t conduct electricity.

**Example 2:** Similarly Connect the wires to the battery properly and take 50 ml of tap water in a beaker and insert the wires of the battery into the beaker, no gas bubbles are formed in the beaker because tap water also doesn’t conduct electricity.

**Example 3:** Similarly Connect the wires to the battery properly and take 50 ml of distilled water in a beaker and add some baking soda and rinse it well, insert the wires of the battery into the beaker, gas bubbles will form in beaker because soda is a good conductor which conducts electricity.

### Derivation of Conductivity

As we know that the Ohm’s law i.e, current (I) is equal to the ratio of voltage (V) and resistance (R). It is expressed as

I=V/R ——–eq(1)

Where ‘I’ is Current

‘V’ is Voltage

‘R’ is Resistance

Resistance is defined as a product of resistivity and length by cross-sectional area. The resistance equation is expressed as

R=ρ*L/A ——–eq (2)

Where ‘R’ is Resistance

From eq (2), the resistivity is expressed as

ρ = R*A/L ——–eq (3)

Where ‘ρ’ Resistivity

‘L’ is Length

An area of the cross-section

Conductivity is defined as a reciprocal of resistivity and that is expressed as

σ = 1/ρ ———eq(4)

Substituting eq (3) in eq (4) will get

σ = 1/R*A/L

Conductivity (σ) = L /R*A ——–eq(5)

Electrical Conductivity (σ) = L /R*A is derived

We know that force is equal to

F = Ee ———eq(6)

F = ma ———eq(7)

Where ‘F’ is Force

‘m’ is mass

‘a’ is an acceleration

equating eq (6) and (7) will get acceleration

Ee = ma

a = Ee/m ———eq(8)

Drift velocity is expressed as

V = aτ ———-eq(9)

Substituting eq (8) in eq (9)

V = Ee/m*τ ———eq(10)

Total charge is expressed as

dq = env Adt

dq/dt = envA

where dq/dt is equal to I, expressed as

I = envA

I/A = env

Where I/A = J

Current density (J) = env ——–eq(11)

Substitute eq (10) in eq(11)

J = en * Ee/m * τ

J = ne2τ/m * E

Where conductivity(σ) = ne2τ/m ——–eq(12)

J = σ*E ——–eq(13)

As we know that conductivity is reciprocal of resistivity i.e σ = 1/ρ

Substitute σ = 1/ρ in eq (12)

J = E/ρ ———eq(14)

Where relaxation time is given as

Relaxation time (τ) = λ√m/3K_{B}Teq (15)

Substitute eq (15) in eq (12) we get the conductivity equation as

Conductivity (σ) = ne^{2}λ/√m*3K_{B}*T

The electrical conductivity equation is derived.

### Applications

Some important applications in industries are

- Water treatment
- Leak detection
- Clean in place
- Interface detection
- Desalination

### Advantages

The advantages of this conductivity include the following.

- Fast
- Reliability
- Repeatability
- Non-destructive
- Durable
- Inexpensive etc

Electrical conductivity is one of the good technology which we are using in our daily life. As we know that, in earlier days people used match sticks, coal, etc for heat purposes but now the technology is developed. Every electrical device is made up of conductors in small sizes. Here is the question for you which conductor is using in mobile phones?