Temperature Coefficient of Resistance: How Temperature Alters Conductivity

When you look at a standard resistance table, you’ll notice every value is quoted at 20 °C. That’s because a material’s specific resistance changes with temperature. If you need the resistance of a conductor at a different temperature, you must apply the temperature‑coefficient formula.

The Greek symbol α (alpha) represents the temperature coefficient of resistance—the percentage change in resistance per degree Celsius. Pure metals have positive α values, meaning their resistance rises as temperature climbs. In contrast, semiconductors like carbon, silicon, and germanium have negative α values, so their resistance falls with heat. Some alloys, such as nichrome, are engineered to have α values close to zero, making them ideal for precision resistors.

Temperature Coefficients of Resistance at 20 °C

* Steel alloy (99.5 % Fe, 0.5 % C)

Let’s explore how temperature influences wire resistance in a simple circuit.

The total resistance of the two wires is 30 Ω at 20 °C. The table below lists voltage, current, and resistance values at that temperature.

At 20 °C we observe 12.5 V across the load and a 0.75 V drop across the wires (0.75 Ω each). If the temperature rises to 35 °C, the copper wires’ resistance increases because α = 0.004041. The new resistance for each wire is:

Re‑calculating the circuit gives the following results:

We see the load voltage drops from 12.5 V to 12.42 V, while the voltage drop across the wires increases from 0.75 V to 0.79 V. These changes may seem minor, but over long power lines the cumulative effect is substantial. Utility companies routinely factor temperature‑induced resistance variations into their load‑capacity calculations.

Key Takeaways

• Conductive materials exhibit temperature‑dependent resistance; tables always reference a standard temperature (usually 20 °C or 25 °C).
• The temperature‑coefficient of resistance (α) quantifies how much resistance changes per degree Celsius.
• Positive α values (typical for pure metals) mean resistance rises with temperature; near‑zero α values (achieved by alloying) provide temperature‑stable resistors.
• Negative α values (found in semiconductors) mean resistance falls as temperature climbs.
• Use the formula shown above to calculate resistance at any temperature outside the standard reference.

For further practice, try the Temperature Coefficient of Resistance Worksheet.