In electrical engineering, it is well known that the resistance of a conductor increases with rise in temperature. This property is important in designing transmission lines, resistors, and electrical machines. But why does this happen? The answer lies in the atomic structure and electron movement within conductors. Let’s explore in detail.
What is Electrical Resistance?
Resistance is the property of a material that opposes the flow of electric current. It is given by:
R = ρ (L / A)
Where, R = Resistance (Ω), ρ = Resistivity of the material, L = Length of conductor, A = Cross-sectional area.
The resistance depends not only on geometry but also on the resistivity (ρ), which is highly temperature-dependent.
Why Does Resistance Increase with Temperature?
Conductors like copper, silver, and aluminum have plenty of free electrons that carry current. When temperature rises:
- The atoms in the conductor vibrate more intensely due to increased thermal energy.
- This causes more collisions between free electrons and vibrating atoms.
- As collisions increase, the mobility of electrons decreases.
- This results in higher opposition to current flow, i.e., increased resistance.
Thus, the increase in resistance with temperature is due to increased electron scattering inside the conductor.
Mathematical Relation Between Resistance and Temperature
The resistance of a conductor at temperature T is given by:
RT = R0 [1 + α (T − T0)]
Where, R0 = Resistance at reference temperature T0 RT = Resistance at temperature T α = Temperature coefficient of resistance (per °C).
For conductors, α is positive, which means resistance increases with temperature.
Example
Suppose the resistance of a copper wire is 10 Ω at 20°C. The temperature coefficient of resistance for copper is approximately 0.004/°C. At 80°C:
R80 = 10 [1 + 0.004 × (80 − 20)] = 10 [1 + 0.24] = 12.4 Ω
Hence, the resistance increases significantly with temperature.
Why Do Metals and Non-Metals Behave Differently?
- Metals (Conductors): Resistance increases with temperature (positive α) because electron scattering increases.
- Semiconductors: Resistance decreases with temperature (negative α) because more charge carriers are released at higher temperature.
- Insulators: At low temperatures they have very high resistance, but with enough heat, some electrons may get free, reducing resistance.
Practical Implications
- Transmission lines heat up under heavy load → resistance increases → more power loss (I²R losses).
- In resistors, materials with stable resistance over temperature (like manganin, constantan) are preferred for accuracy.
- Temperature rise in electrical machines increases copper losses due to higher resistance.
Conclusion
Resistance increases with temperature in conductors because atomic vibrations increase electron collisions, reducing their mobility. This property is expressed using the temperature coefficient of resistance, which is positive for conductors. Understanding this behavior is crucial in designing efficient electrical systems and minimizing power losses.
FAQs on Resistance and Temperature
1. Why does resistance of a conductor increase with temperature?
Because atomic vibrations increase, causing more collisions with free electrons, which reduces current flow.
2. What is the temperature coefficient of resistance?
It is a constant (α) that shows how much resistance changes per degree rise in temperature.
3. Does resistance always increase with temperature?
No, in conductors it increases (positive α), but in semiconductors and insulators it decreases (negative α).
4. Which materials are used for standard resistors?
Alloys like manganin and constantan are used because they have very low temperature coefficients of resistance.
5. How does temperature affect transmission line losses?
As temperature rises, line resistance increases, leading to higher I²R losses in transmission lines.