Formula & Calculator
RTD Resistance-Temperature Relation
Models how a resistance temperature detector's resistance changes linearly with temperature.
Interpretation
RTD resistance‑temperature relation: R_T = R₀(1 + αΔT) is an approximately linear model for resistance temperature detectors.
It is accurate over small temperature ranges.
Example: R₀=100Ω, α=0.00385/°C, ΔT=50°C → R_T = 100(1 + 0.00385×50) = 119.25Ω.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| R_T | Resistance at temperature T | Ω |
| R₀ | Resistance at reference temperature | Ω |
| α | Temperature coefficient of resistance | 1/°C |
| ΔT | Change in temperature | °C |
What it means
Resistance Temperature Detectors (RTDs) have a resistance that increases almost linearly with temperature. The relation is R_T = R₀(1 + αΔT), where R₀ is the resistance at 0°C, α is the temperature coefficient of resistance (TCR), and ΔT is the temperature change. For platinum RTDs, α ≈ 0.00385 per °C. This linear approximation is valid over a limited range. RTDs are used for precise temperature measurement in industrial and laboratory settings. They are more accurate than thermocouples but are slower and more expensive. Example: A Pt100 RTD has R₀ = 100Ω at 0°C. At 50°C, ΔT = 50°C, so R_T = 100(1 + 0.00385*50) = 100(1+0.1925) = 119.25Ω. This resistance is measured to infer the temperature.
Worked example
RTD Resistance–Temperature – Practical Example
Real‑World| Parameter | Value |
|---|---|
| R₀ | 100 Ω |
| α | 0.00385 /°C |
| ΔT | 50 °C |
| Formula | RT = R₀(1 + αΔT) |
Common mistakes
Watch unit consistency and the assumptions behind the formula; misapplying it outside its valid conditions is the most frequent error.Applications
RTD resistance‑temperature relation R_T = R₀(1 + αΔT) is a linear approximation for resistance temperature detectors, used for accurate temperature measurement. Engineers use RTDs in precision industrial applications, where stability and repeatability are required. By measuring the resistance, temperature is inferred. This formula is the basis for RTD calibration and compensation.
- Precision temperature measurement in process control
- HVAC and building automation
- Laboratory instrumentation and calibration
- Food processing and pharmaceuticals
- Educational understanding of RTD sensors
Frequently Asked Questions
For platinum RTDs, the resistance is approximated as R_T = R₀(1 + αΔT) for a limited temperature range, where α is the temperature coefficient of resistance (typically 0.00385 /°C for Pt100).
It is a more accurate polynomial for RTDs: R_T = R₀[1 + A·T + B·T² + C·(T−100)·T³] for T<0°C. It provides higher accuracy over a wide range.
α = 0.00385 /°C for IEC 60751 (European curve). α = 0.00392 /°C for the US curve (older standard).
Common errors: 1) using the wrong α, 2) applying the linear approximation outside its valid range, 3) forgetting the self‑heating effect, 4) using the wrong R₀ (100 Ω for Pt100), 5) not accounting for lead resistance.
Precision temperature measurement in industrial, laboratory, and medical applications.
Using a Wheatstone bridge, a current source (4‑wire method), or a resistance meter. The 4‑wire method eliminates lead resistance.
α = 0.00385 /°C, so for every 1°C change, resistance changes by 0.385 Ω.
RTDs are more accurate and stable but have a narrower range and slower response. Thermocouples have a wider range and faster response but lower accuracy.