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Showing 1561–1590 of 1709 reference entries

PhysicsSimple harmonic motion and period

Linear restoring acceleration produces sinusoidal motion.

ModelPhysicsSimple pendulum and the small-angle limit

The familiar pendulum period requires a small swing.

ModelPhysicsAmplitude, phase, wavelength and polarization direction

A wave’s pattern speed differs from the motion of its medium.

ModelPhysicsEnergy carried by a sinusoidal string wave

Energy transport grows with squared amplitude and frequency in the linear model.

ModelPhysicsSound intensity and decibel level

A decibel value needs a reference and a specified measured quantity.

ModelPhysicsBeats from nearby frequencies

Slow modulation comes from superposing close frequencies.

ModelPhysicsAcoustic Doppler shift in a medium

Source and observer velocities are measured relative to the medium.

ModelPhysics · ChemistryHeat, temperature and specific heat

Heat is energy transferred because of a temperature difference.

ModelPhysicsThermal expansion coefficients

Thermal size changes depend on temperature and constraints.

ModelPhysics · ChemistryPressure–volume work and process paths

Boundary work depends on the process, while internal energy is a state function.

ModelPhysics · ChemistryReversible adiabatic ideal-gas relations

The power law needs an ideal gas and constant heat-capacity ratio.

ModelPhysics · ChemistryReversible and quasistatic processes

Restoring the system alone does not establish reversibility.

ModelPhysics · ChemistryEntropy change and reversible heat transfer

Use a reversible comparison path to calculate a state-function change.

ModelPhysicsRefrigerator and heat-pump performance

A heat pump moves heat as well as consuming work.

ModelPhysics · ChemistryMean free path in a dilute hard-sphere gas

A collision length depends on number density and cross section.

ModelPhysicsAtomic net charge and electrical neutrality

Neutral matter can contain both positive and negative charge.

ModelPhysicsConductors, insulators and electrostatic induction

Charge mobility and polarization are different from net charging.

ModelPhysicsConductors in electrostatic equilibrium

Equilibrium field vanishes in the conducting material, including a charged conductor.

ModelPhysicsElectric potential, voltage and potential energy

Voltage is energy change per unit charge.

ModelPhysicsCurrent density and carrier drift

Current measures signed charge flow across a surface.

ModelPhysicsResistance, resistivity and conductor geometry

Resistance belongs to a device geometry; resistivity is a material response.

ModelPhysicsSeries and parallel resistor networks

Series shares current; parallel shares voltage.

ModelPhysicsElectrical power and Joule heating

Voltage times signed current measures element power.

ModelPhysicsElectromotive force and terminal voltage

An emf is an energy-per-charge quantity, not a force.

ModelPhysicsSeries and parallel capacitor networks

Capacitor network rules differ from resistor rules.

ModelPhysicsEnergy stored in a linear capacitor

Charging work produces electric-field energy.

ModelPhysicsMagnetic flux and Faraday–Lenz induction

Induction responds to flux change, not simply to the presence of a magnetic field.

ModelPhysicsEnergy stored in a linear inductor

Inductive storage and resistive loss are separate.

ModelPhysicsMagnetic fields of a straight wire and circular loop

Field geometry follows the current distribution.

ModelPhysicsIdeal transformer voltage and current ratios

Turns change voltage and current while conserving ideal power.

Model
ModelSource checked

Energy stored in a linear capacitor

Physics

Charging work produces electric-field energy.

Key knowledge

For a fixed linear capacitance C>0 charged from zero, stored energy is U=Q²/(2C)=CV²/2=QV/2. The factor one-half comes from integrating the rising voltage during charging, not multiplying the final voltage by every charge increment. An ideal vacuum parallel-plate capacitor of area A and gap d has C≈ε₀A/d when edge fields are negligible.

Values and equations

U=∫_0^Q V(q)dq=Q²/(2C)=½CV²; C_parallel_plate≈ε₀A/d

U
Stored electric energy relative to uncharged state J
Q,q
Terminal charge and integration charge C
V
Terminal voltage V
C,C_parallel_plate
Capacitance and ideal plate approximation F
ε₀
Vacuum permittivity F m⁻¹
A
Plate area m²
d
Vacuum plate separation m

Conditions and scope

  • Fixed geometry and linear reversible dielectric response; Q and V are consistently signed terminal variables with Q=CV.
  • Nonlinear/hysteretic dielectric response requires the actual ∫V(Q)dQ and loss model. Stored energy is distinct from energy dissipated in a charging resistance. The plate formula assumes d small relative to lateral dimensions.
Sources · 1

References

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

  1. University Physics Volume 2, §8.3: energy stored in a capacitorSamuel J. Ling, Jeff Sanny and William Moebs — OpenStax, Rice University, University Physics (2016)Textbook chapteropenstax.orgRead source

Evidence and review

Read §8.3 energy-density/parallel-plate relation and charging integral8.10. Linear/fixed-response scope qualifies the source’s generic “all capacitors” prose.

2026-10-10 · /root/audit_life_earth_chemistry — independent Chemistry/Life/Earth editor. Independent AI editorial review of this entry's statements, equations, applicability conditions and source coverage. Source checks apply to these claims within their stated limits.

Related reference entries

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

Showing 1–3 of 3 relationships

Scientific relationships · 3 / 3

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

  1. Uses definition
    Relationship sources · 1

    Linked statements

    • For a fixed linear capacitance C>0 charged from zero, stored energy is U=Q²/(2C)=CV²/2=QV/2. The factor one-half comes from integrating the rising voltage during charging, not multiplying the final voltage by every charge increment. An ideal vacuum parallel-plate capacitor of area A and gap d has C≈ε₀A/d when edge fields are negligible.

    This relation concerns the stated energy stored in a linear capacitor claim and its conditions; it does not assert an unqualified prerequisite or an additional theorem.

  2. Uses definition
    Relationship sources · 1

    Linked statements

    • For a fixed linear capacitance C>0 charged from zero, stored energy is U=Q²/(2C)=CV²/2=QV/2. The factor one-half comes from integrating the rising voltage during charging, not multiplying the final voltage by every charge increment. An ideal vacuum parallel-plate capacitor of area A and gap d has C≈ε₀A/d when edge fields are negligible.

    This relation concerns the stated energy stored in a linear capacitor claim and its conditions; it does not assert an unqualified prerequisite or an additional theorem.

  3. Related to
    Relationship sources · 1

    Linked statements

    • For a fixed linear capacitance C>0 charged from zero, stored energy is U=Q²/(2C)=CV²/2=QV/2. The factor one-half comes from integrating the rising voltage during charging, not multiplying the final voltage by every charge increment. An ideal vacuum parallel-plate capacitor of area A and gap d has C≈ε₀A/d when edge fields are negligible.

    This relation concerns the stated energy stored in a linear capacitor claim and its conditions; it does not assert an unqualified prerequisite or an additional theorem.

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