3.2 Resistance and conductance

Resistance and conductance are key concepts in understanding how electricity flows through materials. They're opposites: resistance opposes current flow, while conductance allows it. These properties help us design circuits and choose the right materials for electrical applications.

Resistivity and conductivity are intrinsic material properties that determine resistance and conductance. Measured in ohm-meters and siemens per meter, they help us compare different materials' electrical behavior. Understanding these concepts is crucial for working with electrical systems.

Electrical Properties

Resistance and Conductance

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• Resistance measures the opposition to the flow of electric current through a material
  • Measured in ohms (Ω)
  • Higher resistance indicates greater difficulty for current to pass through
• Conductance quantifies the ease with which electric current can flow through a material
  • Measured in siemens (S)
  • Higher conductance indicates easier passage of current
• Resistance and conductance are inversely related
  • As resistance increases, conductance decreases and vice versa
  • Mathematically expressed as: $G = \frac{1}{R}$, where G is conductance and R is resistance

Resistivity and Conductivity

• Resistivity is an intrinsic property of a material that quantifies its resistance to electric current
  • Measured in ohm-meters (Ω⋅m)
  • Depends on the material's composition and structure
  • Examples: copper (1.68 × 10⁻⁸ Ω⋅m), silicon (640 Ω⋅m), rubber (1 × 10¹³ Ω⋅m)
• Conductivity is the reciprocal of resistivity and measures a material's ability to conduct electric current
  • Measured in siemens per meter (S/m)
  • Higher conductivity indicates better electrical conductivity
  • Mathematically expressed as: $\sigma = \frac{1}{\rho}$, where σ is conductivity and ρ is resistivity

Units of Measurement

Ohm and Siemens

• Ohm (Ω) is the SI unit for measuring electrical resistance
  • Named after German physicist Georg Ohm
  • Defined as the resistance between two points of a conductor when a constant potential difference of 1 volt produces a current of 1 ampere
• Siemens (S) is the SI unit for measuring electrical conductance
  • Named after German inventor Ernst Werner von Siemens
  • Equivalent to the reciprocal of an ohm (1 S = 1/Ω)
  • Commonly used in electrical engineering and circuit analysis

Fundamental Concepts

Inverse Relationship between Resistance and Conductance

• Resistance and conductance are inversely proportional
  • Doubling the resistance halves the conductance, and vice versa
  • This relationship is crucial for understanding the behavior of electrical circuits
  • Allows for the calculation of one quantity when the other is known
• The inverse relationship is expressed mathematically as: $R = \frac{1}{G}$ and $G = \frac{1}{R}$
  • R represents resistance in ohms (Ω)
  • G represents conductance in siemens (S)

Material Properties Affecting Resistance and Conductivity

• The resistance and conductivity of a material depend on its intrinsic properties
  • Atomic structure, electron mobility, and presence of impurities influence these properties
  • Materials with high electron mobility (metals) generally have low resistivity and high conductivity
  • Materials with low electron mobility (insulators) have high resistivity and low conductivity
• Temperature affects the resistance and conductivity of materials
  • For most metals, resistance increases with increasing temperature due to increased atomic vibrations
  • Semiconductors exhibit decreased resistivity with increasing temperature due to the excitation of electrons into the conduction band
• Cross-sectional area and length of a conductor influence its resistance
  • Resistance is directly proportional to the length and inversely proportional to the cross-sectional area
  • Mathematically expressed as: $R = \rho \frac{l}{A}$, where ρ is resistivity, l is length, and A is cross-sectional area