Library / Electrical / ELE-05
Electrical
Resistance and temperature
Resistance of a conductor after a temperature rise, using a linear temperature coefficient.
- Ref
- ELE-05
- Rev
- v1
- Field
- Electrical
- Result
- R [Ω]
R0 is the resistance at the reference temperature, α the temperature coefficient of resistance in 1/°C, and θ the temperature rise above that reference in °C.
Most metals resist current more as they warm up. Over a modest range the rise is close to a straight line: the fractional change in resistance is the coefficient α times the temperature rise θ.
Calculator
- Change ΔR = R − R038.5 Ω
- Fractional change38.5 %
- Slope αR00.385 Ω/°C
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- Resistance rises as a straight line with θ and is directly proportional to R0. A Pt100 sensor (R0 = 100 Ω, α ≈ 0.00385) gains about 0.385 Ω per °C.
- Heating raises the resistance of a metal conductor, so at a fixed current it dissipates more power and at a fixed voltage it dissipates less.
- The straight-line model is an approximation. Over wide ranges the real curve bends, and standards such as IEC 60751 use a polynomial for platinum sensors.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (Ω) | Local step | Change in result |
|---|---|---|---|---|---|---|
| R0 Resistance at reference temperature | 10 to 1,000 Ω | 13.85 | 1,385 | 1,371 | +10% | +10 % |
| θ Temperature rise | 0 to 200 °C | 100 | 177 | 77 | +10% | +2.78 % |
| α Temperature coefficient | 5e-4 to 0.006 1/°C | 105 | 160 | 55 | +10% | +2.78 % |
Sweep of Temperature rise
| Temperature rise (°C) | Resistance at temperature (Ω) |
|---|---|
| 0 | 100 |
| 25 | 109.6 |
| 50 | 119.2 |
| 75 | 128.9 |
| 100 | 138.5 |
| 125 | 148.1 |
| 150 | 157.8 |
| 175 | 167.4 |
| 200 | 177 |
Sweep one variable
Variables and how each one contributes
Resistance at temperature
What the equation gives you. Everything else feeds it.
Resistance at reference temperature
Resistance measured at the reference temperature, often 0 °C or 20 °C. Directly proportional: R scales with R0 and the fractional change stays the same.
Temperature coefficient
Fractional change in resistance per degree. About 0.0039 per °C for copper and 0.00385 for the platinum in Pt100 sensors. Negative for NTC thermistors. Sets the slope. A larger α means resistance changes faster with temperature, which makes a better temperature sensor but a larger heating effect in a power conductor.
Temperature rise
Temperature above the reference temperature at which R0 and α apply. Linear: each extra degree adds αR0 ohms. Valid only while the straight-line approximation holds.
Worked example with the values above
- Fractional change: αθ = 0.00385 × 100 = 0.385.
- Factor: 1 + αθ = 1.385.
- R = R0(1 + αθ) = 100 × 1.385 = 138.5 Ω.
Assumptions and limits
- Linear variation of resistance with temperature, valid over a limited range.
- θ is measured from the reference temperature at which R0 and α are specified (often 0 °C or 20 °C).
- Thermal expansion of the conductor is ignored.
Common mistakes
- Using the absolute temperature instead of the rise above the reference temperature.
- Using an α quoted at 20 °C with an R0 measured at 0 °C. The two must refer to the same reference.
- Applying the formula to thermistors, whose resistance varies non-linearly and for NTC types falls as temperature rises.
Statistics and uncertainty
α is an empirical coefficient, usually quoted for a reference temperature and a given purity of material, and it carries a tolerance. For a sensor, the uncertainty in temperature follows from the uncertainty in resistance: δθ ≈ δR / (αR0). A ±0.1 Ω error on a Pt100 corresponds to about ±0.26 °C.
Where it is used
- Resistance thermometers and temperature sensing.
- Estimating the temperature rise of a copper winding from a resistance measurement.
- Allowing for heating in cable and heater calculations.
Maths you need
- Percentages and ratios: a fractional change αθ, then multiplied by R0
- Units: θ in °C and α in 1/°C