Electric Circuits⚡️🔥

• What are the classifications of materials based on their electrical properties?

  • Conductors
  • Insulators
  • Semi-conductors

  
• What is resistance (R) in an electric circuit?

  The obstruction offered to the flow of current in a conductor

  
• In what unit is resistance measured?

  Ohm (Ω)

  
• What factors affect the resistance of a conductor?


  • Length of the conductor (R ∝ l)
  • Cross-sectional area (R ∝ 1/A)
  • Temperature (R ∝ T)
  • Nature of material
• How does the length of a conductor affect its resistance?

  Resistance is directly proportional to the length of the conductor
• How does the cross-sectional area of a conductor affect its resistance?


  Resistance is inversely proportional to the cross-sectional area

  
• What is the relationship between resistance and temperature?

  Resistance is directly proportional to temperature

  
• What is resistivity (ρ)?


  It is the resistance of a material having unit length and unit area of cross-section

  
• What is the SI unit of resistivity?


  Ohm-meter (Ω·m)
• What does resistivity depend on?

  It depends on relaxation time and temperature
• How is resistivity derived from resistance, length, and area?


  ρ = R * A / l
• What is conductivity (σ)?


  It is the measure of how easily charge carriers can flow through a substance
• What is the relationship between conductivity and resistivity?

  Conductivity is the reciprocal of resistivity

  
• What is the SI unit of conductivity?


  Siemens per meter (S/m)
• What is conductance (G)?


  It is defined as the reciprocal of the resistance of a material

  
• What is the SI unit of conductance?


  Siemens (S)
• What are the classifications of substances based on resistivity, conductivity, and charge carriers?


  • Conductors: High conductivity, low resistivity, charge carriers are electrons
  • Insulators: High resistivity, low conductivity, no charge carriers
  • Semi-conductors: Conductivity between conductors and insulators

  
• What is the resistivity range of metals?

  Between \(10^{-2} \, \Omega \cdot m\) and \(10^{-6} \, \Omega \cdot m\)

  
• What is the resistivity range of insulators?


  Between \(10^{11} \, \Omega \cdot m\) and \(10^{19} \, \Omega \cdot m\)

  
• What is the resistivity range of semi-conductors?


  Between \(10^{-5} \, \Omega \cdot m\) and \(10^{6} \, \Omega \cdot m\)

  
• What are the types of semi-conductors?


  • Elemental semi-conductors: Pure/intrinsic (e.g., silicon, germanium)
  • Compound semi-conductors: Impure/extrinsic (e.g., N-type and P-type)
• What is the valence band in solids?


  The energy band that is completely filled with valence electrons

  
• What is the conduction band in solids?


  The energy band above the valence band that is completely empty

  
• What is the energy gap or forbidden band?


  The space between the conduction band and valence band

  
• How do conductors, insulators, and semi-conductors differ in terms of energy bands?

  • Conductors: Valence and conduction bands overlap, no energy gap
  • Insulators: Large energy gap (> 3 eV), conduction band empty
  • Semi-conductors: Small energy gap (< 3 eV), conduction band empty at 0 K

  
• What is Fermi energy?


  The maximum energy possessed by free electrons at absolute zero
• What is Fermi level?


  The highest energy level that an electron can occupy in the valence band at absolute zero

  
• How does temperature affect the resistivity of conductors, insulators, and semi-conductors?


  • Conductors: Increased temperature increases resistivity and resistance
  • Insulators/Semi-conductors: Increased temperature decreases resistivity and resistance

  
• What is relaxation time?


  The time interval between two successive collisions of electrons in a conductor
• How does the relaxation time change with temperature in conductors?

  Relaxation time decreases with an increase in temperature
• What happens to the number density of free electrons in insulators and semi-conductors when temperature increases?

  The number density of free electrons increases

  
• What is the effect of increased temperature on the resistivity and resistance of semi-conductors and insulators?

  Resistivity and resistance decrease with increased temperature

  
• What is the formula for resistivity in terms of mass, charge, and relaxation time?


  ρ = $\frac{m}{n e^2 \tau}$
• What is the formula for resistance in terms of mass, charge, and relaxation time?


  R = $\frac{m l}{n e^2 A \tau}$
• What are the key points to remember about energy bands in solids?

  • Electrons in outer orbits have different energy levels due to neighboring atoms
  • Energy levels of inner orbit electrons are less affected
  • Grouping of energy levels is called energy bands

  
• What are the characteristics of conductors, insulators, and semi-conductors based on energy bands?


  • Conductors: No energy gap, valence band filled, conduction band partially filled
  • Insulators: Large energy gap, valence band filled, conduction band empty
  • Semi-conductors: Small energy gap, conduction band empty at 0 K

  
• What is the term used to describe the highest energy level that an electron can occupy in the valence band at absolute zero?


  Fermi level

  
• What is the Fermi energy?


  The zero energy level
• What happens to the resistivity and resistance of conductors when temperature increases?


  • Frequency of collision of free electrons increases
  • Relaxation time decreases
  • Resistivity and resistance increase

  
• What is the formula for resistivity in terms of mass, number density, charge, and relaxation time?


  \(\rho = \frac{m}{n e^2 \tau}\)