Potentiometers, Thermistors & Pyrometers
Introduction to Electrical Sensors and Measurement Devices
This module explores three important devices used in electrical circuits for measurement and control:
Potentiometers
Variable resistors with a sliding or rotating contact (wiper) that forms an adjustable voltage divider. Used for volume controls, position sensors, and manual adjustments.
Thermistors
Temperature-sensitive resistors whose resistance changes with temperature. Types include NTC (Negative Temperature Coefficient) and PTC (Positive Temperature Coefficient).
Pyrometers
Non-contact temperature measurement devices that detect thermal radiation emitted by objects. Essential for high-temperature industrial applications.
These devices are fundamental in many electrical and electronic systems, from simple household appliances to complex industrial control systems. Understanding how they work is essential for IGCSE, GCSE and O Level students.
Potentiometers
A potentiometer is a three-terminal resistor with a sliding or rotating contact (wiper) that forms an adjustable voltage divider.
Working Principle
Potentiometers consist of a resistive element with connections at both ends and a movable contact (wiper). The position of the wiper determines the resistance ratio between terminals.
For a potentiometer with total resistance R:
R₁₂ = R × (position of wiper)
R₂₃ = R × (1 - position of wiper)
Where the wiper position ranges from 0 to 1
The total resistance: R = R₁₂ + R₂₃
Voltage Divider Application
The most common application is as a voltage divider, producing a variable output voltage from a fixed input.
The output voltage is:
Vout = Vin × (R₂ / (R₁ + R₂))
Where:
- Vout = Output voltage
- Vin = Input voltage
- R₁ = Resistance from terminal 1 to wiper
- R₂ = Resistance from wiper to terminal 3
Types of Potentiometers
By Construction
- Rotary Potentiometers: Operated by rotating a shaft
- Slide Potentiometers: Operated by sliding along a linear track
- Trimpots: Small potentiometers adjusted with a screwdriver
- Digital Potentiometers: Electronic devices simulating a potentiometer
By Taper (Resistance Variation)
- Linear (Type B): Resistance changes proportionally to position
- Logarithmic (Type A): Changes logarithmically, used in audio controls
- Anti-Log (Type C): Opposite of logarithmic taper
Thermistors
Thermistors are temperature-sensitive resistors whose resistance changes significantly with temperature. The name combines "thermal" and "resistor".
Types of Thermistors
NTC Thermistors
Negative Temperature Coefficient thermistors decrease in resistance as temperature increases.
- Most common type of thermistor
- Made from metal oxides
- Typical resistance at 25°C: 1kΩ to 100kΩ
- Used for temperature measurement and control
PTC Thermistors
Positive Temperature Coefficient thermistors increase in resistance as temperature increases.
- Less common than NTC thermistors
- Two main types: switching PTC and silistor
- Used for circuit protection and self-regulating heating
Mathematical Relationships
NTC Thermistor Equation (Beta Equation)
R = R₀ × eβ(1/T - 1/T₀)
Where:
- R = Resistance at temperature T (in Kelvin)
- R₀ = Resistance at reference temperature T₀ (usually 298.15K or 25°C)
- β = Beta value, a material constant (in Kelvin)
- e = Euler's number (approximately 2.71828)
To find temperature from resistance:
T = β / (ln(R/R₀) + β/T₀)
Applications
- Temperature Measurement: Medical thermometers, appliances, automotive sensors
- Temperature Control: Thermostats, HVAC, incubators, 3D printers
- Circuit Protection: Inrush current limiting, overcurrent protection
- Temperature Compensation: Stabilizing oscillator frequencies, correcting LED brightness
Pyrometers
Pyrometers are non-contact temperature measurement devices that detect thermal radiation emitted by objects. They are useful for measuring high temperatures or when physical contact is impossible.
Working Principle
All objects above absolute zero emit thermal radiation. The intensity and spectral distribution of this radiation depend on the object's temperature.
