Define resistivity and conductivity of a material.
1 Answer
Overview
Resistivity and Conductivity are two fundamental, intrinsic properties of a material that describe how it behaves in the presence of an electric field. They are mathematical reciprocals of each other, meaning they represent opposite characteristics: one measures how much a material opposes electric current, while the other measures how well it allows it.
1. Resistivity (ρ)
Definition:
Resistivity is a measure of how strongly a material opposes the flow of electric current. It is an intrinsic property, meaning it depends only on the material's chemical composition and temperature, not on its size or shape.
A material with high resistivity is a poor conductor of electricity (an insulator), while a material with low resistivity is a good conductor.
Conceptual Understanding:
Imagine you have a block of copper and a block of rubber of the exact same size. The copper will have a very low resistivity, and the rubber will have a very high resistivity. This difference is due to the nature of the materials themselves, specifically how their electrons are arranged.
Formula:
Resistivity (symbol: ρ, the Greek letter "rho") is defined by the formula that relates it to a specific object's resistance (R):
$R = \rho \frac{L}{A}$
Where:
R is the resistance of the object in Ohms (Ω). This is an extrinsic property that depends on shape.
ρ is the resistivity of the material in Ohm-meters (Ω·m).
L is the length of the object in meters (m).
A is the cross-sectional area of the object in square meters (m²).
SI Unit:
The SI unit of resistivity is the Ohm-meter (Ω·m).
Examples:
Copper (Good Conductor): ~ $1.68 \times 10^{-8}$ Ω·m
Silicon (Semiconductor): Varies greatly, but can be ~ $6.4 \times 10^{2}$ Ω·m
* Glass (Good Insulator): ~ $10^{10}$ to $10^{14}$ Ω·m
2. Conductivity (σ)
Definition:
Conductivity is a measure of how easily a material allows the flow of electric current. It is the direct opposite (the reciprocal) of resistivity. It is also an intrinsic property.
A material with high conductivity is a good conductor of electricity, while a material with low conductivity is a poor conductor (an insulator).
Conceptual Understanding:
Using the same example, copper has a very high conductivity because it readily allows electrons to flow through it. Rubber has a very low conductivity because it strongly restricts the flow of electrons.
Formula:
Conductivity (symbol: σ, the Greek letter "sigma") is the mathematical reciprocal of resistivity:
$\sigma = \frac{1}{\rho}$
Where:
σ is the conductivity of the material.
ρ is the resistivity of the material.
SI Unit:
The SI unit of conductivity is Siemens per meter (S/m).
The Siemens (S) is the unit of electrical conductance and is the reciprocal of the Ohm ($S = \frac{1}{\Omega}$).
An older, informal unit you might see is the "mho per meter," where "mho" is "ohm" spelled backward.
Examples:
Copper (Good Conductor): ~ $5.96 \times 10^{7}$ S/m
Silicon (Semiconductor): ~ $1.56 \times 10^{-3}$ S/m
* Glass (Good Insulator): ~ $10^{-11}$ to $10^{-15}$ S/m
Summary Table
| Feature | Resistivity (ρ) | Conductivity (σ) |
| ---------------- | --------------------------------------------- | -------------------------------------------- |
| Concept | Measures opposition to current flow. | Measures ease of current flow. |
| High Value | Indicates an insulator (poor conductor). | Indicates a conductor (good conductor). |
| Low Value | Indicates a conductor (good conductor). | Indicates an insulator (poor conductor). |
| Relationship | $\rho = \frac{1}{\sigma}$ | $\sigma = \frac{1}{\rho}$ |
| SI Unit | Ohm-meter (Ω·m) | Siemens per meter (S/m) |
Analogy: Water Flow in Pipes
Think of electricity as water flowing through a pipe.
- Resistance (R) is like the overall difficulty for water to flow through a specific pipe. A long, narrow pipe has high resistance. A short, wide pipe has low resistance.
- Resistivity (ρ) is like the roughness or friction of the material the pipe is made of. A pipe made of a very rough material (like coarse concrete) has high resistivity. A pipe made of a very smooth material (like polished plastic) has low resistivity. This property is independent of the pipe's length or width.
- Conductivity (σ) is like the slipperiness of the material the pipe is made of. A very slippery inner surface (high conductivity) lets water flow easily, while a very sticky surface (low conductivity) hinders it.