Mobility and Temperature Dependence of Resistivity

Current and Electricity - Resistance (Color coding)

• Definition of resistivity:
  • In physics, resistivity is a property of a material that describes how strongly it resists the flow of electric current.
  • It is denoted by the symbol ‘ρ’ and is measured in ohm-meters (Ω·m).
• Equation of resistivity:
  • ρ = R * A / L, where R is resistance, A is cross-sectional area, and L is length of the material.
• Factors affecting resistivity:
  • Temperature: As temperature increases, resistivity generally increases due to increased atomic vibrations.
  • Impurities and defects: Presence of impurities or defects in a material can increase its resistivity.
  • Composition: Different materials have different resistivities depending on their atomic and molecular structure.
• Temperature dependence of resistivity:
  • Metals: Resistivity generally increases with an increase in temperature due to increased scattering of electrons by lattice vibrations.
  • Non-metals: Resistivity generally decreases with an increase in temperature due to increased activation of charge carriers.
• Mobility:
  • In physics, mobility is a measure of how quickly charge carriers can move in a material in response to an electric field.
  • It is denoted by the symbol ‘μ’ and is measured in square meters per volt-second (m^2/V·s).
• Equation of mobility:
  • μ = q * τ / m, where q is charge, τ is relaxation time, and m is mass of the charge carrier.
• Relationship between resistivity and mobility:
  • Resistivity is related to mobility through the equation: ρ = 1 / (q * n * μ), where n is charge carrier density.
• Color coding of resistors:
  • Resistors are electronic components used to introduce resistance into an electric circuit.
  • They are color-coded to indicate their resistance value and tolerance.
• Color coding scheme:
  • Each color represents a digit or a decimal multiplier.
  • The first two bands represent the first two digits of the resistance value.
  • The third band represents the number of zeros to be appended to the first two digits.
  • The fourth band represents the tolerance of the resistor.
• Example: A resistor with color bands brown-black-red-gold has a resistance value of 1.2Ω with a tolerance of ±5%.

Factors affecting resistivity:

• Temperature: increase leads to increased atomic vibrations, increasing resistivity.
• Impurities and defects: presence increases scattering of charge carriers, increasing resistivity.
• Composition: different materials have different atomic and molecular structures, leading to different resistivities.
• Example: Semiconductors have higher resistivity than metals due to their unique structure.

Temperature dependence of resistivity in metals:

• As temperature increases, resistivity also increases.
• Electrons experience increased scattering due to lattice vibrations.
• Example: Copper has a resistivity of 1.68 x 10^-8 Ω·m at 20°C, but it increases to 1.75 x 10^-8 Ω·m at 100°C.

Temperature dependence of resistivity in non-metals:

• As temperature increases, resistivity typically decreases.
• Activation of charge carriers leads to increased conduction.
• Example: Silicon has a resistivity of 2.3 x 10^3 Ω·m at 0°C, but it decreases to 1.2 x 10^3 Ω·m at 100°C.

Mobility definition:

• Mobility is a measure of how quickly charge carriers can move in a material when subjected to an electric field.
• It determines the ease with which charge carriers can conduct electricity.
• Example: In a semiconductor, mobility describes how quickly electron or hole can move in response to an electric field.

Mobility equation:

• The mobility of a charge carrier is given by the equation: μ = q * τ / m.
• μ is mobility, q is charge of the carrier, τ is relaxation time, and m is the mass of the charge carrier.
• Example: The mobility of electrons in copper is approximately 3.9 x 10^-3 m^2/V·s.

Relationship between resistivity and mobility:

• Resistivity (ρ) and mobility (μ) are inversely related, as given by the equation: ρ = 1 / (q * n * μ).
• n is the charge carrier density.
• Example: In a material with higher mobility, resistivity is lower, indicating better conductivity.

Resistors and their color coding:

• Resistors are electronic components used to introduce resistance into an electric circuit.
• They are color-coded to indicate their resistance value and tolerance.
• Example: A resistor with color bands brown-black-red-gold has a resistance value of 1.2Ω with a tolerance of ±5%.

