Why Ohms law is not applicable at very low temperature?
2 Answers
Ohm's Law, which states that \( V = IR \) (voltage = current × resistance), is a fundamental principle in electrical engineering that holds true under many conditions. However, at very low temperatures, its applicability can be challenged due to changes in the behavior of materials.
Here’s why Ohm's Law might not hold as expected at very low temperatures:
### 1. **Superconductivity:**
At temperatures below a certain critical point, certain materials become superconductors. In a superconducting state, these materials have zero electrical resistance. This means that while Ohm’s Law (which implies a non-zero resistance) doesn't apply in the usual sense, the relationship \( V = IR \) becomes irrelevant because \( R \) is zero, so theoretically, any voltage applied across a superconductor would not result in a current (in a steady-state situation).
### 2. **Temperature Dependence of Resistance:**
For most conductive materials, resistance decreases as temperature decreases. This is due to reduced lattice vibrations and electron scattering. The relationship between resistance and temperature isn’t linear, and in some cases, it follows more complex behaviors like the ones described by the Drude model or the BCS theory for superconductors.
### 3. **Quantum Effects:**
At extremely low temperatures, quantum mechanical effects become significant. The behavior of electrons and phonons (quantum of lattice vibrations) can no longer be described accurately by classical models. In such regimes, resistivity can exhibit phenomena not predicted by Ohm's Law, such as quantized conductance in 2D electron systems.
### 4. **Insulator-to-Metal Transition:**
In certain materials, the nature of the electrical conduction can change drastically with temperature. Some materials that are insulators at higher temperatures may become conductors at very low temperatures due to changes in their electronic structure.
### 5. **Nonlinear Effects:**
At very low temperatures, nonlinear effects can become significant. For example, in some semiconductors, the carrier concentration and mobility can change in non-linear ways with temperature, affecting how current responds to voltage.
### Summary:
Ohm’s Law is a good approximation for many practical situations, but at very low temperatures, deviations can occur due to superconductivity, changes in resistance, quantum effects, insulator-to-metal transitions, and nonlinear effects. In these cases, more complex models and theories are required to describe the electrical behavior accurately.
Here’s why Ohm's Law might not hold as expected at very low temperatures:
### 1. **Superconductivity:**
At temperatures below a certain critical point, certain materials become superconductors. In a superconducting state, these materials have zero electrical resistance. This means that while Ohm’s Law (which implies a non-zero resistance) doesn't apply in the usual sense, the relationship \( V = IR \) becomes irrelevant because \( R \) is zero, so theoretically, any voltage applied across a superconductor would not result in a current (in a steady-state situation).
### 2. **Temperature Dependence of Resistance:**
For most conductive materials, resistance decreases as temperature decreases. This is due to reduced lattice vibrations and electron scattering. The relationship between resistance and temperature isn’t linear, and in some cases, it follows more complex behaviors like the ones described by the Drude model or the BCS theory for superconductors.
### 3. **Quantum Effects:**
At extremely low temperatures, quantum mechanical effects become significant. The behavior of electrons and phonons (quantum of lattice vibrations) can no longer be described accurately by classical models. In such regimes, resistivity can exhibit phenomena not predicted by Ohm's Law, such as quantized conductance in 2D electron systems.
### 4. **Insulator-to-Metal Transition:**
In certain materials, the nature of the electrical conduction can change drastically with temperature. Some materials that are insulators at higher temperatures may become conductors at very low temperatures due to changes in their electronic structure.
### 5. **Nonlinear Effects:**
At very low temperatures, nonlinear effects can become significant. For example, in some semiconductors, the carrier concentration and mobility can change in non-linear ways with temperature, affecting how current responds to voltage.
### Summary:
Ohm’s Law is a good approximation for many practical situations, but at very low temperatures, deviations can occur due to superconductivity, changes in resistance, quantum effects, insulator-to-metal transitions, and nonlinear effects. In these cases, more complex models and theories are required to describe the electrical behavior accurately.
Ohm's Law states that the current (I) passing through a conductor is directly proportional to the voltage (V) across it and inversely proportional to the resistance (R) of the material, expressed as:
\[
V = I \times R
\]
For most materials, this relationship holds true under standard conditions of temperature and pressure. However, at **very low temperatures**, especially near absolute zero, certain materials exhibit unusual behavior where Ohm's Law may no longer apply as straightforwardly. There are several reasons for this:
### 1. **Superconductivity**
At very low temperatures, some materials enter a **superconducting state**, in which they exhibit **zero electrical resistance**. In this state:
- **Superconductors** allow current to flow without any voltage drop, which violates the basic premise of Ohm's Law that \( V = I \times R \), since \( R = 0 \).
- Once the material becomes superconducting, a current can flow indefinitely without the need for a continuous supply of voltage.
The critical temperature (known as the **transition temperature**) below which a material becomes superconducting varies, but it is usually very low, often close to **absolute zero (0 K or -273.15°C)**. Well-known superconducting materials include metals like lead, mercury, and alloys.
### 2. **Non-Linear Behavior of Semiconductors**
At very low temperatures, **semiconductors** behave differently compared to at room temperature. Normally, in semiconductors, the movement of charge carriers (electrons and holes) depends on thermal energy:
- As the temperature decreases, the number of thermally excited charge carriers in a semiconductor decreases drastically, leading to a situation where the current flow is no longer directly proportional to the voltage.
- This means that **Ohm’s Law fails** because the relationship between voltage and current becomes **non-linear** due to the lack of mobile charge carriers.
