Why Ohm's law is not applicable at very low temperature?
2 Answers
Ohm's Law, which states that the current (I) flowing through a conductor between two points is directly proportional to the voltage (V) across those two points, is expressed mathematically as:
\[ V = I \times R \]
where \( R \) is the resistance. This law works well under normal conditions, but its applicability can break down under certain circumstances, particularly at very low temperatures. Here are several reasons why Ohm's Law does not hold true at very low temperatures:
### 1. **Quantum Effects and Electron Behavior**
At very low temperatures (close to absolute zero), the behavior of electrons in conductors can no longer be described adequately by classical physics. Quantum mechanical effects start to dominate, leading to phenomena such as:
- **Quantum tunneling:** Electrons can pass through energy barriers instead of going over them, which affects conductivity.
- **Superconductivity:** Certain materials become superconductors at low temperatures, exhibiting zero electrical resistance. In these materials, an electric current can flow indefinitely without any voltage applied, thus violating the principles of Ohm’s Law.
### 2. **Increased Impurity Scattering**
At low temperatures, the thermal vibrations of atoms in a material decrease, which might suggest reduced resistance. However, impurities and defects in the material can scatter electrons more significantly. This increased scattering can lead to variations in resistance that are not accounted for by Ohm’s Law.
### 3. **Electron-Phonon Interactions**
At low temperatures, the interaction between electrons and lattice vibrations (phonons) becomes significant. The phonons can affect how electrons move through a material, potentially leading to non-linear relationships between current and voltage. This non-linearity means that resistance is not constant, which violates one of the core assumptions of Ohm's Law.
### 4. **Non-metallic Behavior**
In many materials, particularly semiconductors and insulators, the resistance can change dramatically with temperature. At very low temperatures, these materials may behave more like insulators than conductors, leading to behaviors that are inconsistent with Ohm’s Law.
### 5. **Insufficient Thermal Energy**
At low temperatures, the thermal energy available is insufficient to excite electrons to higher energy states. This can lead to a situation where the material does not conduct electricity well, and the relationship between current and voltage becomes more complex than what Ohm's Law describes.
### 6. **Superconductors and Meissner Effect**
When materials enter a superconducting state (usually at very low temperatures), they exhibit the Meissner effect, where they expel magnetic fields and have no electrical resistance. This means that the application of Ohm’s Law (which implies a resistive response to voltage) is not applicable.
### Conclusion
In summary, while Ohm's Law is a fundamental principle in electrical engineering and physics, its application becomes increasingly complex at very low temperatures due to quantum effects, changes in material properties, and the behavior of electrons under different thermal conditions. As temperatures drop, materials may transition to superconducting states or experience significant non-linear effects, making the straightforward relationship defined by Ohm's Law inapplicable. Understanding these phenomena requires a more nuanced approach that incorporates quantum mechanics and the specific material properties at low temperatures.
\[ V = I \times R \]
where \( R \) is the resistance. This law works well under normal conditions, but its applicability can break down under certain circumstances, particularly at very low temperatures. Here are several reasons why Ohm's Law does not hold true at very low temperatures:
### 1. **Quantum Effects and Electron Behavior**
At very low temperatures (close to absolute zero), the behavior of electrons in conductors can no longer be described adequately by classical physics. Quantum mechanical effects start to dominate, leading to phenomena such as:
- **Quantum tunneling:** Electrons can pass through energy barriers instead of going over them, which affects conductivity.
- **Superconductivity:** Certain materials become superconductors at low temperatures, exhibiting zero electrical resistance. In these materials, an electric current can flow indefinitely without any voltage applied, thus violating the principles of Ohm’s Law.
### 2. **Increased Impurity Scattering**
At low temperatures, the thermal vibrations of atoms in a material decrease, which might suggest reduced resistance. However, impurities and defects in the material can scatter electrons more significantly. This increased scattering can lead to variations in resistance that are not accounted for by Ohm’s Law.
### 3. **Electron-Phonon Interactions**
At low temperatures, the interaction between electrons and lattice vibrations (phonons) becomes significant. The phonons can affect how electrons move through a material, potentially leading to non-linear relationships between current and voltage. This non-linearity means that resistance is not constant, which violates one of the core assumptions of Ohm's Law.
### 4. **Non-metallic Behavior**
In many materials, particularly semiconductors and insulators, the resistance can change dramatically with temperature. At very low temperatures, these materials may behave more like insulators than conductors, leading to behaviors that are inconsistent with Ohm’s Law.
### 5. **Insufficient Thermal Energy**
At low temperatures, the thermal energy available is insufficient to excite electrons to higher energy states. This can lead to a situation where the material does not conduct electricity well, and the relationship between current and voltage becomes more complex than what Ohm's Law describes.
