Resistance and Resistors (3.7)

• Resistance

  The opposition offered by a material to the free flow of electrons
• Ohm

  The unit of resistance, represented by the Greek symbol Ω
• Resistance

  • Measured in ohms (Ω)
  • Larger units used for simplicity: kilohms (kΩ), megohms (MΩ)

  
• Factors affecting resistance

  • Length
  • Cross-sectional area
  • Material
  • Temperature
• Resistivity

  The resistance offered by a material per unit length and unit cross-section, measured in ohm-meters

  
• Length of conductor

  Resistance is directly proportional to length
• Cross-sectional area of conductor

  Resistance is inversely proportional to cross-sectional area
• Resistance of a conductor = (length x resistivity) / cross-sectional area

  
• Resistor stability

  Measure of how much a resistor's value drifts with temperature, in parts per million per degree Celsius (ppm/°C)

  
• Resistor colour codes

  Used to identify resistor values and tolerances

  
• Four-band resistor colour code

  First two bands = first two digits, third band = number of zeros, fourth band = tolerance

  
• Five-band resistor colour code

  First three bands = first three digits, fourth band = multiplier, fifth band = tolerance

  
• Resistor markings

  Printed values using R and K as decimal indicators
• EIA standard resistor values

  
• Resistor wattage rating

  Maximum power dissipation before the resistor is damaged
• Resistors in series

  • Total resistance is the sum of individual resistances
  • Current is the same through each resistor

  
• Resistors in parallel

  • Total resistance is less than the smallest individual resistance
  • Current divides among the resistors

  
• Calculating total resistance


  1. For series: add individual resistances

  2. For parallel: use formula 1/Rtotal = 1/R1 + 1/R2 + ...

  3. For series-parallel: break down into series and parallel components

  
• Preferred value system


  System for selecting standard values for resistors, based on manufacturing tolerances

  
• The preferred value system has its origins in the early 20th century, when most resistors were carbon-graphite with relatively poor manufacturing tolerances
• Rationale for preferred value system

  Select values for components based on the tolerances with which they are able to be manufactured
• Preferred values for 10% tolerance resistors between 100 and 1000 Ω


  • 100, 120, 150, 180, 220, 270, 330

  
• EIA E-series for preferred values

  • E3 - 50% tolerance
  • E6 - 20% tolerance
  • E12 - 10% tolerance
  • E24 - 5% tolerance
  • E48 - 2% tolerance
  • E96 - 1% tolerance
  • E192 - 0.5%, 0.25%, 0.1% and higher tolerances
• Wattage rating

  A resistor's ability to dissipate heat, depends on its surface area

  
• Standard size carbon film resistor has a power rating of 0.5 W
• Resistors designed for high currents

  • Cased in aluminium with fins to increase surface area and promote heat dissipation
• Series circuit


  A circuit that contains only one path for current flow

  
• Parallel circuit


  Resistors have their ends connected by a conductor, locating their ends at a common potential

  
• Series-parallel circuit


  A combination of series paths and parallel paths
• Steps to solve a series-parallel circuit

  Merge parallel resistances

  2. Add series resistances

  
• Potentiometer


  A manually adjustable, variable electrical resistor with a resistance element and three contacts

  
• Typical potentiometer values

  • 500 Ω, 1K, 2K, 5K, 10K, 22K, 47K, 50K, 100K, 220K, 470K, 500K, 1 M
• Rheostat


  A device whose resistance depends on the position of a mechanical element or control
• Rheostats are high-current low-resistance devices with a normal maximum value of 100 Ω
• Galvanometer

  A moving-coil electric current detector
• Wheatstone bridge


  An electrical circuit used to measure resistance and precisely compare resistances
• Purpose of Wheatstone bridge

  Determine the resistance of an unknown resistor by adjusting known resistors until current through the galvanometer is zero
• Wheatstone bridge is useful for measuring small changes in resistance, such as in a strain gauge
• Wheatstone bridge

  Circuit used for measuring small changes in resistance, useful for measuring resistance change in a strain gauge
• Strain gauge transforms strain applied to it into a proportional change of resistance