Effect of Change in Temperature on Resistance

The resistance of a material is influenced by various factors, including its temperature. As temperature changes, the resistance of a material can either increase or decrease, depending on the type of material. This relationship is crucial in many applications, from designing electronic circuits to understanding the behavior of sensors.

Temperature Coefficient of Resistance

The temperature coefficient of resistance ($(\alpha)$) is a parameter that quantifies the change in resistance with temperature. It is defined as the change in resistance per unit resistance per degree change in temperature. The coefficient can be positive or negative, indicating whether the resistance increases or decreases with temperature.

The formula to calculate the change in resistance ($(\Delta R)$) due to a change in temperature ($(\Delta T)$) is:

$$ \Delta R = R_0 \cdot \alpha \cdot \Delta T $$

Where:

• $(R_0)$ is the original resistance at a reference temperature (usually 20°C or 25°C).
• $(\alpha)$ is the temperature coefficient of resistance.
• $(\Delta T)$ is the change in temperature.

The new resistance ($(R)$) at temperature $(T)$ can be expressed as:

$$ R = R_0 \cdot $(1 + \alpha \cdot \Delta T)$ $$

Conductors, Semiconductors, and Insulators

Different materials react differently to changes in temperature. Here's a table summarizing the behavior of conductors, semiconductors, and insulators:

Material Type	Temperature Coefficient	Effect on Resistance	Example Materials
Conductor	Positive ($(\alpha > 0)$)	Increases with temperature	Copper, Aluminum
Semiconductor	Negative ($(\alpha < 0)$)	Decreases with temperature	Silicon, Germanium
Insulator	Varies	Typically increases with temperature	Glass, Rubber

Examples

Example 1: Resistance of a Copper Wire

Copper is a conductor with a positive temperature coefficient of resistance. If a copper wire has a resistance of $(100 \Omega)$ at 20°C and its temperature coefficient of resistance is $(0.00393 \text{°C}^{-1})$, what will be its resistance at 100°C?

$$ \Delta T = 100°C - 20°C = 80°C $$ $$ R = R_0 \cdot $(1 + \alpha \cdot \Delta T)$ $$ $$ R = 100 \Omega \cdot $(1 + 0.00393 \text{°C}^{-1} \cdot 80°C)$ $$ $$ R = 100 \Omega \cdot (1 + 0.3144) $$ $$ R = 100 \Omega \cdot 1.3144 = 131.44 \Omega $$

The resistance of the copper wire at 100°C will be $(131.44 \Omega)$.

Example 2: Resistance of a Silicon Semiconductor

Silicon is a semiconductor with a negative temperature coefficient of resistance. If a silicon resistor has a resistance of $(1000 \Omega)$ at 25°C and its temperature coefficient of resistance is $(-0.075 \text{°C}^{-1})$, what will be its resistance at 75°C?

$$ \Delta T = 75°C - 25°C = 50°C $$ $$ R = R_0 \cdot $(1 + \alpha \cdot \Delta T)$ $$ $$ R = 1000 \Omega \cdot $(1 - 0.075 \text{°C}^{-1} \cdot 50°C)$ $$ $$ R = 1000 \Omega \cdot (1 - 3.75) $$ $$ R = 1000 \Omega \cdot (-2.75) = -2750 \Omega $$

However, resistance cannot be negative. This indicates that the temperature coefficient given is too large or the temperature change is too high for the linear approximation to be valid. In reality, the resistance would decrease, but not to a negative value. This example illustrates the importance of using appropriate temperature coefficients and understanding the limits of linear approximations.

Conclusion

The effect of temperature on resistance is a critical factor in the design and operation of electrical and electronic systems. Understanding how different materials respond to temperature changes allows engineers and scientists to predict the behavior of components under varying environmental conditions. The temperature coefficient of resistance is a key parameter in these calculations, and it is essential to apply it correctly to obtain accurate results.