Umair Gaines
The electrical resistance of a material generally increases with temperature. This is because as the temperature rises, the atomic lattice of the conductor vibrates more, leading to increased collisions between the atoms and electrons. This makes it harder for electrons to pass through the conductor, thereby increasing resistance. The relationship between temperature and resistance is quantified by the temperature coefficient of resistance, which varies depending on the material. For example, elemental metals like copper typically experience a resistance increase of about +0.4% per Kelvin near room temperature.
| Characteristics | Values |
|---|---|
| Reason for increase in electrical resistance with temperature | Atoms and molecules in the conductor vibrate more with an increase in temperature, impeding the flow of electrons. |
| Effect on resistivity | Resistivity is directly proportional to temperature. |
| Effect on conductivity | Conductivity increases with an increase in temperature. |
| Effect on electrons | Higher temperatures cause more electrons to be freed from their valence duties, increasing the number of electrons conducting electricity. |
| Effect on collisions | More collisions occur between free and captive electrons due to the increased vibration of atoms. |
| Effect on current | Current increases as more electrons are freed. |
| Materials with a positive temperature coefficient | Conductors generally have a positive temperature coefficient. |
| Materials with a negative temperature coefficient | Insulators generally have a negative temperature coefficient. |
| Exceptions | In some materials, such as silicon, resistance decreases as temperature increases due to an increase in free charge carriers. |
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What You'll Learn
- Vibrations of atoms within a metal lattice increase with temperature
- The number of free electrons increases with temperature
- The mean time between collisions decreases with temperature
- Resistors can be made with resistance independent of temperature
- Conductors have a positive temperature coefficient, insulators have a negative one
Vibrations of atoms within a metal lattice increase with temperature
The vibration of atoms within a metal lattice increases with temperature. This phenomenon is fundamental to understanding why electrical resistance increases with temperature.
When a current is passed through a metal wire, the electrons encounter resistance due to collisions with the metal atoms. As the temperature rises, the atoms in the metal lattice vibrate more vigorously, increasing the likelihood of collisions with electrons. This heightened collision frequency impedes the flow of electrons, leading to increased electrical resistance.
The relationship between temperature and atomic vibrations is such that higher temperatures correspond to more energetic and frequent atomic vibrations. This increase in atomic motion is what ultimately gives rise to the observed increase in electrical resistance.
It is important to note that the impact of temperature on resistance is not solely due to atomic vibrations. The temperature coefficient of resistance, denoted as 'α', also plays a role. This coefficient represents the fractional increase in resistivity per unit rise in temperature. Different materials have distinct temperature coefficients, influencing how their resistance changes with temperature.
Additionally, the effect of temperature on resistance can vary depending on the type of material. For example, in semiconductors, an increase in temperature can lead to a higher number of free electrons available for conduction, resulting in increased conductivity and, consequently, decreased resistance. This behavior is attributed to the unique characteristics of semiconductor materials, where most electrons are typically engaged in valence bonding between atoms.
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The number of free electrons increases with temperature
The number of free electrons in a material is a key factor in determining its electrical conductivity. Materials with many free electrons are good conductors, while those with few free electrons are good insulators. When the temperature increases, the atoms within the material vibrate more violently, shaking free electrons from their valence duties. These freed electrons can then contribute to the conduction of electricity. Therefore, an increase in temperature leads to an increase in the number of free electrons, enhancing the material's electrical conductivity.
In a conductor, the increased temperature causes the atoms to vibrate more, resulting in more collisions between the captive and free electrons. Each collision depletes some energy from the free electron, leading to increased resistance. This phenomenon is observed in materials with a positive temperature coefficient, where resistance increases with temperature.
However, the relationship between temperature and resistance is more complex in semiconductors. In these materials, most electrons are engaged in valence bonding between atoms, with only a small number of free electrons available for conduction. As temperature rises, more electrons are shaken free from their valence bonds, increasing the number of free electrons available for conduction. Consequently, the conductivity of semiconductors increases with temperature.
The impact of temperature on resistance can be quantified using the temperature coefficient of resistance, denoted as "α." This coefficient represents the fractional increase in resistivity per unit rise in temperature. Different materials have distinct temperature coefficients, and the specific value of "α" depends on the material's properties.
The number of free electrons within a material is not the sole determinant of its electrical resistance. Other factors, such as the length and cross-sectional area of the material, also play a significant role. Additionally, the material's composition is crucial, as different substances exhibit varying responses to temperature changes, with some materials, like silicon, demonstrating a decrease in resistance as temperature rises.
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The mean time between collisions decreases with temperature
The movement of electrons through a conductor is impeded by atoms and molecules. As the temperature increases, the vibrations of atoms within the metal lattice increase. This leads to a higher frequency of collisions between electrons and atoms, reducing the mean time between collisions. Consequently, the resistance to electron flow increases.
