Mobility And Temperature Dependence Of Resistivity- Current And Electricity - Problems On Temperature Dependent Resistor

Slide 1:

Mobility and temperature dependence of resistivity

Resistivity is the property of a material that determines how strongly it resists the flow of electric current.
It is denoted by the symbol ρ (rho).
Mobility is a measure of how easily charges can move through a material under the influence of an electric field.
It is denoted by the symbol μ (mu).
Both resistivity and mobility are dependent on temperature.

Slide 2:

Factors affecting resistivity

Atomic structure: Materials with a regular and well-ordered atomic structure have lower resistivity.
Temperature: Resistivity generally increases with temperature for most materials.
Impurities: Introduction of impurities in a material can increase its resistivity.
Crystal lattice defects: Dislocations, vacancies, and interstitials in a crystal lattice can also affect resistivity.
Composition: The type and concentration of elements present in a material affect its resistivity.

Slide 3:

Temperature dependence of resistivity

For metals, resistivity increases with temperature due to increased collisions between electrons and lattice vibrations.
For most insulators, resistivity decreases with an increase in temperature as more charge carriers become available.
For intrinsic semiconductors, resistivity decreases with temperature due to increased mobility of charge carriers.
For extrinsic semiconductors, the temperature dependence of resistivity depends on the dopant concentration and the type of impurity.

Slide 4:

Temperature coefficient of resistivity

The temperature coefficient of resistivity (α) quantifies the change in resistivity with temperature.
It is given by the equation α = (ρ2 - ρ1)/ (ρ1 * (T2 - T1)).
Here, ρ2 and ρ1 are resistivities at temperatures T2 and T1 respectively.
The unit of α is per °C or per K (Kelvin).
Depending on the material, α can have positive, negative, or zero values.

Slide 5:

Mobility

Mobility is a measure of how easily charges can move through a material when subjected to an electric field.
It is defined as the ratio of the average velocity of a charged particle to the magnitude of the electric field.
Mobility is denoted by the symbol μ (mu) and its unit is m^2/Vs (meters squared per volt-second).
It depends on the charge and mass of the carrier, temperature, and the scattering mechanisms present in the material.

Slide 6:

Temperature dependence of mobility

The mobility of charge carriers in a material can be affected by temperature.
In metals, mobility decreases with an increase in temperature due to increased collisions with lattice vibrations.
In intrinsic semiconductors, mobility increases with temperature as the charge carriers gain more energy to overcome lattice scattering.
In extrinsic semiconductors, the temperature dependence of mobility depends on the type of dopant and its concentration.

Slide 7:

Drift velocity

Drift velocity is the average velocity attained by charge carriers (electrons or holes) in a material under the influence of an electric field.
It is given by the equation vd = μ * E, where vd is the drift velocity, μ is the mobility, and E is the electric field.
Drift velocity is directly proportional to the applied electric field and inversely proportional to the mobility of the charge carriers.

Slide 8:

Applications of temperature dependence of resistivity and mobility

Thermistors: Thermistors are temperature-sensitive resistors that can be used as temperature sensors or in circuits that require temperature-dependent resistance.
Semiconductors: The temperature dependence of resistivity and mobility is crucial in understanding the behavior of semiconductor devices such as diodes, transistors, and integrated circuits.
Superconductors: Superconductors have zero resistivity at very low temperatures, enabling the flow of electric current without any loss of energy.

Slide 9:

Example: Temperature coefficient of resistivity calculation

Let’s calculate the temperature coefficient of resistivity for a metal wire using the given values:
- Resistivity at room temperature (ρ1) = 1.5 x 10^-6 Ω m
- Resistivity at higher temperature (ρ2) = 1.8 x 10^-6 Ω m
- Room temperature (T1) = 25 °C = 298 K
- Higher temperature (T2) = 90 °C = 363 K
Using the formula α = (ρ2 - ρ1)/ (ρ1 * (T2 - T1)), substitute the values and calculate the temperature coefficient of resistivity.

Slide 10:

Equation: Temperature coefficient of resistivity (α)

The temperature coefficient of resistivity (α) can be calculated using the equation: α = (ρ2 - ρ1)/ (ρ1 * (T2 - T1))
Here, ρ2 and ρ1 are resistivities at temperatures T2 and T1 respectively.
The unit of α is per degree Celsius (°C) or per Kelvin (K).
This equation helps us understand how the resistivity changes with temperature in different materials.

