⚡ Chapter 38: Electrical Resistivity and Conductivity (Class XII)
🔷 1. Introduction
We have already learned that every conductor offers some opposition to the flow of electric current. This opposition is called Resistance. However, resistance depends not only on the material of the conductor but also on its length and cross-sectional area.
To compare different materials independently of their size and shape, we define a property called Electrical Resistivity. The reciprocal of resistivity is called Electrical Conductivity, which measures how easily a material allows electric current to flow.
🔷 2. What is Electrical Resistivity?
Ethan: Professor, what is electrical resistivity?
Professor: Electrical resistivity is an intrinsic property of a material that indicates how strongly it opposes the flow of electric current. Unlike resistance, resistivity depends only on the nature of the material and its temperature.
Academic Definition
Electrical resistivity is the resistance offered by a material having unit length and unit cross-sectional area to the flow of electric current.
🔷 3. Relation Between Resistance and Resistivity
Ethan: Professor, how are resistance and resistivity related?
Professor: Experiments show that resistance is directly proportional to the length of the conductor and inversely proportional to its cross-sectional area.
R ∝ L
R ∝ 1/A
Combining these relations,
R = ρL/A
where,
- R = Resistance (Ω)
- ρ (rho) = Electrical Resistivity
- L = Length of conductor
- A = Cross-sectional area
🔷 4. Physical Meaning of Resistivity
Ethan: Professor, what does resistivity tell us physically?
Professor: Resistivity tells us how difficult it is for electrons to move through a material.
- Low resistivity means electrons move easily.
- High resistivity means electrons face greater opposition.
- Thus, low resistivity materials are good conductors.
🔷 5. SI Unit of Resistivity
Ethan: Professor, what is the SI unit of resistivity?
Professor: The SI unit of resistivity is Ohm metre (Ω·m).
SI Unit of Resistivity = Ω·m
🔷 6. Factors Affecting Resistivity
Ethan: Professor, does resistivity change?
Professor: Yes. Resistivity mainly depends on:
- The nature of the material.
- Temperature.
It does not depend upon:
- Length of the conductor.
- Cross-sectional area.
- Shape of the conductor.
🔷 7. What is Electrical Conductivity?
Ethan: Professor, then what is conductivity?
Professor: Conductivity measures how easily electric current flows through a material. It is exactly opposite to resistivity.
Academic Definition
Electrical conductivity is the ability of a material to allow electric current to flow through it.
🔷 8. Relation Between Resistivity and Conductivity
Ethan: Professor, how are resistivity and conductivity related?
Professor: Conductivity is the reciprocal of resistivity.
σ = 1/ρ
where,
- σ (sigma) = Conductivity
- ρ (rho) = Resistivity
🔷 9. SI Unit of Conductivity
Ethan: Professor, what is the SI unit of conductivity?
Professor: Since conductivity is the reciprocal of resistivity, its SI unit is:
Siemens per metre (S/m)
🔷 10. Physical Meaning of Conductivity
Ethan: Professor, what does conductivity tell us physically?
Professor: Conductivity tells us how easily electrons can move inside a material.
- High conductivity means current flows easily.
- Low conductivity means current flows with difficulty.
- Good conductors have high conductivity.
- Insulators have very low conductivity.
🔷 11. Comparison Between Resistivity and Conductivity
| Electrical Resistivity | Electrical Conductivity |
|---|---|
| Opposes current flow. | Facilitates current flow. |
| Symbol: ρ | Symbol: σ |
| Unit: Ω·m | Unit: S/m |
| High for insulators. | High for conductors. |
| Lower value indicates better conductor. | Higher value indicates better conductor. |
🔷 12. Examples of Materials
| Material | Resistivity | Conductivity |
|---|---|---|
| Silver | Very Low | Very High |
| Copper | Low | High |
| Nichrome | High | Low |
| Glass | Extremely High | Extremely Low |
📦 13. Important Results (Must Remember)
- Resistance depends on length, area, and material.
- Resistivity is a property of the material.
- R = ρL/A
- Conductivity is the reciprocal of resistivity.
- σ = 1/ρ
- SI unit of resistivity = Ω·m.
- SI unit of conductivity = S/m.
- Low resistivity means high conductivity.
- High resistivity means poor conduction.
- Temperature affects both resistivity and conductivity.
🧠 14. Conceptual Questions
🔹 Q1
Ethan: What is electrical resistivity?
Professor: It is the intrinsic property of a material that measures its opposition to electric current.
🔹 Q2
Ethan: What is conductivity?
Professor: Conductivity is the ability of a material to allow electric current to pass through it.
🔹 Q3
Ethan: Why is copper used in electrical wiring?
Professor: Because it has very low resistivity and high conductivity.
🔹 Q4
Ethan: Which has higher resistivity: copper or glass?
Professor: Glass has a much higher resistivity than copper.
🔹 Q5
Ethan: Can resistivity depend on the size of a conductor?
Professor: No. Resistivity depends only on the material and temperature.
🔷 15. Applications
- Selection of materials for electrical wiring.
- Manufacture of resistors and heating elements.
- Design of transmission lines.
- Semiconductor technology.
- Electronic circuit design.
- Electrical insulation and safety.
🔷 16. Summary
Electrical resistivity is an intrinsic property of a material that measures its opposition to the flow of electric current, whereas electrical conductivity measures the ease with which current flows through the material. They are reciprocal quantities and are related by σ = 1/ρ. Materials with low resistivity possess high conductivity and are excellent conductors, while materials with high resistivity act as good insulators. These properties are fundamental in selecting materials for electrical and electronic applications.
✨ End of Topic: Electrical Resistivity and Conductivity ✨
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