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Courses/Electrical Fundamentals/Kirchhoff's Laws

lesson · 9min · Lesson 17 of 37

KVL: Kirchhoff's Voltage Law

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 · 9min
KCL: CURRENT AT A NODEI₁I₂I₃I₁ = I₂ + I₃KVL: VOLTAGE ROUND A LOOPVV₁V₂V = V₁ + V₂ (ΣV = 0)
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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

KVL: Kirchhoff's Voltage Law

Electrical Fundamentals · Lesson 17 · Beginner

BeginnerReview: professional review pending

Purpose

Apply conservation of energy around a closed circuit loop with consistent voltage polarities.

Before you beginPotential difference · Ohm's law · Series circuits

Learning objectives

  • State KVL
  • Mark voltage polarities
  • Write a loop equation
  • Check source and load balance

Kirchhoff's voltage law expresses energy conservation: after one complete loop, the algebraic sum of potential changes is zero.

KVL: LOOP BALANCEKVL: LOOP BALANCEincomingbranch 1branch 2ΣV = 0

Core theory

Crossing a source from negative to positive is a voltage rise; crossing a passive resistor in the assumed current direction is a drop.

Any loop direction works when signs are applied consistently.

KVL remains valid with multiple sources; their polarities determine whether they aid or oppose.

Terms, symbols, and units
TermMeaningSymbolUnit
LoopClosed path returning to its starting nodeNot applicableNot applicable
KVLAlgebraic voltage sum around a loop is zeroNot applicableNot applicable
PolarityAssigned positive and negative terminals for voltageNot applicableNot applicable
ΣV = 0

Add signed voltage rises and drops around one closed path.

V
Worked exampleA 15 V source drives 2 Ω and 3 Ω in series.

Assumptions: Ideal source and wires.

  1. Current: I = 15/(2+3) = 3 A.
  2. Drops: V1 = 6 V and V2 = 9 V.
  3. Loop: +15 − 6 − 9 = 0 V.

The loop balances with 3 A and drops of 6 V and 9 V.

Reasonableness check: All source energy per coulomb is transferred in the resistors.

Common mistakes
  • Using resistor drops with inconsistent current direction
  • Omitting a source
  • Summing magnitudes without polarity

Where this appears in practice

KVL supports series circuits, control loops, voltage-drop diagnosis, and mesh equations.

SafetyMeasured voltage may include induced, stored, or backfeed sources not present in a simplified diagram. Prove isolation at the work point using an approved method.
Local code checkThese analysis laws are universal. Installation design, conductor selection, protection, testing, and permitted work must follow current local standards and manufacturer data.

Knowledge check

A 24 V loop has known drops of 7 V and 9 V. What is the remaining drop?

8 V. The drops must sum to the 24 V source rise.

Answer: 8 V. The drops must sum to the 24 V source rise.

Practical exercise

Mark polarities and write KVL for two opposing sources and two resistors before inserting numbers.

Summary

  • KVL expresses energy conservation
  • Polarity controls signs
  • Loop rises and drops balance

Sources and review

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

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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