Slide 11:

Mobility and temperature dependence of resistivity

Resistivity is the property of a material that determines how strongly it resists the flow of electric current.
It is denoted by the symbol ρ (rho).
Mobility is a measure of how easily charges can move through a material under the influence of an electric field.
It is denoted by the symbol μ (mu).
Both resistivity and mobility are dependent on temperature.

Slide 12:

Factors affecting resistivity

Atomic structure: Materials with a regular and well-ordered atomic structure have lower resistivity.
Temperature: Resistivity generally increases with temperature for most materials.
Impurities: Introduction of impurities in a material can increase its resistivity.
Crystal lattice defects: Dislocations, vacancies, and interstitials in a crystal lattice can also affect resistivity.
Composition: The type and concentration of elements present in a material affect its resistivity.

Slide 13:

Temperature dependence of resistivity

For metals, resistivity increases with temperature due to increased collisions between electrons and lattice vibrations.
For most insulators, resistivity decreases with an increase in temperature as more charge carriers become available.
For intrinsic semiconductors, resistivity decreases with temperature due to increased mobility of charge carriers.
For extrinsic semiconductors, the temperature dependence of resistivity depends on the dopant concentration and the type of impurity.

Slide 14:

Temperature coefficient of resistivity

The temperature coefficient of resistivity (α) quantifies the change in resistivity with temperature.
It is given by the equation α = (ρ2 - ρ1)/ (ρ1 * (T2 - T1)).
Here, ρ2 and ρ1 are resistivities at temperatures T2 and T1 respectively.
The unit of α is per °C or per K (Kelvin).
Depending on the material, α can have positive, negative, or zero values.

Slide 15:

Mobility

Mobility is a measure of how easily charges can move through a material when subjected to an electric field.
It is defined as the ratio of the average velocity of a charged particle to the magnitude of the electric field.
Mobility is denoted by the symbol μ (mu) and its unit is m^2/Vs (meters squared per volt-second).
It depends on the charge and mass of the carrier, temperature, and the scattering mechanisms present in the material.

Slide 16:

Temperature dependence of mobility

The mobility of charge carriers in a material can be affected by temperature.
In metals, mobility decreases with an increase in temperature due to increased collisions with lattice vibrations.
In intrinsic semiconductors, mobility increases with temperature as the charge carriers gain more energy to overcome lattice scattering.
In extrinsic semiconductors, the temperature dependence of mobility depends on the type of dopant and its concentration.

Slide 17:

Drift velocity

Drift velocity is the average velocity attained by charge carriers (electrons or holes) in a material under the influence of an electric field.
It is given by the equation vd = μ * E, where vd is the drift velocity, μ is the mobility, and E is the electric field.
Drift velocity is directly proportional to the applied electric field and inversely proportional to the mobility of the charge carriers.

Slide 18:

Applications of temperature dependence of resistivity and mobility

Thermistors: Thermistors are temperature-sensitive resistors that can be used as temperature sensors or in circuits that require temperature-dependent resistance.
Semiconductors: The temperature dependence of resistivity and mobility is crucial in understanding the behavior of semiconductor devices such as diodes, transistors, and integrated circuits.
Superconductors: Superconductors have zero resistivity at very low temperatures, enabling the flow of electric current without any loss of energy.

Slide 19:

Example: Temperature coefficient of resistivity calculation

Let’s calculate the temperature coefficient of resistivity for a metal wire using the given values:
- Resistivity at room temperature (ρ1) = 1.5 x 10^-6 Ω m
- Resistivity at higher temperature (ρ2) = 1.8 x 10^-6 Ω m
- Room temperature (T1) = 25 °C = 298 K
- Higher temperature (T2) = 90 °C = 363 K
Using the formula α = (ρ2 - ρ1)/ (ρ1 * (T2 - T1)), substitute the values and calculate the temperature coefficient of resistivity.

Slide 20:

Equation: Temperature coefficient of resistivity (α)

The temperature coefficient of resistivity (α) can be calculated using the equation: α = (ρ2 - ρ1)/ (ρ1 * (T2 - T1))
Here, ρ2 and ρ1 are resistivities at temperatures T2 and T1 respectively.
The unit of α is per degree Celsius (°C) or per Kelvin (K).
This equation helps us understand how the resistivity changes with temperature in different materials.