Stefan-Boltzmann Law
The total power radiated per unit area by a black body is proportional to the fourth power of its temperature:
j* = σT⁴
Where:
- j* = Total power radiated per unit area (W/m²)
- σ = Stefan-Boltzmann constant (5.67 × 10-8 W/m²K⁴)
- T = Absolute temperature in Kelvin
Types of Pyrometers
Radiation Pyrometers
Measure total radiation over a wide range of wavelengths.
- Temperature range: 0°C to 4000°C
- Affected by emissivity variations
Optical Pyrometers
Compare brightness of an object to a calibrated reference.
- Temperature range: 700°C to 3000°C
- Used for high-temperature industrial applications
Infrared Pyrometers
Measure infrared radiation in specific wavelength bands.
- Temperature range: -50°C to 3000°C
- Single or dual-wavelength types
Emissivity Concept
Emissivity is a measure of how efficiently a surface emits thermal radiation compared to a perfect emitter (black body).
Emissivity (ε) = Radiation emitted by an object / Radiation emitted by a black body at the same temperature
Values range from 0 (perfect reflector) to 1 (perfect emitter or black body)
For pyrometer temperature correction when emissivity is known:
Ttrue⁴ = Tmeasured⁴ × (εsetting/εactual)
Interactive Calculators
Potentiometer Voltage Divider Calculator
Results
Resistance between terminal 1 and wiper: Ω
Resistance between wiper and terminal 3: Ω
Output voltage: V
Thermistor Temperature Calculator
Results
Temperature: °C
Pyrometer Emissivity Correction Calculator
Results
Corrected Temperature: °C
Temperature Error: °C
Temperature Conversion Calculator
Conversion Results
Converted Value:
Examples and Practice Problems
Example 1: Potentiometer as a Voltage Divider
Problem: A potentiometer with a total resistance of 5 kΩ is connected across a 12V power supply. If the wiper is positioned at 30% from the ground end, what is the output voltage measured at the wiper?
Solution:
Given:
- Total resistance of potentiometer: 5 kΩ
- Input voltage: 12V
- Wiper position: 30% from ground end
Using the voltage divider formula:
Vout = Vin × (Wiper position)
Vout = 12V × 0.3
Vout = 3.6V
Answer: The output voltage at the wiper is 3.6V.
Example 2: NTC Thermistor Temperature Calculation
Problem: An NTC thermistor has a resistance of 10 kΩ at 25°C and a beta value of 3950K. If the measured resistance is 25.4 kΩ, what is the temperature?
Solution:
Given:
- Reference resistance (R₂₅): 10 kΩ at 25°C (298.15K)
- Beta value (β): 3950K
- Measured resistance (R): 25.4 kΩ
Using the beta equation for NTC thermistors:
1/T = 1/T₀ + (1/β) × ln(R/R₀)
1/T = 1/298.15 + (1/3950) × ln(25.4/10)
1/T = 0.00335 + (0.00025) × 0.932
1/T = 0.00335 + 0.000233
1/T = 0.003583
T = 1/0.003583 = 279.1K
Converting to Celsius: T = 279.1 - 273.15 = 5.95°C ≈ 6°C
Answer: The temperature is approximately 6°C.
Example 3: Pyrometer Emissivity Correction
Problem: A pyrometer with an emissivity setting of 1.0 reads a temperature of 850°C when measuring a steel surface with an actual emissivity of 0.75. What is the true temperature of the steel surface?
Solution:
Given:
- Measured temperature (Tmeasured): 850°C
- Pyrometer emissivity setting (εsetting): 1.0
- Actual emissivity of steel (εactual): 0.75
For radiation pyrometers, using Stefan-Boltzmann Law:
Ttrue⁴ = Tmeasured⁴ × (εsetting/εactual)
Converting temperatures to Kelvin:
Tmeasured = 850°C + 273.15 = 1123.15K
Ttrue⁴ = (1123.15)⁴ × (1.0/0.75)
Ttrue⁴ = 1.5922 × 1012 × (1/0.75)
Ttrue⁴ = 2.1229 × 1012
Ttrue = ⁴√(2.1229 × 1012)
Ttrue = 1181.57K
Converting back to Celsius:
Ttrue = 1181.57 - 273.15 = 908.42°C ≈ 908°C
Answer: The true temperature of the steel surface is approximately 908°C.
