Detailed Notes on Mobility and Temperature Dependence of Resistivity - Current and Electricity

1. Drift Velocity and Mobility

Reference: NCERT Class 12, Chapter 3: Current Electricity

• Drift Velocity (vd)**: The average velocity acquired by charge carriers (electrons or holes) in a conductor under the influence of an electric field.

$$v_d = \frac{I}{neA}$$

Where,

• I is the current flowing through the conductor

• n is the number of charge carriers per unit volume (carrier concentration)

• e is the charge of an electron (1.6 x 10^-19 Coulombs)

• A is the cross-sectional area of the conductor

• Mobility (µ): The proportionality constant relating the drift velocity to the applied electric field.

$$\mu = \frac{v_d}{E}$$

Where,

• E is the electric field strength

• Mobility depends on the following factors:

  • Temperature: Mobility generally decreases with increasing temperature due to increased lattice vibrations and scattering of charge carriers.
  • Impurities: Impurities can act as scattering centers for charge carriers, reducing mobility.
  • Crystal Structure: The arrangement of atoms in a crystal lattice influences the mobility of charge carriers.

2. Temperature Dependence of Resistivity

Reference: NCERT Class 12, Chapter 3: Current Electricity

• Resistivity (ρ): The measure of a material’s opposition to the flow of electric current.

$$\rho = \frac{RA}{l}$$

Where,

• R is the resistance of the conductor

• l is the length of the conductor

• The temperature dependence of resistivity varies for different materials:

  • Metals: Resistivity increases with increasing temperature due to increased lattice vibrations and scattering of electrons.
  • Semiconductors: Resistivity decreases with increasing temperature due to increased carrier concentration and mobility.
  • Insulators: Resistivity remains relatively constant over a wide range of temperatures.

• The behavior of resistivity with temperature can be explained based on the band theory of solids. At higher temperatures, more electrons gain enough energy to move from the valence band to the conduction band, increasing the number of charge carriers and reducing resistivity.

3. Resistivity and Conductivity

Reference: NCERT Class 12, Chapter 3: Current Electricity

• Conductivity (σ): The measure of a material’s ability to conduct electric current.

$$\sigma = \frac{1}{\rho}$$

• Resistivity and conductivity are inversely related. High resistivity corresponds to low conductivity, and vice versa.

• The resistivity and conductivity of materials depend on various factors such as temperature, impurities, and crystal structure.

4. Superconductivity

Reference: NCERT Class 12, Chapter 3: Current Electricity

• Superconductivity: The phenomenon where a material exhibits zero electrical resistance and perfect diamagnetism (Meissner effect) below a certain critical temperature (Tc).

• Properties of superconductors:

  • Zero electrical resistance: Superconductors allow electric current to flow without any energy loss.
  • Meissner effect: Superconductors expel magnetic fields from their interiors.

• Applications of superconductivity:

  • Power transmission: Superconducting materials can be used to construct power lines with minimal energy loss.
  • Medical imaging: Superconducting magnets are used in MRI (Magnetic Resonance Imaging) scanners.
  • Particle accelerators: Superconducting magnets are used to guide and accelerate charged particles in particle accelerators.

5. Semiconductors and Their Properties

Reference: NCERT Class 12, Chapter 14: Semiconductors

• Semiconductors: Materials with electrical conductivity intermediate between metals and insulators.

• Energy band structure: Semiconductors have a forbidden energy gap (Eg) between the valence band and the conduction band.

• Doping: Adding impurities (dopants) to semiconductors can create two types of semiconductors:

  • N-type semiconductors: Formed by doping with atoms that have one extra electron in their outermost shell (e.g., phosphorus). These extra electrons become mobile charge carriers.
  • P-type semiconductors: Formed by doping with atoms that have one less electron in their outermost shell (e.g., boron). These missing electrons create positively charged holes that act as mobile charge carriers.

• Properties of semiconductors depend on factors such as bandgap energy, carrier concentration, and impurities.

• Applications of semiconductors:

  • Electronic devices: Semiconductors are essential components of various electronic devices such as diodes, transistors, and integrated circuits (ICs).
  • Solar cells: Semiconductors are used in solar cells to convert sunlight into electrical energy.
  • Light-emitting diodes (LEDs): Semiconductors are used in LEDs to produce light through electroluminescence.

6. Thermoelectricity

Reference: NCERT Class 12, Chapter 14: Semiconductors

• Thermoelectric effects: Phenomena that involve the direct conversion of heat into electricity or vice versa.

• Seebeck effect: When two different conductors are joined at their ends and a temperature difference is maintained between the junctions, an electromotive force (EMF