3.4 Temperature effects on resistance

Temperature affects resistance in materials, changing how they conduct electricity. This relationship is crucial for understanding electrical systems and device behavior under varying conditions.

Resistance can increase or decrease with temperature, depending on the material. Metals typically show increased resistance when heated, while semiconductors often exhibit decreased resistance. This knowledge is vital for designing and troubleshooting electrical circuits.

Temperature Coefficients

Impact of Temperature on Resistance

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• Temperature has a significant effect on the electrical resistance of materials
• As temperature changes, the resistance of a material can increase or decrease depending on its temperature coefficient
• Temperature coefficient of resistance quantifies how much the resistance changes per degree of temperature change
• Represented by the Greek letter alpha (α) and typically expressed in units of $\frac{1}{°C}$ or \frac{%}{°C}

Types of Temperature Coefficients

• Positive Temperature Coefficient (PTC) materials exhibit an increase in resistance as temperature rises
• Common PTC materials include metals like copper and aluminum
• Negative Temperature Coefficient (NTC) materials display a decrease in resistance with increasing temperature
• Semiconductors and certain ceramics often have NTC behavior
• Material-specific behavior determines whether a substance has a PTC or NTC and the magnitude of the change

Calculating Resistance Change

• The change in resistance due to temperature can be calculated using the formula: $R_T = R_0[1 + \alpha(T - T_0)]$
• $R_T$ represents the resistance at the new temperature $T$
• $R_0$ is the initial resistance at the reference temperature $T_0$
• $\alpha$ is the temperature coefficient of resistance for the specific material
• Example: A copper wire with $\alpha = 0.00393 \frac{1}{°C}$ and $R_0 = 10\Omega$ at $T_0 = 20°C$ will have a resistance of $R_T = 10[1 + 0.00393(50 - 20)] = 11.18\Omega$ at $T = 50°C$

Temperature-Sensitive Devices

Thermistors

• Thermistors are temperature-sensitive resistors that exploit the NTC behavior of certain semiconductor materials
• As temperature increases, the resistance of a thermistor decreases significantly
• Thermistors are commonly used in temperature measurement, control systems, and thermal protection circuits
• Examples of thermistor applications include temperature sensors in home appliances, automotive temperature monitoring, and industrial process control

Linear Approximation

• For small temperature ranges, the resistance-temperature relationship of a thermistor can be approximated as linear
• The linear approximation simplifies calculations and allows for easier integration into control systems
• The linear approximation formula is given by: $R_T \approx R_0[1 + \beta(T - T_0)]$
• $\beta$ is the temperature coefficient of the thermistor, typically expressed in $\frac{1}{°C}$ or \frac{%}{°C}
• The linear approximation is valid for temperature changes of around $\pm10°C$ to $\pm20°C$ from the reference temperature

Reference Temperature and Resistance

• Thermistor specifications often include a reference temperature ($T_0$) and the corresponding resistance at that temperature ($R_0$)
• Common reference temperatures are $25°C$ and $20°C$
• The reference resistance is used as a baseline for calculating the resistance at other temperatures
• Example: A thermistor with $\beta = -0.04 \frac{1}{°C}$, $R_0 = 1000\Omega$ at $T_0 = 25°C$ will have an approximate resistance of $R_T \approx 1000[1 + (-0.04)(30 - 25)] = 800\Omega$ at $T = 30°C$ using the linear approximation