---
title: "Temperature coefficient and effect on resistance"
subject: "Basic Electrical Engineering"
chapter: 1
key: "semester_1/basic_electrical_engineering:temperature-coefficient-effect-on-resistance"
source: https://www.bctengineer.com/q/semester_1/basic_electrical_engineering/temperature-coefficient-effect-on-resistance
site: BCT Engineering
---

# Temperature coefficient and effect on resistance

Basic Electrical Engineering · Chapter 1: General Electric System

- Asked in: 2069 Asar, 6 marks
- Video: [Effect of Temperature on Resistance | Electrical and Electronics Engineering](https://www.youtube.com/watch?v=yYD5X0jttvw) — Magic Marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_1/basic_electrical_engineering/temperature-coefficient-effect-on-resistance
- Whole chapter: https://www.bctengineer.com/md/semester_1/basic_electrical_engineering/chapter-1

## Question

Define the temperature coefficient of resistance and explain the effect of temperature on resistance of a substance.

## Short answer

Temperature coefficient of resistance α is the change in resistance per ohm per °C: α₀ = (R_t − R₀)/(R₀·t). For pure metals α is positive and resistence rises with temperature; for semi-conductors, insulators, carbon it is negative; for alloys like manganin it is nearly zero.

## Answer

#### Temperature coefficient of resistance
The **temperature coefficient of resistance (α)** is the change in resistance per ohm of original resistance per degree rise in temperature:

α₀ = (R_t − R₀)/(R₀ · t), so R_t = R₀ (1 + α₀ t)

Unit: per °C. The value depends on the reference temperature: α_t = α₀/(1 + α₀ t).

#### Effect of temperature on resistance

| Material | α | Effect of rising temperature |
|---|---|---|
| Pure metals (Cu, Al, Fe) | positive | Resistance increases nearly linearly |
| Semiconductors, insulators, carbon, electrolytes | negative | Resistance decreases |
| Alloys (manganin, constantan) | almost zero | Resistance almost unchanged |

**Reason for metals:** at a higher temperature the atoms vibrate more, so free electrons collide more often and their drift is opposed more.
**Reason for semiconductors:** heat frees more electron-hole pairs, and this increase in charge carriers outweighs the effect of the extra collisions, so conductivity rises.

```text
   Metal            Alloy             Semiconductor
 R |      /       R |               R |\
   |    /           |---------        |  \
   |  /             |                 |    \____
   +-------- T      +-------- T       +---------- T
```

Examples: a lamp filament has a much lower resistance when cold than when hot; manganin is used for standard resistors because of its near-zero α.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. alpha0 is defined by:
   A. alpha0 = R0 / (Rt t)
   B. alpha0 = (Rt - R0)/(R0 t), so Rt = R0 (1 + alpha0 t)
   C. alpha0 = (Rt + R0) / t
   D. alpha0 = Rt x R0 x t
   Answer: B. It is change in resistance per ohm of original resistance per degC. (Key point: Definition)

2. Which material has a negative temperature coefficient?
   A. Copper
   B. Aluminium
   C. Manganin
   D. Semiconductors
   Answer: D. Semiconductors, insulators, carbon and electrolytes lose resistance as temperature rises. (Key point: Sign by material)

3. Why does a metal's resistance rise with temperature?
   A. More electron-hole pairs form
   B. Atoms vibrate more, so free electrons collide more often
   C. Free electron density rises sharply
   D. Atoms stop vibrating
   Answer: B. Greater lattice vibration increases collisions, opposing electron drift. (Key point: Why metals increase)

4. Why is manganin used for standard resistors?
   A. Its alpha is large and negative
   B. Its alpha is large and positive
   C. Its alpha is almost zero, so resistance stays steady
   D. It has zero resistivity
   Answer: C. Near-zero alpha means resistance barely changes with temperature. (Key point: Alloys)

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