Mobility and Temperature Dependence of Resistivity:

Notes:

• Resistivity (ρ):

  • Measure of a material’s opposition to the flow of electric current.
  • SI unit: Ohm-meter (Ω-m).

• Factors Affecting Resistivity:

  • Temperature (T): Increases with T for metals, decreases for semiconductors and insulators.
  • Impurities: Increases with impurity concentration.

• Temperature Dependence of Resistivity:

  • Metals:
    • Resistivity increases with temperature due to increased scattering of charge carriers by lattice vibrations (phonons).
  • Semiconductors:
    • Resistivity decreases with temperature due to the generation of additional charge carriers (electron-hole pairs) with increasing T.
  • Insulators:
    • Resistivity decreases slightly with temperature due to the thermal excitation of a few charge carriers.

• Mobility (μ):

  • Measure of the drift velocity of charge carriers under an applied electric field.
  • SI unit: square meters per volt-second (m²/V-s).

• Factors Affecting Mobility:

  • Temperature (T): Decreases with T due to increased scattering of charge carriers.
  • Impurities: Decreases with impurity concentration due to increased scattering.
  • Crystal Structure: Depends on the material’s crystal structure and the nature of charge carriers.

References:

• NCERT Physics Class 12, Chapter 14: Semiconductors.
• NCERT Physics Class 11, Chapter 15: Solids and Semiconductors.

Applications of Mobility and Temperature Dependence of Resistivity:

Notes:

• Thermistors:

  • Resistors whose resistance changes significantly with temperature.
  • Used in temperature sensing and control applications (e.g., thermometers, thermostats).

• Resistive Temperature Detectors (RTDs):

  • Precision temperature sensors based on the principle of resistance change with temperature.
  • Used in various industrial, scientific, and medical temperature measurement applications.

• Semiconductor Devices:

  • Transistors and diodes rely on the mobility of charge carriers and their temperature dependence for their operation.

• Superconductivity:

  • Materials with zero electrical resistance at very low temperatures.
  • Applications include energy transmission and maglev trains.

• Effect of Temperature on Electrolytes:

  • Conductivity of electrolytes increases with temperature due to increased mobility of ions.
  • Used in electrochemical cells and batteries.

• Thermoelectric Materials:

  • Convert temperature differences into electrical energy (Seebeck effect).
  • Applications in temperature-based energy conversion.

• Piezoresistive Sensors:

  • Change resistance under mechanical strain or pressure.
  • Used in pressure sensors, accelerometers, and strain gauges.

References:

• NCERT Physics Class 12, Chapter 14: Semiconductors.
• NCERT Physics Class 11, Chapter 15: Solids and Semiconductors.
• Various JEE textbooks and reference books.

Numerical Problems and Derivations:

Notes:

• Practice numerical problems involving resistivity, mobility, and temperature dependence.
• Derive equations relating these properties and analyze experimental data.
• Refer to textbooks, study materials, and previous years’ JEE papers for practice problems and derivations.

References:

• NCERT Physics textbooks.
• JEE previous years’ question papers.
• JEE practice books and study materials.