Electrical Conductivity

Dhristi JEE 2022-24

What is Electrical Conductivity?

Electrical conductivity is just the reciprocal of electrical resistivity. It is also known as specific conductance that represents a material's ability to conduct electric current. Commonly, we signify electrical conductivity by the Greek letter σ (sigma). However, in the field of electrical engineering, we represent it by κ (kappa), and γ (gamma) is sometimes used. The SI unit of electrical conductivity is siemens per meter (S/m). Likewise, electrical resistance, we do have a formula of electrical conductivity and a specific method to determine its unit that we will understand on this page.

Here, we will also consider various electrical conductivity examples in day-to-day life.


The Formula of Electrical Conductivity

Let us assume an ideal case that a piece of resistive material has a uniform cross-section and physical composition. Further, the electric field and current density are both parallel and constant everywhere. However, various resistors and conductors do have a uniform cross-section with a uniform flow of electric current and are formed of a single material, so that this is a good model. So, in this case, the electrical resistivity (ρ) can be calculated by the following formula:

$R=\rho {\frac{1}{2}}.......(1)$

Here, 

R - electrical resistance of a uniform specimen of the material

- specific resistance or resistivity

l - length of the material

A - cross-sectional area of the material

We know that the electrical conductivity of a given material is just the reciprocal of the resistivity, so the formula for this statement is:

$\sigma ={\frac{1}{2}}$

Now, let us derive the unit of electrical conductivity.

Since the resistance of any material is directly proportional to the length and inverse to the area of cross-section.

So,                      

$\rho ={\frac{RA}{l}}$

Substituting their units:

$\rho =\frac{ohm,m^{2}}{m}=ohm.m$

The reverse of the resistivity is ohm-1m-1or mho/m. 

Since, ohm-1is written as S (Siemens), so the unit of electrical conductivity becomes Siemens/meter or S/m….(2)

Besides this, the dimensional formula of electrical conductance can be derived as:

We know that the dimensional formula for the resistance (Ohm) is [M1 L2 T-3 A-2], so the reverse, i.e., mho becomes [M-1 L-2 T-3 A2].

This mho is equivalent to S (Siemens) = [M-1 L-2 T3 A2]

And,

The dimensional formula of m is [L1]

So, substituting these formulas in our main formula in equation (2):

$\sigma=\frac{\text{seimens}}{\text{meter}}=\frac{M^{-1}L^{-2}T^{3}A^{2}}{L^1}$

On solving, the dimensional formula of electrical conductivity becomes:

[M-1 L-3 T3 A2]. Somewhere, you may find this formula as [M-1 L-3 T3 I2].


Another Formula of Electrical Conductivity

In an ideal case, the resistivity at a particular point is expressed as the ratio of the electric field to the density of the current it creates at that point:

$\rho= \frac{E}{J}$

Here,

⍴- The resistivity of a conducting material

E - the magnitude of the electric field

J - The magnitude of the current density

As the conductivity is the reverse of the resistivity of this material, so we have the following equation:                    

$\sigma= \frac{J}{E}$

The unit of the current density is ampere per metre square, and the dimensional formula is [A1 L-2].

The unit of E is kg⋅m⋅s−3⋅A−1. The dimensional formula is [M1 L1T−3A−1].

$\sigma =\frac{Am^-{2}}{kg.m.s^{-3}A^1}$ = Kg-1m-3s3A2 or mho. m  or S/m

On solving, the dimensional formula of σ will be again as follows:

$\sigma =\frac{A^1L^{-2}}{M^1L^1T^{-3}{A^{1}}}$ = [M-1 L-3 T3 A2]

From the above equation (1), R and describe how difficult it is for a current to flow through any material/substance. However, resistance is an extrinsic property, while resistivity is intrinsic. 

By this statement, we mean that all pure copper wires (that were not subjected to distortion of their crystalline structure), irrespective of their shape and size, have the same resistivity.

However, a long, thin copper wire has a much larger resistance than a thick, short copper wire. 

So, in the nutshell, every material has its own characteristic resistivity. For example, rubber has a far larger resistivity than copper, which is why the conductivity of copper is higher than that of rubber. 

Moreover, talking about metals and liquids, metals have more free electrons than liquids, which means metals have electrical conductivity than liquids.

Now, let us understand the science behind the electrical conductivity of metals and liquids.

Below is the data for the electrical conductivity of metals at 20 ℃:


Electrical Conductivity of Metals with Examples

Material

Electrical Conductivity (S/m) 

Silver

6.30 × 107

Copper

5.8 ×107

Calcium

2.82 × 107

Magnesium

2.15 × 107

Cobalt

1.60 ×107

Platinum

9.44 × 106

Factors affecting the electrical conductivity of earth materials is influenced by the following reasons:

  • Metal content (sulfides) in the rock, 

  • Porosity, 

  • Clay content, 

  • Permeability, and 

  • Degree of pore saturation.


Electrical Conductivity of Liquids with Examples

The electrical conductivity of liquids is a measure of water's capability to allow electrical flow. This ability directly links with the concentration of ions in the water. 

Moreover, compounds that dissolve into ions are known as electrolytes 40. Thus, the more ions present, the higher the conductivity of water.

Factors affecting the electrical conductivity of liquids are: 

  • The concentrations of ions, 

  • The type of ions, and 

  • The temperature of the solution.


Electrical Conductivity Examples

Metals and plasma are examples of materials with high electrical conductivity.


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One of the electrical conductors having the best electrical conductivity is silver.


Facts on Electrical Conductivity

  • Though electricity does not conduct through all liquids, like lemon juice, milk, vinegar, common salt solution, sulphuric acid solution, seawater, and rainwater can conduct electricity. While, sugar solution, distilled water, and honey cannot conduct electricity.

  • Drinking water has a conductivity from 200 to 800 µS/cm.

  • Electrical conductivity is a significant parameter to measure when undertaking environmental or process monitoring. This parameter is helpful in determining various changes, such as conductivity change can indicate pollution.

So, from our text on what is electrical conductivity, its formula, unit, and examples, we summarise our topic with a statement that materials via which electric current can pass through easily are called conductors of electricity. Electrical conductivity describes the ability of a substance to allow the flow of an electric current that can be calculated by the formula of σ  =  $\frac{1}{\rho }$and $\frac{J}{E }$ both. 

Additionally, solids metals and graphite are good conductors of electricity that have high electrical conductivity. However, some liquids, like saltwater and lemon juice are also good conductors.

FAQs on Electrical Conductivity

1. List the factors that the electrical conductivity of liquids relies on.

The electrical conductivity of a liquid relies upon the number of ions per unit volume and upon their drift velocity. 


Additionally, the drift velocity of ion changes with the following parameters: 

  • Electric field intensity, 

  • Types of ions,

  • The mass of the ion, and

  • The temperature of ions.

2. What causes electrical conductivity?

Electrical conductivity in metals/liquids is a consequence of the motion of electrically charged particles. The "free electrons" in metals/liquids allow material to conduct electricity. 


Especially, in metals, valence electrons are free to move, and they can travel through the lattice that forms the physical structure of a metal. This is because metals are better conductors of electricity than liquids.

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