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Questions and Answers
What is the mean free path of an electron defined as?
What is the mean free path of an electron defined as?
- The total distance an electron can travel in a conductor.
- The average speed of an electron.
- The time taken by an electron to collide.
- The average distance an electron travels between collisions. (correct)
Which factor does NOT influence collision time?
Which factor does NOT influence collision time?
- Wavelength of electrons (correct)
- Impurities
- Density
- Temperature
In the equation for electrical conductivity $\sigma = \frac{\tau m_e}{nqe^2}$, what does $m_e$ represent?
In the equation for electrical conductivity $\sigma = \frac{\tau m_e}{nqe^2}$, what does $m_e$ represent?
- The speed of electrons
- The electron mass (correct)
- The charge of electrons
- The electric field strength
What does the relaxation time indicate in the context of free electrons?
What does the relaxation time indicate in the context of free electrons?
Given a resistivity of $1.54 \times 10^{-8} \Omega \cdot m$, which material is typically being referred to?
Given a resistivity of $1.54 \times 10^{-8} \Omega \cdot m$, which material is typically being referred to?
What is the average drift velocity of electron in a silver wire under an electric field of 1 V/cm?
What is the average drift velocity of electron in a silver wire under an electric field of 1 V/cm?
What unit is mobility expressed in based on the given problems?
What unit is mobility expressed in based on the given problems?
Which of the following describes the average speed of electrons in a conductor?
Which of the following describes the average speed of electrons in a conductor?
What happens to resistivity for pure metals and copper-nickel alloys as temperature increases above about -2200°C?
What happens to resistivity for pure metals and copper-nickel alloys as temperature increases above about -2200°C?
In the equation for impurity resistivity $\rho_i = A c_i (1 - c_i)$, what does $A$ represent?
In the equation for impurity resistivity $\rho_i = A c_i (1 - c_i)$, what does $A$ represent?
What contributes to the increased resistivity due to plastic deformation?
What contributes to the increased resistivity due to plastic deformation?
Which factor does NOT influence the electrical resistivity of metal?
Which factor does NOT influence the electrical resistivity of metal?
The relationship between resistivity and temperature for pure metals can be mathematically represented as which of the following equations?
The relationship between resistivity and temperature for pure metals can be mathematically represented as which of the following equations?
What does an increase in temperature above -2200°C primarily impact in terms of electrical properties of metals?
What does an increase in temperature above -2200°C primarily impact in terms of electrical properties of metals?
What is the effect of adding a single impurity in a solid solution on the resistivity?
What is the effect of adding a single impurity in a solid solution on the resistivity?
What role do electron-scattering centers play in the context of resistivity?
What role do electron-scattering centers play in the context of resistivity?
What primarily determines the conductivity of a material?
What primarily determines the conductivity of a material?
Which type of elements are considered the best conductors of electricity?
Which type of elements are considered the best conductors of electricity?
Which of the following is NOT a characteristic of conducting materials?
Which of the following is NOT a characteristic of conducting materials?
What is the effect of applying an electric potential difference across a conducting material?
What is the effect of applying an electric potential difference across a conducting material?
Which of the following metals is a well-known good conductor of electricity?
Which of the following metals is a well-known good conductor of electricity?
How do conducting materials differ from insulators in terms of electrons?
How do conducting materials differ from insulators in terms of electrons?
What role do free electrons play in the electrical resistivity of metals?
What role do free electrons play in the electrical resistivity of metals?
Which of the following elements is least likely to be a good conductor of electricity?
Which of the following elements is least likely to be a good conductor of electricity?
What is the formula for current (i) in terms of charge carrier density (n), charge of each electron (qe), area of cross-section (A), drift velocity (v), and time increment (dt)?
What is the formula for current (i) in terms of charge carrier density (n), charge of each electron (qe), area of cross-section (A), drift velocity (v), and time increment (dt)?
Which factor does NOT influence carrier mobility?
Which factor does NOT influence carrier mobility?
What does 'collision time' refer to in the context of electron movement?
What does 'collision time' refer to in the context of electron movement?
