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# Temperature Dependent PTC Resistors

Some metallic resistors, usually made of platinum or nickel, have a positive temperature coefficient, i.e. their resistance increases with the temperature. Their resistance characteristic is predominantly linear. The diagram below illustrates the resistances of platinum and nickel as a function of the temperature.

The characteristic is described by the following equation:

J is the temperature in °C and *R*_{0} the resistance at the reference temperature J_{0}. *A* and *B* are material constants. The values for platinum are

*A* = 3.90802·10^{-3} K^{-1}

and

*B* = -0.580195·10^{-6} K^{-2}.

Over the temperature range between 0°C and 100°C, resistance can be calculated with the following approximation:

a is represented by the average temperature coefficient a_{0.100}. This material-specific coefficient is listed in Table 1 below.

Used mainly for technical temperature measurements, platinum resistance thermometers are highly accurate. Careful measurements using appropriate equipment can achieve an accuracy of ±0.01 K.

A constant, reproducible temperature coefficient a can be specified for platinum, nickel and copper resistors. This permits temperatures to be ascertained purely on the basis of resistance measurements.

Table 1 provides an overview of the operating ranges of various resistor materials. Also indicated is the average temperature coefficient a_{0.100} between 0°C and 100°C.

Material |
Operating range |
a_{0.100} |

Platinum |
- 220 °C ... + 850 °C |
3.85 · 10^{-3} K^{-1} |

Nickel |
- 60 °C ... + 180 °C |
6.17 · 10^{-3} K^{-1} |

Copper |
- 50 °C ... + 150 °C |
4.27 · 10^{-3} K^{-1} |

Table 1: Operating range and average temperature coefficient of various materials.

Due to their extremely high precision, platinum resistors are preferred for practical measurement applications. Due to their relatively high temperature coefficient, nickel resistors are of significance in low-temperature and differential-temperature measurements. Copper resistors are used only for special types of measurement. The resistance characteristic of copper is used, for instance, to measure the temperature of windings on electrical machines. The windings themselves serve as the measurement resistors in this case.

Only platinum resistors are in widespread international use. They come in various designs with standardised electrical values. A series of basic values has been established for resistance thermometers. These values define the relationship between the temperature and resistance of a standardized measuring resistor. The standard applicable here is DIN 43760 which specifies 100 W as the rated value of a calibrated resistor at 0°C, the permissible tolerance being ±0.1 W. Calibrated platinum resistors conforming to this standard are termed Pt100 for short.