Variable Resistors !

Variable Resistors !
Variable Resistors !
Variable Resistors !
Variable Resistors !
Variable Resistors !
Variable Resistors !
Variable Resistors !
Variable Resistors !
Variable Resistors !

Temperature-dependent NTC Resistors:

NTC (Negative Temperature Coefficient) resistors are semiconductors made of poly-crystalline, mixed-oxide ceramics and used mainly for temperature measurement. Since they are responsive to heat, they, and the positive-temperature coefficient resistors we shall later, are commonly dubbed with the name, thermistors. THe way they work is as follows: in semiconductors, the number of free charge carriers increases with the temperature, causing the electrical resistance to decrease. Hence the term negative temperature coefficient. At room temperature, this value is around -3 to -5% per degree. The temperature range, typically -60ºC to +200ºC, is given by the following equation:

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Temperature in K



Reference temperature



Specific material constant

The reference temperature and specific material constant B are provided on the component's data sheet. Temperatures must be expressed in Kelvin (temperature referred to absolute zero). Conversion to the Kelvin scale is performed with the equation T = (J + 273°C).

Much more sensitive than metallic-resistor thermometers, NTC resistors are suitable for all types of temperature measurement and control. However, the fact that their resistance characteristic is exponential instead of linear frequently proves disadvantageous. In such cases, it may be necessary to perform a process of linearisation.

The basic values exemplified in the table below represent a NTC resistor with a reference temperature T0 = 25°C and a corresponding resistance R25 = 5 kW.

Table 1: Basic values of a NTC resistor (R25 = 5kW)

Measured temperature in °C









Basic resistance value in ohms









The diagram below shows the related characteristic (red) and that of a similar resistor with a reference value of 10 kW (blue).

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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.

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The characteristic is described by the following equation:

Variable Resistors !

J is the temperature in °C and R0 the resistance at the reference temperature J0. A and B are material constants. The values for platinum are

A = 3.90802·10-3 K-1


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:

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a is represented by the average temperature coefficient a0.100. 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 a0.100 between 0°C and 100°C.

MaterialOperating rangea0.100
Platinum- 220 °C ... + 850 °C3.85 · 10-3 K-1
Nickel- 60 °C ... + 180 °C6.17 · 10-3 K-1
Copper- 50 °C ... + 150 °C4.27 · 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.

Voltage-dependent Resistor VDR:

The resistance of certain semiconductors (e.g. silicon carbide) depends notably on the applied voltage. Such materials are termed varistors or VDRs (Voltage Dependent Resistor).

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VDRs are voltage-dependent semiconductors whose resistance decreases notably as the applied voltage increases.

Above a certain threshold voltage specific to each varistor, its resistance drops sharply, i.e. the varistor's switching characteristic exhibits a distinct bend at this point. The characteristic is symmetric with respect to the voltage, i.e. polarity does not have any influence. Illustrated below are a varistor's circuit symbol (left) and characteristic (right). 

Variable Resistors !Variable Resistors !

Varistors are suitable for protection against overvoltage. Their resistance is extremely high under normal operating conditions but drops abruptly to a minimal level on application of an overvoltage, thus permitting charge to be drained easily. VDRs are therefore used for protecting sensitive electronic circuits as well as high-tension networks.

At present, varistors are usually based on zinc oxide (ZnO). In combination with other metal oxides such as bismuth oxide, chromium oxide or manganese oxide, the semiconductor powder is pressed and sintered into tablets. The resultant blank is bonded on both sides with silver or aluminium and furnished with connections.

Photoresistor (LDR):

A resistor whose value changes with light intensity is termed a photoresistor. This type of passive, opto-electronic component is frequently abbreviated to LDR (Light Dependent Resistor). A photoresistor's action is based on an internal, photoelectric effect. The energy (photons) of light impinging on a semiconductor releases valence electrons from their lattice bonds. The higher the light intensity, the greater the number of released charge carriers. Consequently, the electric resistance drops as the light intensity rises.

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Photoresistors are passive, electronic components whose light dependence stems from an internal, photoelectric effect.

Photoresistors are made of mixed crystals based on cadmium sulphide (CdS) and lead sulphide (PbS). Because a photoresistor's electrical resistance drops sharply on exposure to light, it is necessary to protect the photoresistor in bright conditions against damage by excessively high currents. One problem posed by photoresistors is their relatively delayed response, inversely proportional to brightness and usually amounting to a few milliseconds. For this reason, circuits equipped with LDRs only achieve switching frequencies of up to roughly 100 Hz.

A photoresistor's characteristic data include:

Dark resistance R0 (value one minute after complete blackout); standard values for R0: 106 ... 108 W
Bright resistance RH, measured at a light intensity E = 1000 lux; standard values for RH: 102 ... 104 W
Response time (up to a few milliseconds)
Maximum sensitivity wavelength
Temperature coefficient

To achieve a linear change in luminance, you can cover the LDR partly with a strip about 1.5 cm wide and adjust the illuminated area to vary the light quantity impinging on the LDR's surface. 


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