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Courses/Electrical Fundamentals/Series & Parallel Circuits

lesson · 10min · Lesson 12 of 37

Parallel circuits: characteristics and rules

Course syllabusCourse overview
01Atoms, Electrons & Electric Charge
  1. ReadWhat is electricity?: atomic model
  2. ReadElectric charge and the coulomb
  3. ReadConductors, insulators, and semiconductors
  4. ReadConventional current vs electron flow
  5. quizModule quiz
02Voltage, Current & Resistance
  1. ReadPotential difference: the driving force
  2. ReadCurrent: the rate of charge flow
  3. ReadResistance and resistivity
  4. ReadOhm's Law: derivation and examples
  5. exerciseWorked examples: Ohm's Law problems
03Series & Parallel Circuits
  1. ReadSeries circuits: characteristics and rules
  2. ReadParallel circuits: characteristics and rules
  3. ReadCombined series-parallel networks
  4. ReadVoltage dividers and current dividers
  5. exerciseCircuit analysis practice
04Kirchhoff's Laws
  1. ReadKCL: Kirchhoff's Current Law
  2. ReadKVL: Kirchhoff's Voltage Law
  3. ReadMesh and nodal analysis
  4. exerciseKirchhoff's law problems set
05Power & Energy
  1. ReadElectrical power: watts and horsepower
  2. ReadEnergy: kilowatt-hours and joules
  3. ReadEfficiency and power loss in cables
  4. quizPower quiz
06Alternating Current Fundamentals
  1. ReadAC vs DC: why AC won
  2. ReadSinusoidal waveforms: peak, RMS, average
  3. ReadFrequency and period
  4. ReadPhase relationships
  5. ReadAC circuit analysis introduction
07Capacitors & Inductors
  1. ReadCapacitor construction and capacitance
  2. ReadCapacitors in AC circuits: reactance
  3. ReadInductor construction and inductance
  4. ReadInductors in AC circuits: reactance
  5. ReadRC and RL circuits: time constants
08Measurement & Instruments
  1. ReadMultimeters: AC/DC voltage and current
  2. ReadClamp meters and measuring live current
  3. ReadOscilloscopes: reading waveforms
  4. quizFinal assessment
Lesson · 10min
SERIESVR₁R₂Rₜ = R₁ + R₂same current everywherePARALLELVR₁R₂1/Rₜ = 1/R₁ + 1/R₂same voltage across each
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In this lesson

PurposeCore theoryWorked exampleKnowledge checkSources

In this lesson

PurposeCore theoryWorked exampleKnowledge checkSources
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ElectraCore lesson handout

Parallel circuits: characteristics and rules

Electrical Fundamentals · Lesson 12 · Beginner

BeginnerReview: professional review pending

Purpose

Analyse parallel resistors using common voltage, branch current, and reciprocal equivalent resistance.

Before you beginOhm's law · Series circuits · Fractions

Learning objectives

  • Identify common-node parallel branches
  • Calculate parallel equivalent resistance
  • Find branch currents
  • Check total current and power

Parallel components connect across the same two nodes, so every branch has the same voltage while current divides by branch resistance.

PARALLEL: COMMON VOLTAGEPARALLEL: COMMON VOLTAGER₁R₂1/Req = Σ1/R

Core theory

Parallel conductances add: 1/Req = Σ(1/Rn). Equivalent resistance is lower than the smallest positive branch resistance.

Total current is the sum of branch currents, consistent with charge conservation at each node.

Adding a parallel load lowers equivalent resistance and increases source current for a fixed ideal voltage.

Terms, symbols, and units
TermMeaningSymbolUnit
Parallel connectionBranches connected to the same two nodesNot applicableNot applicable
Branch currentCurrent in one parallel pathIₙA
ConductanceReciprocal of resistanceGsiemens (S)
1/Req = 1/R₁ + 1/R₂ + …; It = ΣIₙ

Add reciprocal resistances and add branch currents.

Ω, S, and A
Worked exampleConnect 6 Ω and 3 Ω across 12 V.

Assumptions: Ideal source; Linear resistors.

  1. Equivalent: 1/Req = 1/6 + 1/3 = 1/2, so Req = 2 Ω.
  2. Branches: I₁ = 12/6 = 2 A; I₂ = 12/3 = 4 A.
  3. Check: It = 6 A and 12/2 = 6 A.

Req = 2 Ω; branch currents 2 A and 4 A; total 6 A.

Reasonableness check: Equivalent resistance is below 3 Ω and the lower-resistance branch carries more current.

Common mistakes
  • Adding parallel resistances directly
  • Assuming branch currents are equal with unequal resistance
  • Accepting Req greater than the smallest branch

Where this appears in practice

Building circuits, socket loads, lighting branches, and electronic bias networks commonly operate in parallel.

SafetyAdding parallel loads can overload a source or conductor even though each load voltage stays unchanged. Protective coordination and conductor capacity still matter.
Local code checkThe physical relationships are universal. Installation methods, permitted work, test procedures, and equipment ratings must be checked against current local rules and manufacturer instructions.

Knowledge check

What must be equal for ideal parallel branches?

Voltage across each branch. Their endpoints are the same two nodes.

Answer: Voltage across each branch. Their endpoints are the same two nodes.

Practical exercise

Calculate equivalent resistance and branch currents for 24 Ω and 8 Ω across 24 V.

Summary

  • Parallel branches share voltage
  • Branch currents add
  • Equivalent resistance is below the smallest branch

Sources and review

  • The International System of Units (SI Brochure): BIPM; 9th edition, updated 2026; International
  • SI Units: Electric Current: NIST; Current web edition; United States / SI reference
  • University Physics Volume 2: OpenStax; Current web edition; Physics reference

Editorial review date: 2026-08-21. Professional electrical review is pending.

Educational material for learning and preliminary checks. Verify current local requirements and exact equipment instructions. This lesson does not replace competent professional work.

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