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Courses/Electrical Fundamentals/Series & Parallel Circuits

lesson · 10min · Lesson 11 of 37

Series 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

Series circuits: characteristics and rules

Electrical Fundamentals · Lesson 11 · Beginner

BeginnerReview: professional review pending

Purpose

Analyse series resistors using shared current, additive voltage drops, and equivalent resistance.

Before you beginOhm's law · Closed circuits

Learning objectives

  • Identify a true series path
  • Calculate series equivalent resistance
  • Find individual voltage drops
  • Check voltage and power balance

Components are in series only when the same current must pass through each one with no branching node between them.

SERIES: ONE CURRENT PATHSERIES: ONE CURRENT PATHR₁R₂Req = ΣR

Core theory

Series equivalent resistance is the sum of individual resistances because their voltage drops add for the same current.

The supply voltage divides in proportion to resistance for linear resistors.

Opening any point in a single series path stops current throughout that path.

Terms, symbols, and units
TermMeaningSymbolUnit
Series connectionComponents sharing one unbranched current pathNot applicableNot applicable
Equivalent resistanceSingle resistance with the same terminal behaviourReqΩ
Voltage dropPotential difference across a passive componentVV
Req = R₁ + R₂ + …; Vₙ = I Rₙ

Add series resistances, calculate loop current, then each drop.

Ω and V
Worked exampleA 12 V source feeds 100 Ω and 200 Ω in series.

Assumptions: Ideal 12 V source; Linear resistors.

  1. Equivalent: Req = 100 + 200 = 300 Ω.
  2. Current: I = 12/300 = 0.040 A.
  3. Drops: V₁ = 4 V and V₂ = 8 V; total = 12 V.

Req = 300 Ω, I = 40 mA, drops are 4 V and 8 V.

Reasonableness check: The larger resistor receives twice the drop, and the drops equal the supply.

Common mistakes
  • Calling components series when a branch exists
  • Adding conductances instead of resistances
  • Forgetting to verify voltage sum

Where this appears in practice

Series elements appear in sensing chains, LED current limiting, measurement circuits, and voltage dividers.

SafetyA series calculation does not guarantee adequate resistor voltage, power, impulse, or insulation ratings. Confirm every component rating.
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

Three series resistors carry 2 A. What current passes through the middle resistor?

2 A. There is no branch where current can divide.

Answer: 2 A. There is no branch where current can divide.

Practical exercise

Analyse 5 V with 150 Ω and 350 Ω, then verify current, both drops, and total power.

Summary

  • Series means one current path
  • Resistances and voltage drops add
  • Use balance checks

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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