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Courses/Electrical Fundamentals/Kirchhoff's Laws

lesson · 9min · Lesson 16 of 37

KCL: Kirchhoff's Current 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

KCL: Kirchhoff's Current Law

Electrical Fundamentals · Lesson 16 · Beginner

BeginnerReview: professional review pending

Purpose

Apply conservation of charge at circuit junctions using explicit current directions.

Before you beginCurrent direction · Parallel branches · Algebra

Learning objectives

  • State KCL
  • Assign branch directions
  • Write a node equation
  • Interpret negative solutions

Kirchhoff's current law turns charge conservation into a node equation: in steady operation, charge cannot accumulate indefinitely at a junction.

KCL: CURRENT BALANCEKCL: CURRENT BALANCEincomingbranch 1branch 2ΣI = 0

Core theory

The algebraic sum of currents at a node is zero when entering and leaving currents use consistent signs.

An equally valid form is total current entering equals total current leaving.

A negative result means the real current opposes its assumed arrow; it is not automatically an error.

Terms, symbols, and units
TermMeaningSymbolUnit
NodeConductively common connection pointNot applicableNot applicable
KCLAlgebraic current sum at a node is zeroNot applicableNot applicable
BranchPath between two nodes carrying one branch currentNot applicableNot applicable
ΣI = 0 or ΣIin = ΣIout

Choose and document one current sign convention.

A
Worked exampleAt a node, 5 A enters; 1.2 A and 2.3 A leave. Find the remaining leaving current.

Assumptions: No time-varying stored charge at the node.

  1. Equation: 5 = 1.2 + 2.3 + Ix.
  2. Rearrange: Ix = 5 − 3.5.
  3. Calculate: Ix = 1.5 A leaving.

The remaining branch carries 1.5 A away from the node.

Reasonableness check: Outgoing currents total 5 A, matching incoming current.

Common mistakes
  • Counting one branch twice
  • Changing sign convention mid-equation
  • Treating a negative answer as impossible

Where this appears in practice

KCL supports parallel-load analysis, nodal methods, current measurement checks, and fault-current paths.

SafetyDo not infer safe touch current from a simplified node model. Real fault paths include people, earth, protective conductors, capacitance, and source impedance.
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

Two currents of 3 A and 2 A enter a node and 4 A leaves. What must the other branch do?

1 A must leave. Total entering and leaving current must balance.

Answer: 1 A must leave. Total entering and leaving current must balance.

Practical exercise

Assign arrows to a four-branch node, write KCL, and solve one unknown twice using both equation forms.

Summary

  • KCL expresses charge conservation
  • Directions are references
  • Verify that entering equals leaving

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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