Notes from Toppers

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.