In the formula for carrier mobility (µ), what does 'E' represent?
In the formula for carrier mobility (µ), what does 'E' represent?
Which statement correctly describes drift velocity?
Which statement correctly describes drift velocity?
If the area of cross-section of a conductor increases, what effect does it have on the current, assuming all other factors remain constant?
If the area of cross-section of a conductor increases, what effect does it have on the current, assuming all other factors remain constant?
Which of the following best defines the term 'carrier mobility'?
Which of the following best defines the term 'carrier mobility'?
What is the relationship between the current (i), charge (dq), and time (dt)?
What is the relationship between the current (i), charge (dq), and time (dt)?
What does electrical conductivity (σ) represent in a conductor?
What does electrical conductivity (σ) represent in a conductor?
Which of the following statements is incorrect regarding the classical free electron theory?
Which of the following statements is incorrect regarding the classical free electron theory?
What is the unit of electrical conductivity?
What is the unit of electrical conductivity?
Which equation correctly represents electrical conductivity?
Which equation correctly represents electrical conductivity?
What occurs when free electrons collide with positive ions in a lattice?
What occurs when free electrons collide with positive ions in a lattice?
In the context of electrical resistivity, which of the following is true?
In the context of electrical resistivity, which of the following is true?
Which of the following best describes the motion of free electrons in metals?
Which of the following best describes the motion of free electrons in metals?
What aspect of electrical conductivity does the term 'current density' refer to?
What aspect of electrical conductivity does the term 'current density' refer to?
Study Notes
Conducting Materials
- Conductivity depends on free electrons.
- Materials with one valence electron are best conductors due to low opposition to electron gain/loss.
- Examples include Au, Ag, Cu.
- Good conductors of electricity and heat.
Electrical Conductivity
- Defined as charge flow rate per unit area per unit potential gradient.
- Formula: σ = J/E (σ = conductivity, J = current density, E = electric field).
- Unit: S/m.
- Reciprocal of resistivity.
Classical Free Electron Theory
- Assumes numerous free electrons moving randomly within the metal volume.
- Electrons collide with positive ions or each other, with no energy loss.
- Current (i) formula: i = nqeAv, where n is electron density, qe is electron charge, A is cross-sectional area, and v is drift velocity.
Carrier Mobility
- Defined as drift velocity per unit electric field: µ = vdrift / E.
- Affected by temperature, material impurities, and material type.
Collision Time (τ)
- Average time between electron collisions.
- Formula: τ = σme / nqe², where me is electron mass.
- Affected by temperature, density, impurities, and electric field.
Mean Free Path (λ)
- Average distance between collisions.
- Formula: λ = vave τ (vave = average electron speed).
Relaxation Time
- Time for an electron to reach equilibrium from a disturbed state under an electric field.
- Essentially the same as collision time (τ).
Influence of Temperature on Resistivity
- For pure metals, resistivity rises linearly with temperature above roughly -220°C.
- Formula: ρt = ρ0 + aT (ρt = resistivity at temperature t, ρ0 & a are constants).
- Increase due to thermal vibrations and lattice irregularities.
Influence of Impurities on Resistivity
- Impurity resistivity (ρi) relates to impurity concentration (ci): ρi = Aci(1 − ci).
- A is a constant depending on the impurity and host metals.
Influence of Plastic Deformation on Resistivity
- Plastic deformation increases resistivity due to increased electron-scattering dislocations.
- Dislocation movement causes lattice distortions, scattering electrons.
Example Problems
- Problem 1: Given silver wire resistivity, electric field, and electron density, calculate drift velocity and mobility. (Solution provided: µ = 6.9973 × 10⁻³ m²V⁻¹s⁻¹, vdrift = 0.69973 m/s)
- Problem 2: Given copper data (density, resistivity, atomic weight), calculate mobility and average collision time. (Solution not provided).
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Description
Explore the principles of electrical conductivity, focusing on the role of free electrons in conductive materials. This quiz covers key concepts such as conductivity, carrier mobility, and the classical free electron theory, providing examples of good conductors like gold, silver, and copper.
