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).
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Factors Affecting Resistivity:
- Temperature (T): Increases with T for metals, decreases for semiconductors and insulators.
- Impurities: Increases with impurity concentration.
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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.
- Metals:
-
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).
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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).
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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.
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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.
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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.