### 6. **Superconductors and Meissner Effect**
When materials enter a superconducting state (usually at very low temperatures), they exhibit the Meissner effect, where they expel magnetic fields and have no electrical resistance. This means that the application of Ohm’s Law (which implies a resistive response to voltage) is not applicable.
### Conclusion
In summary, while Ohm's Law is a fundamental principle in electrical engineering and physics, its application becomes increasingly complex at very low temperatures due to quantum effects, changes in material properties, and the behavior of electrons under different thermal conditions. As temperatures drop, materials may transition to superconducting states or experience significant non-linear effects, making the straightforward relationship defined by Ohm's Law inapplicable. Understanding these phenomena requires a more nuanced approach that incorporates quantum mechanics and the specific material properties at low temperatures.
Ohm's Law states that the current through a conductor between two points is directly proportional to the voltage across the two points, provided that the temperature remains constant. However, Ohm's Law is not universally applicable under all conditions, particularly at very low temperatures. Here's why:
### 1. **Material Properties Change:**
At extremely low temperatures, the electrical properties of materials can undergo significant changes. For example, in many materials (especially metals), the resistivity decreases as the temperature lowers, due to the reduction in lattice vibrations that scatter electrons.
- **Superconductivity**: For some materials, when they reach a critical low temperature, they enter a state called *superconductivity*, where their electrical resistance drops to zero. In this state, Ohm's Law breaks down completely because the relationship between current and voltage is no longer linear. A superconductor can carry current without any applied voltage.
### 2. **Quantum Effects**:
At very low temperatures, quantum mechanical effects become dominant, especially in conductors or semiconductors. The behavior of electrons in such materials deviates from classical physics (which Ohm's Law is based on), and phenomena like *quantum tunneling* and *electron wave interference* can occur, where the electron's behavior cannot be accurately described by Ohm's Law.
### 3. **Non-Linear Conduction**:
In some materials, at low temperatures, conduction becomes non-linear due to the effects of impurities, defects, or the atomic structure of the material itself. This non-linearity means the current is not proportional to the applied voltage, violating the assumption that Ohm’s Law holds.
### 4. **Semiconductor Behavior**:
In semiconductors, as the temperature drops, the number of thermally excited charge carriers (electrons and holes) decreases. This reduction in charge carriers can cause the material to behave more like an insulator, and the current may not follow a simple linear relationship with voltage, which violates Ohm’s Law.
### 5. **Phonon Scattering Reduction**:
At lower temperatures, there is reduced phonon scattering (the interaction between electrons and the vibrating atoms in a material), which affects the resistivity of the material. The drastic change in resistivity does not always allow for a simple application of Ohm's Law.
In summary, at very low temperatures, the behavior of materials often deviates from the conditions under which Ohm’s Law applies, mainly due to changes in the material's electrical properties, the onset of quantum effects, and the possible transition to superconductivity.
### 1. **Material Properties Change:**
At extremely low temperatures, the electrical properties of materials can undergo significant changes. For example, in many materials (especially metals), the resistivity decreases as the temperature lowers, due to the reduction in lattice vibrations that scatter electrons.
- **Superconductivity**: For some materials, when they reach a critical low temperature, they enter a state called *superconductivity*, where their electrical resistance drops to zero. In this state, Ohm's Law breaks down completely because the relationship between current and voltage is no longer linear. A superconductor can carry current without any applied voltage.
### 2. **Quantum Effects**:
At very low temperatures, quantum mechanical effects become dominant, especially in conductors or semiconductors. The behavior of electrons in such materials deviates from classical physics (which Ohm's Law is based on), and phenomena like *quantum tunneling* and *electron wave interference* can occur, where the electron's behavior cannot be accurately described by Ohm's Law.
### 3. **Non-Linear Conduction**:
In some materials, at low temperatures, conduction becomes non-linear due to the effects of impurities, defects, or the atomic structure of the material itself. This non-linearity means the current is not proportional to the applied voltage, violating the assumption that Ohm’s Law holds.
### 4. **Semiconductor Behavior**:
In semiconductors, as the temperature drops, the number of thermally excited charge carriers (electrons and holes) decreases. This reduction in charge carriers can cause the material to behave more like an insulator, and the current may not follow a simple linear relationship with voltage, which violates Ohm’s Law.
### 5. **Phonon Scattering Reduction**:
At lower temperatures, there is reduced phonon scattering (the interaction between electrons and the vibrating atoms in a material), which affects the resistivity of the material. The drastic change in resistivity does not always allow for a simple application of Ohm's Law.
In summary, at very low temperatures, the behavior of materials often deviates from the conditions under which Ohm’s Law applies, mainly due to changes in the material's electrical properties, the onset of quantum effects, and the possible transition to superconductivity.