The mean time between collisions is influenced by the temperature-dependent mobility of the material. As temperature rises, the mobility of the material decreases, resulting in a shorter interval between collisions. This relationship is described by the equation μd ∝ 1/T, where μd represents the mobility of the material and T denotes the temperature.
The impact of temperature on resistance is also associated with the temperature coefficient of resistance, denoted by α. This coefficient quantifies the fractional increase in resistivity per unit rise in temperature. It is calculated using the formula α = 1/ρ*(dρ/dT), where ρ represents the resistivity.
The temperature coefficient of resistance varies among materials. Conductors typically exhibit a positive temperature coefficient, indicating that their resistance increases with temperature. On the other hand, insulators generally demonstrate a negative temperature coefficient, signifying that their resistance decreases as temperature rises.
The decrease in the mean time between collisions with increasing temperature is a critical factor contributing to the overall increase in electrical resistance. The heightened atomic vibrations and the resulting increase in collisions act as obstacles to the flow of electrons, leading to higher resistance within the conductor.
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Resistors can be made with resistance independent of temperature
The relationship between temperature and resistance is a unique one. Resistance depends on the geometry of a conductor, the material it is made of, and the temperature. Electrons flowing through a conductor are impeded by atoms and molecules. As the temperature increases, the vibrations of the atoms within the metal lattice increase, and this leads to increased resistance to the electron flow.
However, in some materials, such as silicon, the resistance decreases as the temperature increases. This is because an increase in temperature can free more charge carriers, which would be associated with an increase in current. This means that the increase in resistance experienced by one resistor can be offset by the decrease in resistance experienced by another. This can be exploited to make a resistor with a resistance that is almost independent of temperature.
Some metallic alloys, such as nichrome, manganin, constantan, and eureka, have large resistivities and very low temperature coefficients. These materials can also be used to create resistors with resistance that is relatively independent of temperature. By using these materials, the impact of temperature changes on resistance can be minimised, resulting in a more stable and consistent resistor performance.
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Conductors have a positive temperature coefficient, insulators have a negative one
The temperature coefficient of resistance, a, of a metal or other substance is the fractional increase in its resistivity per unit rise in temperature. A positive temperature coefficient indicates that a material's resistance increases with an increase in temperature, while a negative temperature coefficient indicates that a material's resistance decreases with an increase in temperature.
Conductors, such as pure metals, have a positive temperature coefficient of resistance. This means that as the temperature increases, the resistance of the conductor also increases. This is because conductors have a large number of free electrons flowing through them, and when the temperature rises, the atoms in the conductor vibrate more violently, causing more collisions between the free electrons and the atoms. These collisions impede the flow of electrons, increasing the resistance. Additionally, in some conductors, an increase in temperature can lead to a decrease in the mean time or path length between collisions, further contributing to the increased resistance.
Insulators, on the other hand, typically have a negative temperature coefficient, especially at high temperatures. Insulating materials have hardly any free electrons, as most of the electrons are tightly bound within their respective atoms. When an insulator is heated, the atoms vibrate, and if heated sufficiently, the atoms vibrate violently enough to shake some electrons free. This results in an increased number of free electrons available to carry the current, leading to a decrease in resistance despite the increased collisions. Materials used for practical insulators, such as glass and plastic, only exhibit this behaviour at very high temperatures and remain good insulators within their working temperature range.
It is important to note that the temperature coefficient of resistance can vary among different materials within the same group. For example, some metallic alloys have very low temperature coefficients, meaning their resistance changes only slightly with temperature fluctuations. Additionally, semiconductor materials, such as carbon, silicon, and germanium, typically have negative temperature coefficients, meaning their resistance decreases as temperature increases.
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Frequently asked questions
The resistance of a conductor increases with temperature because as the temperature increases, the atomic lattice of the conductor vibrates more due to having more energy. This makes it more likely for electrons travelling within the conductor to interact with atoms, increasing resistance.
Electrons flowing through a conductor are impeded by atoms and molecules. The more these atoms and molecules vibrate, the harder it is for electrons to pass through. Electrons can be shaken free from their valence duties and contribute to conducting electricity as temperature increases.
The temperature coefficient of resistance, α, of a metal or other substance, is the fractional increase in its resistivity per unit rise in temperature. It is expressed in SI units as K-1. A positive temperature coefficient indicates that resistance increases with temperature, while a negative temperature coefficient indicates that resistance decreases as temperature increases.
The material of a conductor plays a significant role in determining its resistance to temperature. Different materials have different temperature coefficients, and the resistivity of a material is directly proportional to temperature. Elemental metals like copper typically increase in resistance by about +0.4% per Kelvin near room temperature.
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