2.2.2 Resistors in Series & Parallel

• Resistors in Series


  In a series circuit, resistors are connected end-to-end, so the same current flows through each resistor.
• Key Characteristics of Series Circuits

  • Current (I): The current flowing through each resistor is the same
  • Voltage (V): The total voltage across the series circuit is the sum of the voltages across each resistor
  • Resistance (R): The total resistance is the sum of their individual resistances
• Voltage calculation in Series

  Vtotal=V1+V2+⋯+Vn
• Resistance calculation in Series

  Rtotal=R1+R2+⋯+Rn
• Resistors in Parallel

  In a parallel circuit, resistors are connected across the same two points, creating multiple paths for the current.
• Key Characteristics of Parallel Circuits

  • Voltage (V): The voltage across each resistor is the same and equal to the voltage of the source
  • Current (I): The total current is the sum of the currents through each resistor
  • Resistance (R): The total resistance is found using the reciprocal formula
• Voltage calculation in Parallel

  Vtotal=V1=V2=⋯=Vn
• Current calculation in Parallel

  Itotal=I1+I2+⋯+In
• Resistance calculation in Parallel

  1Rtotal=1R1+1R2+⋯+1Rn
• Comparing Series and Parallel Circuits

  • Series Circuits: Current: Same through all components
  • Voltage: Total voltage is divided among the resistors
  • Resistance: Total resistance increases with more resistors
  • Parallel Circuits: Current: Divides among branches; each resistor gets the same voltage
  • Voltage: Same across all resistors
  • Resistance: Total resistance decreases with more resistors
• Practical Applications of Series Circuits


  • Example: Christmas lights often use series circuits where a single failed bulb turns off the entire string
  • Usage: Simple circuits where current must flow through all components sequentially
• Practical Applications of Parallel Circuits

  • Example: Household wiring uses parallel circuits to ensure that appliances work independently of each other
  • Usage: More complex circuits requiring multiple pathways for current and where components need to operate independently
• Series Circuit Experiment

  1. Setup: Connect resistors in series with a power supply, ammeter, and voltmeter

  2. Measure the current through the circuit

  3. Measure the voltage across each resistor

  4. Calculate the total resistance and verify using Ohm’s Law
• Parallel Circuit Experiment

  1. Setup: Connect resistors in parallel with a power supply, ammeter, and voltmeter

  2. Measure the voltage across each resistor

  3. Measure the current through each resistor

  4. Calculate the total resistance and verify using the reciprocal formula
• Understanding resistors in series and parallel helps you analyze and design electrical circuits.
• Series circuits have the same current throughout and a sum of resistances, while parallel circuits have the same voltage across components and a combined resistance that decreases with additional resistors.
• Mastery of these concepts is crucial for solving circuit problems and designing functional electronic systems.
• Resistors in Series


  In a series circuit, resistors are connected end-to-end, so the same current flows through each resistor.
• Key Characteristics of Series Circuits

  • Current (I): The current flowing through each resistor is the same
  • Voltage (V): The total voltage is the sum of the voltages across each resistor
  • Resistance (R): The total resistance is the sum of their individual resistances
• Voltage calculation in series

  Vtotal=V1+V2+⋯+Vn
• Resistance calculation in series

  Rtotal=R1+R2+⋯+Rn
• Resistors in Parallel

  In a parallel circuit, resistors are connected across the same two points, creating multiple paths for the current.
• Key Characteristics of Parallel Circuits

  • Voltage (V): The voltage across each resistor is the same
  • Current (I): The total current is the sum of the currents through each resistor
  • Resistance (R): The total resistance is found using the reciprocal formula
• Voltage calculation in parallel


  Vtotal=V1=V2=⋯=Vn
• Current calculation in parallel

  Itotal=I1+I2+⋯+In
• Resistance calculation in parallel

  1Rtotal=1R1+1R2+⋯+1Rn
• Comparing Series and Parallel Circuits

  • Series Circuits: Current same through all components, Voltage divided among resistors, Resistance increases with more resistors
  • Parallel Circuits: Current divides among branches, Voltage same across all resistors, Resistance decreases with more resistors
• Practical Applications of Series Circuits


  • Christmas lights often use series circuits where a single failed bulb turns off the entire string
  • Simple circuits where current must flow through all components sequentially
• Practical Applications of Parallel Circuits

  • Household wiring uses parallel circuits to ensure that appliances work independently
  • More complex circuits requiring multiple pathways for current
• Series Circuit Experiment Setup

  1. Connect resistors in series with a power supply, ammeter, and voltmeter

  2. Measure the current through the circuit

  3. Measure the voltage across each resistor

  4. Calculate the total resistance and verify using Ohm’s Law
• Parallel Circuit Experiment Setup

  1. Connect resistors in parallel with a power supply, ammeter, and voltmeter

  2. Measure the voltage across each resistor

  3. Measure the current through each resistor

  4. Calculate the total resistance and verify using the reciprocal formula
• Understanding resistors in series and parallel helps you analyze and design electrical circuits.
• Series circuits have the same current throughout and a sum of resistances, while parallel circuits have the same voltage across components and a combined resistance that decreases with additional resistors.
• Mastery of these concepts is crucial for solving circuit problems and designing functional electronic systems.