Series & Parallel Circuits

Series & Parallel Circuit Comparison

Series Parallel
Voltage additive  constant
Current constant  additive
Resistance additive  additive
Power additive  additive
Voltage Drop

Series Circuits

  • Closed Loop circuit with only one path where current may flow
  • Used for Controls and Signaling mostly


Series Circuit Rules
Rule 1 Current total equals the current in any part of the circuit
Rule 2 Voltage total equals the sum of all voltages
Rule 3 Resistance total equals the sum of all resistances


Series circuit Total current: I=Es/Rt

Series Circuit Calculations:

  1. Determine each circuit resistors resistance
  2. Calculate circuit total resistance
    • Rt = R1 + R2 + R3
  3. Calculate the current
    1. I = Es / Rt

Series Circuit Summary

  • Resistors are measured across
  • Current is same value through all resistances
  • Source voltage = Sum of all resistances voltage drops
  • All resistances power consumed sum = Total power consumed by the circuit

Parallel Circuits

  • Open-Loop Circuit with more than one path for current to flow
  • Resistance is additive
  • Voltage Drop across each resistance is equal to the voltage drop supplied by the power source
Parallel Circuit Rules
Rule 1 Current total equals the sum of all currents in all circuit branches
Rule 2  Voltage total equals the sum of all voltages
Rule 3  Resistance total is found by applying Ohm’s Law to the total values (Rt=Et/It) NEED SUPERSCRIPT CODE Note: Total resistance is always less than the resistance of any branch.

3 Methods to calculate Total Resistance in Parallel Circuits

  • Equal Resistance
    • Rt = 1 resistor Ω / number of resistors
      • Note: All resistors must have same resistance
  • Product-over-Sum
    • Rt = (R1 x R2) / (R1 + R2)
      • Note: Only uses 2 resistors per equation
        • If more then 2 resistors, then use the equivalent resistance of the last 2 resistors as a ‘new’ resistance for the next equation
  • Reciprocal
    • Rt = 1/[(1/R1) + (1/R2) + (1/R3)…]
      • Note: Preferred method because this can be used for as many resistors as contained within a circuit

Parallel Circuit Summary

  • Voltage is same across each circuit component
  • Total power Consumed = Sum of the Power in all branches
  • Ris always less then smallest individual resistor
  • Rt calculation = 1/[(1/R1) + (1/R2) + (1/R3)…]
  • Has 2 or more paths for current to flow
  • Total Current = is provided by Source voltage and sum of all currents in all branches

Series-Parallel Circuit Summary

Obtain different voltages of series circuits combined with different currents of parallel circuits

Power Supplies

voltage is additiveVoltage constant
current constantcurrent increases


  • voltage is additive
  • current constant


  • Voltage constant
  • current increases

Series-connected Delta/Delta

  • Transformer power supply, 3Ø = 3 transformers connected in series