Slide 21:

Mobility and temperature dependence of resistivity

Resistivity is the property of a material that determines how strongly it resists the flow of electric current.
It is denoted by the symbol ρ (rho).
Mobility is a measure of how easily charges can move through a material under the influence of an electric field.
It is denoted by the symbol μ (mu).
Both resistivity and mobility are dependent on temperature.

Slide 22:

Factors affecting resistivity

Atomic structure: Materials with a regular and well-ordered atomic structure have lower resistivity.
Temperature: Resistivity generally increases with temperature for most materials.
Impurities: Introduction of impurities in a material can increase its resistivity.
Crystal lattice defects: Dislocations, vacancies, and interstitials in a crystal lattice can also affect resistivity.
Composition: The type and concentration of elements present in a material affect its resistivity.

Slide 23:

Temperature dependence of resistivity

For metals, resistivity increases with temperature due to increased collisions between electrons and lattice vibrations.
For most insulators, resistivity decreases with an increase in temperature as more charge carriers become available.
For intrinsic semiconductors, resistivity decreases with temperature due to increased mobility of charge carriers.
For extrinsic semiconductors, the temperature dependence of resistivity depends on the dopant concentration and the type of impurity.

Slide 24:

Temperature coefficient of resistivity

The temperature coefficient of resistivity (α) quantifies the change in resistivity with temperature.
It is given by the equation α = (ρ2 - ρ1)/ (ρ1 * (T2 - T1)).
Here, ρ2 and ρ1 are resistivities at temperatures T2 and T1 respectively.
The unit of α is per °C or per K (Kelvin).
Depending on the material, α can have positive, negative, or zero values.

Slide 25:

Mobility

Mobility is a measure of how easily charges can move through a material when subjected to an electric field.
It is defined as the ratio of the average velocity of a charged particle to the magnitude of the electric field.
Mobility is denoted by the symbol μ (mu) and its unit is m^2/Vs (meters squared per volt-second).
It depends on the charge and mass of the carrier, temperature, and the scattering mechanisms present in the material.

Slide 26:

Temperature dependence of mobility

The mobility of charge carriers in a material can be affected by temperature.
In metals, mobility decreases with an increase in temperature due to increased collisions with lattice vibrations.
In intrinsic semiconductors, mobility increases with temperature as the charge carriers gain more energy to overcome lattice scattering.
In extrinsic semiconductors, the temperature dependence of mobility depends on the type of dopant and its concentration.

Slide 27:

Drift velocity

Drift velocity is the average velocity attained by charge carriers (electrons or holes) in a material under the influence of an electric field.
It is given by the equation vd = μ * E, where vd is the drift velocity, μ is the mobility, and E is the electric field.
Drift velocity is directly proportional to the applied electric field and inversely proportional to the mobility of the charge carriers.

Slide 28:

Applications of temperature dependence of resistivity and mobility

Thermistors: Thermistors are temperature-sensitive resistors that can be used as temperature sensors or in circuits that require temperature-dependent resistance.
Semiconductors: The temperature dependence of resistivity and mobility is crucial in understanding the behavior of semiconductor devices such as diodes, transistors, and integrated circuits.
Superconductors: Superconductors have zero resistivity at very low temperatures, enabling the flow of electric current without any loss of energy.

Slide 29:

Example: Temperature coefficient of resistivity calculation

Let’s calculate the temperature coefficient of resistivity for a metal wire using the given values:
- Resistivity at room temperature (ρ1) = 1.5 x 10^-6 Ω m
- Resistivity at higher temperature (ρ2) = 1.8 x 10^-6 Ω m
- Room temperature (T1) = 25 °C = 298 K
- Higher temperature (T2) = 90 °C = 363 K
Using the formula α = (ρ2 - ρ1)/ (ρ1 * (T2 - T1)), substitute the values and calculate the temperature coefficient of resistivity.

Slide 30:

Equation: Temperature coefficient of resistivity (α)

The temperature coefficient of resistivity (α) can be calculated using the equation: α = (ρ2 - ρ1)/ (ρ1 * (T2 - T1))
Here, ρ2 and ρ1 are resistivities at temperatures T2 and T1 respectively.
The unit of α is per degree Celsius (°C) or per Kelvin (K).
This equation helps us understand how the resistivity changes with temperature in different materials.