Ideal Voltage and Current Sources

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Core Idea

Ideal voltage sources maintain constant voltage independent of current drawn; ideal current sources maintain constant current independent of voltage across them. Dependent sources have their output determined by another circuit voltage or current. These idealized elements are fundamental to circuit theory, with real devices having internal impedance.

Explainer

From your study of electric potential and current flow, you know that voltage is the energy per unit charge driving current around a circuit, and that current is the rate of charge movement. Sources are the elements that supply this energy — they are the "pumps" that push charge through the network. Understanding ideal sources precisely is essential because every circuit analysis method (KVL, KCL, Thévenin equivalents, node voltage, mesh current) assumes you can characterize sources exactly.

An ideal voltage source enforces a fixed potential difference across its terminals, regardless of how much current flows through it. Imagine a 9V battery that stays at exactly 9V whether you connect a 1 kΩ resistor (drawing 9 mA) or a 10 Ω resistor (drawing 0.9 A) — the voltage never wavers. The source simply supplies whatever current the external circuit demands to maintain that voltage. This means an ideal voltage source has zero internal resistance: no energy is lost inside it, and no voltage drops across it internally. In practice, every real source has some internal resistance (a battery has internal resistance of a few tenths of an ohm), and its terminal voltage sags as more current is drawn. The ideal model is accurate when the load resistance is much larger than the internal resistance.

An ideal current source is the dual: it enforces a fixed current through itself, regardless of the voltage that appears across its terminals. A 2 mA ideal current source pushes exactly 2 mA through the circuit whether the load is 100 Ω or 10 kΩ — the voltage across it adjusts automatically to whatever the circuit requires. An ideal current source has infinite internal resistance: it resists any change in current by presenting an arbitrarily high impedance. Real approximations include transistor circuits biased to behave as nearly constant current sources. Voltage and current sources are duals of each other — every property of one has a mirror-image statement for the other, and Thévenin's theorem (voltage source + series resistance) and Norton's theorem (current source + parallel resistance) formalize this duality.

Dependent sources (also called controlled sources) are a distinct and important category. Unlike independent sources whose output is fixed, a dependent source's output is proportional to some other voltage or current elsewhere in the circuit. There are four types: voltage-controlled voltage source (VCVS, output voltage = μ·v_x), current-controlled voltage source (CCVS), voltage-controlled current source (VCCS, output current = g_m·v_x), and current-controlled current source (CCCS, output current = β·i_x). These models are not exotic abstractions — they are the circuit-theoretic representations of active devices. A BJT's collector current g_m·v_be is a VCCS. An op-amp's output is modeled as a VCVS with very high gain. Mastery of dependent sources is the bridge between passive circuit analysis and electronic amplifier design; you cannot analyze transistor circuits without them.

Practice Questions 5 questions

Prerequisite Chain

Counting to 10Counting to 20Understanding ZeroThe Number ZeroCounting to FiveOne-to-One CorrespondenceCombining Small Groups Within 5Addition Within 10Addition Within 20Two-Digit Addition Without RegroupingTwo-Digit Addition with RegroupingAddition Within 100Repeated Addition as MultiplicationMultiplication Facts Within 100Division as Equal SharingDivision as Grouping (Measurement Division)Division: Grouping (Repeated Subtraction) ModelDivision: Fair Sharing ModelDivision as Equal SharingDivision as GroupingBasic Division FactsDivision Facts Within 100Two-Digit by One-Digit DivisionDivision with RemaindersRemainders and Quotients in DivisionDivision Word ProblemsIntroduction to Long DivisionFactors and MultiplesPrime and Composite NumbersEquivalent FractionsRelating Fractions and DecimalsDecimal Place ValueReading and Writing DecimalsComparing and Ordering DecimalsAdding and Subtracting DecimalsMultiplying DecimalsDividing DecimalsDividing FractionsMixed Number ArithmeticOrder of OperationsInteger Order of OperationsVariable ExpressionsCombining Like TermsOne-Step EquationsTwo-Step EquationsSolving Multi-Step EquationsEquations with Variables on Both SidesAngle Pairs: Complementary, Supplementary, and VerticalParallel Lines and TransversalsCorresponding AnglesAlternate Interior AnglesTriangle Angle Sum TheoremExterior Angle TheoremTriangle Inequality TheoremSimilar Triangles: AA SimilaritySimilar Triangles: SSS and SAS SimilarityProportions in Similar TrianglesRight Triangle Trigonometry IntroductionTrigonometric Ratios ReviewRadian MeasureConverting Between Degrees and RadiansThe Unit CircleGraphing Sine and CosineGraphing Tangent and Reciprocal Trigonometric FunctionsDerivatives of Trigonometric FunctionsAntiderivativesIterated Integrals and Fubini's TheoremDouble Integrals in Cartesian CoordinatesDouble Integrals over Rectangular RegionsDouble Integrals in Polar CoordinatesDouble Integrals: Definition and SetupIterated Integrals and Fubini's TheoremDouble Integrals over Rectangular RegionsDouble Integrals over General RegionsApplications of Double Integrals: Area, Mass, and MomentsTriple Integrals in Cartesian CoordinatesTriple Integrals in Cylindrical and Spherical CoordinatesChange of Variables and the Jacobian DeterminantApplications of Triple Integrals: Volume and MassVector Fields and Their RepresentationsLine Integrals of Vector FieldsGreen's TheoremSurface Integrals and Flux of Vector FieldsSurface Integrals and Flux of Vector FieldsDivergence Theorem: Flux and OutflowDivergence TheoremElectric FluxGauss's LawConductors in Electrostatic EquilibriumCapacitance and CapacitorsDielectricsDielectric Constant and Relative PermittivityElectric Field Inside Dielectric MaterialsDielectric Materials and PolarizationDielectric Susceptibility and PermittivityEnergy Density in Electric FieldsElectric Current and Current DensityElectrical Resistance and ResistivityOhm's Law and Circuit ElementsElectromotive Force (EMF) and BatteriesKirchhoff's Circuit Laws: Voltage and CurrentDC Circuit Network Analysis MethodsTransient Response in RC CircuitsRC CircuitsLC and RLC CircuitsAC Circuits: FundamentalsImpedance and ReactanceAC Power and ResonanceElectromagnetic WavesFrequency-Dependent Permittivity and DispersionElectromagnetic Waves in Anisotropic MediaBirefringence and DichroismWave Plates: Quarter-Wave and Half-Wave PlatesCircular and Elliptical Polarization ProductionPolarization States: Linear, Circular, and EllipticalLinear Superposition of WavesSuperposition Principle in ElectrostaticsElectric Field Lines and VisualizationElectric Potential and Potential EnergyElectric Potential and VoltageIdeal Voltage and Current Sources

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