3. Resistors In Series + Parallel

• Series


  A "string" in which there is only one path for the current to flow
• Series circuit


  • One path for the current between two points
  • Same current flow through each series resistor

  
• Total Series Resistance


  The total resistance of a series circuit is equal to the sum of the resistances of the individual resistors

  
• Series resistance formula


  RT = R1 + R2 + R3 …… + RN
• Equal value series resistors

  RT = N x R

  
• Ohm's Law in Series Circuits

  1. Calculate the voltage across each resistor and find Vs

  2. Find the maximum value of Vs before the fuse blows

  
• Voltage Sources in Series

  The total voltage is equal to the algebraic sum of the individual source voltages

  
• Kirchhoff's Voltage Law


  The algebraic sum of the voltages around a closed path is zero
• General Form of Kirchhoff's Voltage Law

  VS1 + VS2 + … + VSN = V1 + V2 + …+ VM

  
• General Form of the Voltage Divider

  VX = RX VS / RT
• Power in a Series Circuit

  Total Power = sum of individual powers
• Power formulae in Series Circuits

  1. PT = VSI

  2. PT = I2RT

  3. PT = VS2 / RT

  
• Circuit Ground


  • Voltage is always measured relative to another point in the circuit
  • Reference point is termed 'ground'
  • Ground can be earth ground or chassis ground

  
• Parallel


  • Two or more resistors connected between the same two points
  • More than one current path for the current
  • Voltage between the two points also appears across each of the branches

  
• Voltage drop in Parallel Circuits

  The voltage across any branch of a parallel circuit is equal to the voltage across each of the other branches in parallel

  
• Kirchhoff's Current Law


  The sum of the currents into a junction is equal to the total current out of that junction
• Total Parallel Resistance


  Total resistance of a parallel circuit is always less than the value of the smallest resistor

  
• Ohm's Law in Parallel Circuits

  Calculate the voltage across the parallel circuit

  
• Current Source


  Energy source that provides a constant current to a load even if the resistance of that load changes
• Current Dividers


  General Formulae for two branches
• Power in Parallel Circuits

  Total Power = sum of individual powers

  
• Power formulae in Parallel Circuits

  1. PT = VSI

  2. PT = I2 RT

  3. PT = VS2 / RT

  
• Applications of Parallel Circuits

  • Automotive
  • Residential
• When one lamp opens

  Total current decreases and other branch currents remain unchanged