Color coding scheme for resistors:

• Each color represents a specific digit or decimal multiplier.
• The first two bands represent the first two digits of the resistance value.
• The third band represents the number of zeros to be appended to the first two digits.
• Example: A resistor with color bands brown-black-orange-gold has a resistance value of 10KΩ with a tolerance of ±5%.

Interpreting the color bands:

• Use a color code chart or mnemonic to identify the numerical value associated with each color.
• Example: For a resistor with color bands orange-orange-orange-gold, the value is 33KΩ with a tolerance of ±5%.

Summary:

• Resistivity is a property of a material that describes how strongly it resists the flow of electric current.
• Temperature and impurities affect resistivity, leading to various behaviors in different materials.
• Mobility is a measure of how easily charge carriers can move in a material.
• Resistors are color-coded to indicate their resistance value and tolerance.
• Understanding the color coding scheme helps identify the resistance value of a resistor.

Examples of resistivity values:

• Copper: 1.68 x 10^-8 Ω·m at 20°C
• Aluminum: 2.7 x 10^-8 Ω·m at 20°C
• Silver: 1.59 x 10^-8 Ω·m at 20°C
• Silicon: 2.3 x 10^3 Ω·m at 0°C

Examples of mobility values:

• Electrons in copper: 3.9 x 10^-3 m^2/V·s
• Electrons in silicon: 1.4 x 10^-3 m^2/V·s
• Electrons in germanium: 0.39 m^2/V·s
• Holes in silicon: 0.17 m^2/V·s

Example calculation of resistivity:

• Given: resistance R = 10 Ω, cross-sectional area A = 0.01 m^2, length L = 2 m
• Using the resistivity formula, ρ = R * A / L, we find ρ = (10 Ω) * (0.01 m^2) / (2 m) = 0.05 Ω·m

Example calculation of mobility:

• Given: charge q = 1.6 x 10^-19 C, relaxation time τ = 1 x 10^-13 s, mass m = 9.1 x 10^-31 kg
• Using the mobility formula, μ = q * τ / m, we find μ = (1.6 x 10^-19 C) * (1 x 10^-13 s) / (9.1 x 10^-31 kg) = 1.76 m^2/V·s

Example calculation of resistivity using mobility:

• Given: charge carrier density n = 1 x 10^23 m^-3, mobility μ = 1 x 10^-3 m^2/V·s
• Using the resistivity formula, ρ = 1 / (q * n * μ), we find ρ = 1 / ((1.6 x 10^-19 C) * (1 x 10^23 m^-3) * (1 x 10^-3 m^2/V·s)) = 6.25 x 10^-9 Ω·m

Color coding example:

• Brown (1st band) = 1
• Black (2nd band) = 0
• Red (3rd band) = 00 (two zeros to be appended)
• Gold (4th band) = ±5% tolerance
• Resistance value = 10 Ω with ±5% tolerance

Color coding example:

• Orange (1st band) = 3
• Orange (2nd band) = 3
• Orange (3rd band) = 000 (three zeros to be appended)
• Gold (4th band) = ±5% tolerance
• Resistance value = 33 KΩ with ±5% tolerance

Color coding example:

• Blue (1st band) = 6
• Green (2nd band) = 5
• Yellow (3rd band) = 000,000 (six zeros to be appended)
• Silver (4th band) = ±10% tolerance
• Resistance value = 65 MΩ with ±10% tolerance

Color coding example:

• Violet (1st band) = 7
• Brown (2nd band) = 1
• Grey (3rd band) = 00,000,000 (eight zeros to be appended)
• Gold (4th band) = ±5% tolerance
• Resistance value = 71 MΩ with ±5% tolerance

Summary:

• Resistivity is influenced by factors such as temperature, impurities, and material composition.
• Temperature dependence of resistivity varies for metals and non-metals.
• Mobility describes the ease with which charge carriers can move in a material.
• Resistors are color-coded to indicate their resistance value and tolerance.
• Understanding the color coding scheme helps identify the resistance value of a resistor.