In this article, we will learn about the difference between resistance and resistivity. Students first come across these terms while studying Electricity where the concept of electric current, resistance, and resistivity are introduced.
For the basic introduction visit our notes on electricity.
TLDR – Too Long Don’t Read
Both resistance and resistivity describe how difficult it is to make electrical current flow through a material. But there is a very basic difference between resistance and resistivity. Electric resistivity is an intrinsic property of the material whereas resistance is the property of the object. For example, all copper wires have the same resistivity but, their resistance differs depending on their size and shape.
We will now begin by looking at the definition of both resistance and resistivity.
What is resistance?
Resistance Definition: Electric resistance of a conductor is the obstruction offered by the conductor to the flow of the current through it.
The flow of charge or current through any material encounters an opposing force similar to the force of friction in mechanics in some aspects. Resistance is nothing but the opposing force of the material to the flow of electric current. It is measured in Ohms which is represented by symbol \(\Omega\) (see omega symbol physics). The circuit symbol of resistance is \(R\).
Resistance is represented by the formula
\[R=\rho\frac{l}{A}\]
where,
\(l\) is the length of the conductor
\(A\) is the cross-sectional area of the conductor and
\(\rho\) is the resistivity of the material
It must be noted that resistance depends on the area and length of the conductor but we have used resistivity as a constant of proportionality which remains the same for a particular material.
What is resistivity?
Resistivity Definition: Resistivity or specific resistivity of the material is an intrinsic property that quantifies how strongly a given material opposes the flow of electric current.
It is given by the formula
\[\rho = \frac{RA}{l}\]
Where \(l\) – length of the conductor
\(A\) – cross-section area of conductor
\(R\) – Resistance of the material
We use this formula to calculate resistivity when the resistance and dimensions of the conductor are known. This formula is obtained by rearranging the formula for resistance and by no means we can assume that resistivity depends on the length of the material under consideration.
It is measured in Ohms-meter which is represented by symbol \(\Omega m\). The symbol for representing resistivity is \(\rho\)
Resistance Vs. Resistivity in tabular form
| Comparison | Resistance | Resistivity |
| Definition | It is the obstruction offered by the conductor to the flow of the current through it | It is the intrinsic property that quantifies how strongly a given material opposes the flow of electric current |
| Formula | \[R=\rho \frac {l}{A}\] | \[\rho = \frac{RA}{l}\] |
| Unit | Ohms | Ohms-meter |
| Symbol | \(R\) | \(\rho\) |
| Dependence | It is directly proportional to the length of the conductor and inversely proportional to the area of the cross-section through which current is flowing. | It depends on the physical conditions like temperature and nature of the material. |
The key differences
- Both these terms describe how difficult it is to make electrical current flow through a material, but unlike resistance, resistivity is an intrinsic property of the material.
- The unit of resistance is Ohms whereas a unit of resistivity is Ohm-meter.
- The formula of resistance is \(R=\rho \frac {l}{A}\) whereas the formula of resistivity is \( \rho = \frac{RA}{l} \).
- The resistivity of a conductor is always the same and is independent of its shape or size. The resistance of a conductor depends on its length or size.
Further References
1. https://en.wikipedia.org/wiki/Electrical_resistivity_and_conductivity
2. http://hyperphysics.phy-astr.gsu.edu/hbase/electric/resis.html
Image Credits: Images in this article is created using the premium version of canva.com and https://app.diagrams.net/