At extremely low temperatures, many semiconductors can behave more like insulators because the thermal energy is insufficient to promote electrons from the valence band to the conduction band.
### 3. **Quantum Effects in Conductors**
At temperatures close to absolute zero, **quantum mechanical effects** dominate the behavior of electrons in conductors. In this regime:
- **Electron transport** is no longer dominated by classical behavior, but rather by quantum tunneling and other effects, which can result in **non-linear current-voltage relationships**.
- Ohm's Law assumes that current flow is due to electrons scattering off impurities or lattice vibrations (phonons), which produce a constant resistance. But at low temperatures, **phonon activity is minimal**, so electron behavior is governed more by quantum interference and coherence, not by scattering as it is at higher temperatures.
### 4. **Contact and Interface Resistance**
At very low temperatures, certain materials may experience changes at the **interfaces between different materials**. In particular:
- **Contact resistance** between a conductor and a device can become significant, and its behavior can become temperature-dependent.
- Interfaces between different materials can cause non-ohmic behavior, where resistance varies in a non-linear way with the applied voltage.
### 5. **Changes in Material Properties**
- Many materials undergo structural changes at low temperatures, which can alter their **resistive properties**. For example, the mobility of electrons or the density of charge carriers may change, which directly affects the resistance of the material.
- **Insulating materials** can undergo changes that make them more conductive or less conductive at extremely low temperatures, further complicating the application of Ohm’s Law.
### Summary
At very low temperatures, Ohm's Law is not applicable in certain cases due to phenomena like superconductivity, quantum effects, and the non-linear behavior of semiconductors. These effects lead to situations where the voltage-current relationship is no longer linear, as Ohm’s Law predicts. In superconductors, for example, the resistance becomes zero, causing current to flow without any applied voltage, while in semiconductors, the reduced thermal energy can prevent the creation of charge carriers necessary for current flow.
Thus, the classical understanding of Ohm's Law holds true primarily at **moderate temperatures** and under normal conditions but breaks down in these extreme low-temperature scenarios.
\[
V = I \times R
\]
For most materials, this relationship holds true under standard conditions of temperature and pressure. However, at **very low temperatures**, especially near absolute zero, certain materials exhibit unusual behavior where Ohm's Law may no longer apply as straightforwardly. There are several reasons for this:
### 1. **Superconductivity**
At very low temperatures, some materials enter a **superconducting state**, in which they exhibit **zero electrical resistance**. In this state:
- **Superconductors** allow current to flow without any voltage drop, which violates the basic premise of Ohm's Law that \( V = I \times R \), since \( R = 0 \).
- Once the material becomes superconducting, a current can flow indefinitely without the need for a continuous supply of voltage.
The critical temperature (known as the **transition temperature**) below which a material becomes superconducting varies, but it is usually very low, often close to **absolute zero (0 K or -273.15°C)**. Well-known superconducting materials include metals like lead, mercury, and alloys.
### 2. **Non-Linear Behavior of Semiconductors**
At very low temperatures, **semiconductors** behave differently compared to at room temperature. Normally, in semiconductors, the movement of charge carriers (electrons and holes) depends on thermal energy:
- As the temperature decreases, the number of thermally excited charge carriers in a semiconductor decreases drastically, leading to a situation where the current flow is no longer directly proportional to the voltage.
- This means that **Ohm’s Law fails** because the relationship between voltage and current becomes **non-linear** due to the lack of mobile charge carriers.
At extremely low temperatures, many semiconductors can behave more like insulators because the thermal energy is insufficient to promote electrons from the valence band to the conduction band.
### 3. **Quantum Effects in Conductors**
At temperatures close to absolute zero, **quantum mechanical effects** dominate the behavior of electrons in conductors. In this regime:
- **Electron transport** is no longer dominated by classical behavior, but rather by quantum tunneling and other effects, which can result in **non-linear current-voltage relationships**.
- Ohm's Law assumes that current flow is due to electrons scattering off impurities or lattice vibrations (phonons), which produce a constant resistance. But at low temperatures, **phonon activity is minimal**, so electron behavior is governed more by quantum interference and coherence, not by scattering as it is at higher temperatures.
### 4. **Contact and Interface Resistance**
At very low temperatures, certain materials may experience changes at the **interfaces between different materials**. In particular:
- **Contact resistance** between a conductor and a device can become significant, and its behavior can become temperature-dependent.
- Interfaces between different materials can cause non-ohmic behavior, where resistance varies in a non-linear way with the applied voltage.
### 5. **Changes in Material Properties**
- Many materials undergo structural changes at low temperatures, which can alter their **resistive properties**. For example, the mobility of electrons or the density of charge carriers may change, which directly affects the resistance of the material.
- **Insulating materials** can undergo changes that make them more conductive or less conductive at extremely low temperatures, further complicating the application of Ohm’s Law.
### Summary
At very low temperatures, Ohm's Law is not applicable in certain cases due to phenomena like superconductivity, quantum effects, and the non-linear behavior of semiconductors. These effects lead to situations where the voltage-current relationship is no longer linear, as Ohm’s Law predicts. In superconductors, for example, the resistance becomes zero, causing current to flow without any applied voltage, while in semiconductors, the reduced thermal energy can prevent the creation of charge carriers necessary for current flow.
Thus, the classical understanding of Ohm's Law holds true primarily at **moderate temperatures** and under normal conditions but breaks down in these extreme low-temperature scenarios.