🌡️ Chapter 44: Temperature Dependence of Resistance (Class XII)
🔷 1. Introduction
The electrical resistance of a conductor is not always constant. It depends on several factors such as the material, length, cross-sectional area, and temperature.
When the temperature of a material changes, the motion of its atoms and the movement of charge carriers also change. As a result, the electrical resistance of the material either increases or decreases depending on the type of material.
🔷 2. What is Temperature Dependence of Resistance?
Ethan: Professor, what is meant by the temperature dependence of resistance?
Professor: It refers to the change in the electrical resistance of a material when its temperature changes.
Academic Definition
The variation of electrical resistance of a material with temperature is called the temperature dependence of resistance.
🔷 3. Why Does Resistance Change with Temperature?
Ethan: Professor, why does the resistance of a material change when its temperature changes?
Professor: In a material, electric current is carried by free electrons. These electrons move through the material by passing between atoms.
When the temperature increases, the atoms of the material vibrate more vigorously. These increased vibrations cause more frequent collisions between the free electrons and the atoms. As a result, the movement of electrons becomes more difficult, and the electrical resistance changes.
🔷 4. Temperature Dependence in Metallic Conductors
Ethan: Professor, how does temperature affect the resistance of metals?
Professor: In metallic conductors, an increase in temperature increases the vibrations of metal ions. Consequently, electrons experience more collisions, reducing their mobility and increasing the resistance.
Temperature ↑ ⇒ Resistance ↑
Therefore, metals have a positive temperature coefficient of resistance.
🔷 5. Temperature Dependence in Semiconductors
Ethan: Professor, what happens in semiconductors?
Professor: In semiconductors, increasing temperature generates more free charge carriers (electrons and holes). Since more charge carriers become available for conduction, the electrical resistance decreases.
Temperature ↑ ⇒ Resistance ↓
Thus, semiconductors have a negative temperature coefficient of resistance.
🔷 6. Temperature Coefficient of Resistance
Ethan: Professor, what is the temperature coefficient of resistance?
Professor: It is a quantity that indicates how much the resistance of a material changes for every one-degree change in temperature.
Academic Definition
The temperature coefficient of resistance is the fractional change in resistance per unit change in temperature.
It is represented by the Greek letter α (alpha).
🔷 7. Mathematical Relation
Ethan: Professor, what is the mathematical relation between resistance and temperature?
Professor: For a small range of temperatures, the resistance varies approximately linearly with temperature.
R = R₀ [1 + α(T − T₀)]
where,
- R = Resistance at temperature T
- R₀ = Resistance at reference temperature T₀
- α = Temperature coefficient of resistance
- T = Final temperature
- T₀ = Initial or reference temperature
🔷 8. Positive and Negative Temperature Coefficients
| Positive Temperature Coefficient | Negative Temperature Coefficient |
|---|---|
| Resistance increases with temperature. | Resistance decreases with temperature. |
| Observed in metals. | Observed in semiconductors and thermistors. |
| α is positive. | α is negative. |
🔷 9. Graph of Resistance vs Temperature
Ethan: Professor, how does the graph of resistance versus temperature look?
Professor:
- For metallic conductors, the graph is approximately a straight line with a positive slope.
- For semiconductors, the graph slopes downward because resistance decreases with increasing temperature.
🔷 10. Applications
- Design of electrical wiring.
- Electric heaters and heating elements.
- Resistance Temperature Detectors (RTDs).
- Thermistors for temperature sensing.
- Electronic temperature control systems.
- Electrical safety devices.
📦 11. Important Results (Must Remember)
- Resistance depends on temperature.
- In metals, resistance increases with temperature.
- In semiconductors, resistance decreases with temperature.
- Temperature coefficient of resistance is represented by α.
- For metals, α is positive.
- For semiconductors, α is negative.
- Resistance-temperature relation: R = R₀ [1 + α(T − T₀)].
- The relation is approximately linear over a small temperature range.
🧠 12. Conceptual Questions
🔹 Q1
Ethan: Why does the resistance of a metal increase with temperature?
Professor: Because higher temperatures increase atomic vibrations, causing more collisions between electrons and atoms.
🔹 Q2
Ethan: Why does the resistance of a semiconductor decrease with temperature?
Professor: Because higher temperatures generate more free charge carriers, increasing electrical conductivity.
🔹 Q3
Ethan: What is the temperature coefficient of resistance?
Professor: It is the fractional change in resistance per unit change in temperature.
🔹 Q4
Ethan: Which materials have a positive temperature coefficient?
Professor: Metallic conductors.
🔹 Q5
Ethan: Which materials have a negative temperature coefficient?
Professor: Semiconductors and thermistors.
🔷 13. Summary
The electrical resistance of a material changes with temperature due to changes in the motion of atoms and charge carriers. In metallic conductors, increasing temperature causes greater atomic vibrations, leading to more electron collisions and higher resistance. In semiconductors, increasing temperature generates more charge carriers, resulting in lower resistance. The relationship between resistance and temperature is described by the temperature coefficient of resistance and is approximately linear over a limited temperature range.
✨ End of Topic: Temperature Dependence of Resistance ✨
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