Electric Potential and Voltage

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Core Idea

Electric potential is the work per unit charge needed to move charge in an electric field. Voltage is the potential difference between two points and represents energy per unit charge provided by a source. In circuits, voltages are defined relative to a reference node (ground) and measured across components using two-point measurements.

Explainer

You already understand charge and current flow — charges moving through a conductor constitute current. But what makes charges move in the first place? The answer is energy differences, and electric potential is the tool that quantifies that energy on a per-charge basis. Think of it as the "electrical height" of a point in a circuit: just as water flows downhill from high gravitational potential to low, positive charges tend to flow from high electric potential to low.

Electric potential at a point is defined as the work per unit charge required to bring a positive test charge from a reference point (usually infinity in field theory, or ground in circuit analysis) to that point. Its unit is the volt (V), which equals one joule per coulomb. When we say a point in a circuit is at 5 V, we mean that moving one coulomb of positive charge from ground to that point requires 5 joules of work done by an external agent against the electric field. The field itself would do that same 5 joules of work if the charge moved from that point back to ground — that's the energy available to do useful work.

Voltage — more precisely, potential difference — is what appears in circuit analysis. It is always the difference between the potentials at two points: V_AB = V_A − V_B. This matters because absolute potential has no physical meaning in circuits; only differences do. A 9-volt battery doesn't mean the positive terminal is at 9 V in some absolute sense — it means the positive terminal is 9 V higher than the negative terminal. By convention, we assign one node in the circuit the label ground (0 V) and express all other node potentials relative to it. This choice is arbitrary but necessary: it gives us a consistent reference for writing and solving circuit equations.

A crucial distinction is between a voltage source (which maintains a fixed potential difference between its terminals, doing whatever work is necessary to sustain it) and the voltage across a passive component (which is the result of current flowing through it and energy being dissipated or stored). When current flows through a resistor, the resistor has a voltage drop across it — work is done on the charge by the field, and that work is converted to heat. When current charges a capacitor, work is stored as electric field energy between the plates. In both cases, the potential difference is the bookkeeping tool that tracks how energy is distributed around the circuit. Kirchhoff's Voltage Law — the sum of voltage rises and drops around any closed loop equals zero — is simply conservation of energy stated in these potential-difference terms.

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 Voltage

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