Understanding Electrical Resistance

• The opposition to the flow of charge through any material is called resistance
• Resistance is the conversion of electrical energy into another form of energy, such as heat
• The unit of measurement for resistance is the ohm, symbolized by Ω (Greek letter omega)

Resistance Factors

• Resistance is determined by material, length, cross-sectional area, and temperature
• Conductors allow generous charge flow with low resistance
• Insulators have high resistance
• Resistance is directly proportional to length and inversely proportional to area

Resistance Formula

• At 20°C, resistance (R) is related to resistivity (ρ), length (l), and cross-sectional area (A) by: R = ρ(l/A)
• The units of measurement depend on the application
• Metric units are common in integrated circuits

Circular Wires

• For two wires of the same physical size and temperature, the higher the resistivity, the more the resistance
• The longer the length of a conductor, the more the resistance
• The smaller the area of a conductor, the more the resistance
• For metallic wires of identical construction and material, the higher the temperature, the more the resistance

Units for Circular Wires

• Resistivity (ρ): CM – ohms/ft at T = 20°C
• Length (l): ft
• Area (A): circular mils (CM)

Area Calculation

• Area is measured in circular mils (CM), not square meters/inches
• Area (circle) = πr² = (πd²)/4

Mil Definition

• Mil is a unit of measurement for length related to the inch by 1 mil = 1/1000 in

Circular Mil (CM)

• A wire with a diameter of 1 mil has an area of 1 circular mil (CM)

Metric Units

• Resistive elements in thin-film resistors and integrated circuits use metric units
• Resistivity is measured in ohm-meters, area in square meters, and length in meters
• Centimeters are commonly used due to meter being too large

Metric Unit Dimensions

• Resistivity (ρ): ohms - centimeters
• Length (l): centimeters
• Area (A): square centimeters

Resistivity Unit

• Defined as ρ = (RA)/l = Ω · cm

Temperature Effects

• Temperature significantly affects the resistance of conductors, semiconductors, and insulators

Conductors

• Conductors have many free electrons, so thermal energy has little impact on the number of free carriers
• Thermal energy increases particle motion, hindering electron drift
• For good conductors, increased temperature results in increased resistance (positive temperature coefficient)

Semiconductors

• In semiconductors, increased temperature increases the number of free carriers for conduction
• Increased temperature results in decreased resistance (negative temperature coefficient)

Insulators

• Similar to semiconductors, increased temperature results in decreased resistance (negative temperature coefficient)

Inferred Absolute Temperature

• The resistance of copper increases almost linearly with temperature
• Approximating the resistance curve allows determining resistance at any temperature
• For copper, the straight dashed line intersects the temperature scale at -234.5°C
• Similar triangles can develop a relationship between resistances at different temperatures
  • x/R₁ = y/R₂
  • Where x and y are distances from -234.5°C to temperatures T₁ and T₂, respectively
  • (234.5 + T₁)/R₁ = (234.5 + T₂)/R₂
• The inferred absolute temperature varies for different conducting materials

Common Inferred Absolute Temperatures (°C)

• Silver: -243
• Copper: -234.5
• Gold: -274
• Aluminium: -236
• Tungsten: -204
• Nickel: -147
• Iron: -162
• Nichrome: -2250
• Constantan: -125000

Modified Equation

• To adapt to any material, insert the proper inferred absolute temperature: |T1|+ T₁ / R₁ = |T1| + T₂ / R₂
• Sign is only associated with T₁ and T₂

Temperature Coefficient of Resistance Formula

• α20 = 1 / (|T1| + 20°C)
• Determines resistance R₁ at temperature T₁ with R20 at 20°C
• Different materials have different values of α20
• R₁ = R20[1 + a20(T1 - 20°C)]
• This can be written as R1 = ρ/A [1 + a20(T₁ − 20°C)]

Superconductors

• Superconductors are conductors of electric charge that, for all practical purposes, have zero resistance

Conductance Measurement

• Conductance measures how well a material conducts electricity, it is the reciprocal of resistance
• Conductance has the symbol G
• It is measured in siemens (S)

Conductance Formulas

• G = 1/R
• G = A/ρl
• Increasing area or decreasing length/resistivity increases conductance

Explore electrical resistance, its measurement in ohms, and factors influencing it: material, length, area, and temperature. Learn how conductors and insulators differ in resistance. Understand the formula R = ρ(l/A) and its applications.