How Temperature Influences Electrical Resistance

The resistance of a material changes with temperature. Understanding the effect of temperature on resistance is important in electrical circuits, especially for conductors, semiconductors, insulators, and alloys. This concept is fundamental for solving various physics problems involving current and potential difference.

Definition of Resistance and Its Temperature Dependence

Resistance is a property that opposes the flow of electric current in a material. It is determined by the nature, dimensions, and temperature of the material. The SI unit of resistance is the ohm ($\Omega$). The relationship between temperature and resistance is crucial in physics and forms a part of the study of electrical properties of materials.

Effect of Temperature on Resistance of Conductors

In metallic conductors like copper, gold, and aluminium, resistance increases with a rise in temperature. This occurs because the lattice ions vibrate more vigorously at higher temperatures, causing increased collisions with electrons and decreasing the mobility of charge carriers.

The temperature dependence of resistance in metals is approximately linear over a moderate temperature range and can be expressed as:

$R_t = R_0 (1 + \alpha \Delta T)$

Here, $R_t$ is the resistance at temperature $T$, $R_0$ is the resistance at a reference temperature (often $0^\circ$C or $20^\circ$C), $\alpha$ is the temperature coefficient of resistance, and $\Delta T$ is the change in temperature. For metals, $\alpha$ is positive, indicating a positive temperature coefficient of resistance.

This positive temperature coefficient means resistance increases with temperature in conductors. The study of Properties of Solids and Liquids is essential to understand the microscopic mechanisms behind this behaviour.

Effect of Temperature on Resistance of Alloys

Certain alloys like nichrome, manganin, and constantan exhibit much less change in resistance with temperature. In these materials, the temperature coefficient of resistance is very small and may be either positive or negative depending on the alloy composition.

Due to this property, alloys are widely used in making standard resistors and heating elements, as their resistance values remain nearly constant over a wide temperature range.

Effect of Temperature on Resistance of Semiconductors

Semiconductors such as silicon and germanium show a decrease in resistance as temperature increases. In these materials, thermal energy excites more electrons from the valence band to the conduction band, greatly increasing the number of charge carriers.

This results in a negative temperature coefficient of resistance, with resistance decreasing rapidly as temperature rises. The energy band model explains this phenomenon and is essential for semiconductor devices.

This trend can be contrasted with conductors using suitable Electric Potential concepts that govern charge carrier dynamics.

Effect of Temperature on Resistance of Insulators

Insulators like rubber, glass, and mica have a very high resistance at low temperatures. As temperature increases, some electrons gain sufficient thermal energy to move into the conduction band, resulting in a decrease in resistance.

The resistance of insulators decreases with the rise in temperature, indicating a negative temperature coefficient similar to semiconductors. However, the initial resistance values are typically much higher in insulators.

Effect of Temperature on Electrolytes

In electrolytes, resistance decreases with a rise in temperature because the viscosity of the solvent reduces, making the mobility of ions greater. Therefore, electrolytes also exhibit a negative temperature coefficient of resistance.

Summary Table: Temperature Coefficient of Resistance

Mathematical Expression: Temperature Dependence of Resistivity

The resistivity ($\rho$) of a material varies with temperature according to:

$\rho_{t_2} = \rho_{t_1} [1 + \alpha (t_2 - t_1)]$

Here, $\rho_{t_1}$ is the resistivity at temperature $t_1$, and $\alpha$ is the temperature coefficient of resistivity at reference temperature $t_1$. This relationship is valid for moderate temperature changes in conductors and alloys.

Physical Explanation of Temperature Effects

For metals, the number of free electrons remains nearly constant as temperature changes. However, the increased lattice vibrations at higher temperature cause more frequent electron-lattice collisions, hindering the movement of electrons and increasing resistance.

In semiconductors and insulators, number of charge carriers increases dramatically with temperature due to excitation across the energy band gap, causing resistance to decrease. These differences arise from the underlying band structures of each material.

An understanding of Electric Field Intensity provides insight into how charge carrier mobility is affected by temperature in different materials.

Applications of Temperature Dependence of Resistance

• Material selection for resistors and heating elements
• Temperature sensors and thermistors
• Improvement of circuit stability in varying thermal conditions
• Fabrication of semiconductor devices and integrated circuits

Special Cases: Superconductors and Critical Temperature

Superconductors are materials that exhibit zero resistance below a specific temperature known as the critical temperature. Above this critical temperature, the material behaves as a normal conductor with measurable resistance.

This phenomenon is distinctly different from the temperature dependence observed in metals, semiconductors, and insulators, and is an important research area in condensed matter physics.

Key Points in the Effect of Temperature on Resistance

• Metals: resistance increases with temperature
• Semiconductors: resistance decreases with temperature
• Alloys: resistance remains nearly unchanged
• Insulators: resistance decreases with temperature

Conclusion on Temperature and Resistance Relationship

The effect of temperature on resistance depends on the type of material. Conductors show a positive temperature coefficient, while semiconductors, insulators, and electrolytes have a negative temperature coefficient. Alloys possess almost temperature-independent resistance in the practical range. These properties are essential in material selection and circuit design.

Knowledge of temperature effects is important for analyzing electrical circuits and devices, and helps in understanding related concepts such as Solve Any Electric Circuit and the functioning of devices like Heat Pump and different Temperature Scales.