GLOBAL KNOWLEDGE ARK

Reference library

Foundations

Explore concepts, laws, equations and methods, with clear explanations of their use and sources. Choose an area of study or find a specific entry.

More filters

Reference entries

Showing 181–210 of 1709 reference entries

InformationFinite graphs and trees

Graphs represent pairwise connections; trees impose acyclicity.

DefinitionInformationData-structure interfaces and operation costs

An interface defines operations; an implementation determines costs.

MethodInformationLoop invariants and total correctness

An invariant establishes correctness only with its proof obligations.

MethodInformationComparison sorting lower bound

Distinct-key comparisons need enough branches to distinguish orders.

Mathematical statementInformationBreadth-first and depth-first traversal

Graph searches visit reachable vertices using different orders.

MethodInformationShortest-path algorithm conditions

Edge weights determine which shortest-path method applies.

MethodInformationTuring machines and effective computation

Finite instructions can act on an unbounded writable tape.

DefinitionInformationRelations and tabular data

A relation is a set of tuples from declared domains.

DefinitionPhysicsCentre-of-mass dynamics

External force controls the mass-weighted centre's acceleration.

ModelPhysicsRigid-body inertia tensor

A tensor relates rotation to angular momentum.

ModelPhysicsEuler equations for a rigid body

Body-axis angular acceleration includes rotation of the axes.

ModelPhysics · Mathematics & logicEuler–Lagrange equations

Stationary action supplies coordinate equations of motion.

Mathematical statementPhysics · Mathematics & logicHamilton's canonical equations

Canonical coordinates and momenta evolve from the Hamiltonian.

Mathematical statementPhysicsFluid mass continuity

Density change balances mass flux through a region.

ModelPhysicsBernoulli's streamline relation

An ideal steady flow balances pressure, motion and height.

ModelPhysicsIncompressible Navier–Stokes equation

Fluid inertia balances pressure, viscosity and gravity.

ModelPhysicsReynolds number

Compare inertial and viscous scales of a flow.

ModelPhysicsDriven damped oscillator

A linear restoring force, damping and periodic drive determine response.

ModelPhysicsIdeal-string wave equation

A local differential equation determines small string disturbances.

ModelPhysics · Mathematics & logicWave superposition and interference

Linear disturbances add; their relative phase determines reinforcement.

ModelPhysicsFixed-end string modes

Boundary conditions select standing-wave frequencies.

ModelPhysicsSnell's refraction relation

Angles at an interface depend on refractive indices.

ModelPhysicsThin-lens image equation

A paraxial lens relates object and image distances.

ModelPhysicsSingle-slit diffraction minima

An aperture's finite width selects dark far-field directions.

ModelPhysicsLinear polarization and Malus's law

An ideal analyzer transmits the field component along its axis.

ModelPhysicsElectromagnetic potentials

Scalar and vector potentials encode electric and magnetic fields.

ModelPhysicsCapacitance

A linear two-conductor arrangement stores separated charge.

DefinitionPhysicsSelf-inductance

Changing current changes linked magnetic flux and induced emf.

ModelPhysicsElectromagnetic energy balance

The rate of field-energy change balances outward energy flow and power transferred to charges.

ModelPhysicsKirchhoff circuit balances

Lumped circuit models balance node currents and loop voltages.

Model
ModelSource checked

Kirchhoff circuit balances

Physics

Lumped circuit models balance node currents and loop voltages.

Key knowledge

In a quasistatic lumped circuit without appreciable node charge accumulation, signed currents sum to zero at a node. Consistently defined element voltage drops and source rises sum to zero around a loop.

Values and equations

Σ_node I_signed = 0; Σ_loop V_signed = 0

I_signed
Signed branch current A
V_signed
Consistently oriented element voltage or source emf V

Conditions and scope

  • Circuit dimensions and delays permit a lumped model; include inductive emf in the element/source representation.
  • A loop linked to changing external magnetic flux needs its induced emf; electrostatic potential differences alone are insufficient.
Sources · 2

References

Sources retain their recorded scope. A source link alone does not establish verification of every statement.

  1. University Physics 2: Kirchhoff's RulesSamuel J. Ling, Jeff Sanny and William Moebs / OpenStax, Rice UniversityTextbook chapteropenstax.orgRead source
  2. Electromagnetic Fields and Energy, chapter 12.1: electrodynamic potentialsHermann A. Haus and James R. Melcher / MITTextbook chapter · PDFocw.mit.eduRead source

Evidence and review

OpenStax junction/loop rules; Haus–Melcher Faraday/potential distinction supplies changing-field scope.

2026-10-10 · Ideal lumped balance equations only; distributed transmission lines and unrepresented induction excluded.

Related reference entries

Explore relationships within this area of study and its connections to other areas.

Showing 1–5 of 5 relationships

Scientific relationships · 5 / 5

The relationship type describes the connection. Its linked statements, sources and conditions define the scope.

  1. Uses definition
    Relationship sources · 2

    Linked statements

    • In a quasistatic lumped circuit without appreciable node charge accumulation, signed currents sum to zero at a node. Consistently defined element voltage drops and source rises sum to zero around a loop.

    Signed branch charge-flow rates at a node without appreciable charge accumulation.

  2. Derived from
    Relationship sources · 1

    Linked statements

    • An ideal series RC circuit driven by constant voltage V₀ from an initially uncharged capacitor has Q(t) = CV₀(1 − e^(−t/RC)). Source-free discharge from Q₀ has Q(t) = Q₀e^(−t/RC).

    Ideal lumped loop balance with resistor drop and capacitor voltage.

  3. Uses definition
    Relationship sources · 1

    Linked statements

    • For ideal positive ohmic resistors in a lumped network, a series chain without intermediate branches has R_eq=ΣR_i. Resistors connected across the same two nodes are parallel and obey 1/R_eq=Σ1/R_i. Apparent physical proximity in a drawing does not establish either connection; node connectivity does.

    This relation concerns the stated series and parallel resistor networks claim and its conditions; it does not assert an unqualified prerequisite or an additional theorem.

  4. Uses definition
    Relationship sources · 1

    Linked statements

    • A source emf measures supplied work per unit charge and has units of volts. An ideal emf source with a series internal resistance r models a discharging battery’s terminal voltage as V_terminal=ε−Ir, where I leaves its positive terminal. At zero current this model gives V_terminal=ε; under load internal dissipation lowers terminal voltage.

    This relation concerns the stated electromotive force and terminal voltage claim and its conditions; it does not assert an unqualified prerequisite or an additional theorem.

  5. Uses definition
    Relationship sources · 1

    Linked statements

    • Ideal linear capacitors across the same two nodes have C_parallel=ΣC_i. A series chain with initially neutral floating intermediate conductors has 1/C_series=Σ1/C_i: charge magnitudes on its capacitors are equal while voltage drops add. Pre-existing intermediate charge can shift individual voltages and must be retained.

    This relation concerns the stated series and parallel capacitor networks claim and its conditions; it does not assert an unqualified prerequisite or an additional theorem.

Entry detailsPermanent link to this entry ↗
Record identity
physics-kirchhoff-rules
Revision
university-reference.1
Structured reference record
University reference