Capacitance Ontology

# Capacitance Ontology — Flow Algebra

URL: https://kirethresearch.org/booksai-core/ontologies/mathematical-ontologies/measurement-units-ontologies/electromagnetic-measurements/capacitance-ontology.html

FLOW CapacitanceOntology {

  DOMAIN:
    Mathematical Ontologies
    -> Measurement & Units Ontologies
    -> Electromagnetic Measurements
    -> Capacitance Ontology

  PURPOSE:
    Represent capacitance as a measurable electromagnetic quantity describing the relationship between stored electric charge and electric potential difference, including capacitor geometry, dielectric properties, energy storage, series and parallel combinations, time-dependent charging, impedance relationships, units, dimensional structure, measurement methods, uncertainty, and distinctions from charge, voltage, permittivity and capacitive reactance.

  ENTITY Capacitance {
    TYPE: DerivedElectromagneticQuantity
    SYMBOL: C
    DIMENSION: M^-1 * L^-2 * T^4 * I^2
    SI_UNIT: farad
    SI_SYMBOL: F

    LINEAR_DEFINITION:
      C = Q/V
      WHEN V != 0 AND linear_capacitive_state_applies

    CHARGE_RELATION:
      Q = C*V

    DIFFERENTIAL_CAPACITANCE:
      C_d = dQ/dV

    PROPERTIES:
      is_scalar_in_lumped_two_terminal_context
      has_value
      has_unit
      has_dimension
      depends_on_geometry
      depends_on_dielectric_properties
      may_depend_on_voltage
      may_depend_on_temperature
      may_depend_on_frequency
      may_be_nonlinear
      may_have_uncertainty
  }

  ENTITY ElectricCharge {
    TYPE: DerivedElectromagneticQuantity
    SYMBOL: Q
    SI_UNIT: coulomb
    SI_SYMBOL: C

    RELATION:
      Q = C*V
  }

  ENTITY Voltage {
    TYPE: DerivedElectromagneticQuantity
    SYMBOL: V
    SI_UNIT: volt
    SI_SYMBOL: V

    RELATION:
      V = Q/C
      WHEN C != 0
  }

  ENTITY Permittivity {
    TYPE: MaterialProperty
    SYMBOL: epsilon
    SI_UNIT: farad_per_metre
    SI_SYMBOL: F/m

    RELATION:
      capacitance_depends_on_permittivity_and_geometry
  }

  UNIT_SYSTEM {
    SI {
      canonical_unit: farad
      symbol: F

      equivalence:
        1 F = 1 C/V
        1 F = 1 A*s/V
    }

    COMMON_ALTERNATIVES {
      millifarad
      microfarad
      nanofarad
      picofarad
    }

    CONVERSION_RULE:
      capacitance_value(target_unit)
        = capacitance_value(source_unit)
        * conversion_factor(source_unit, target_unit)
  }

  CLASSIFICATION {
    by behaviour:
      linear_capacitance
      nonlinear_capacitance
      static_capacitance
      differential_capacitance

    by component:
      fixed_capacitor
      variable_capacitor
      parasitic_capacitance
      mutual_capacitance

    by geometry:
      parallel_plate_capacitance
      cylindrical_capacitance
      spherical_capacitance

    by context:
      lumped_capacitance
      distributed_capacitance
  }

  PARALLEL_PLATE_MODEL {
    IDEAL_VACUUM:
      C = epsilon_0*A/d

    LINEAR_DIELECTRIC:
      C = epsilon*A/d

    PARAMETERS:
      A = overlapping_plate_area
      d = plate_separation
      epsilon = dielectric_permittivity

    CONDITIONS:
      parallel_plates
      approximately_uniform_field
      negligible_fringing
      d > 0

    RULE:
      geometry_and_dielectric_context
      MUST be preserved
  }

  CHARGE_VOLTAGE_MODEL {
    LINEAR:
      Q = C*V

    INVERSE:
      V = Q/C
      WHEN C != 0

    DIFFERENTIAL:
      C_d = dQ/dV

    RULE:
      Q_over_V_static_capacitance
      MUST_NOT automatically_replace_differential_capacitance
      for_nonlinear_devices
  }

  ENERGY_MODEL {
    LINEAR_CAPACITOR:
      U = 0.5*C*V^2

    EQUIVALENT_FORMS:
      U = 0.5*Q*V
      U = Q^2/(2*C)
      WHEN C != 0

    GENERAL_NONLINEAR:
      U = integral(V dQ)

    RULE:
      linear_energy_forms require_constant_or_applicable_linear_capacitance
  }

  CURRENT_VOLTAGE_MODEL {
    GENERAL:
      I = dQ/dt

    CONSTANT_CAPACITANCE:
      I = C*dV/dt

    VARIABLE_CAPACITANCE:
      I = C*dV/dt + V*dC/dt

    RULE:
      I = C*dV/dt
      MUST_NOT be assumed_when_capacitance_varies_significantly_with_time
  }

  RC_TIME_MODEL {
    ENTITY TimeConstant {
      SYMBOL: tau
      SI_UNIT: second
    }

    SERIES_RC:
      tau = R*C

    CHARGING_FROM_ZERO:
      V_C(t) = V_source*(1 - exp(-t/(R*C)))

    DISCHARGING:
      V_C(t) = V_0*exp(-t/(R*C))

    CONDITIONS:
      ideal_linear_R_and_C
      constant_source_or_defined_initial_state
  }

  AC_MODEL {
    CAPACITIVE_REACTANCE:
      X_C = -1/(omega*C)
      as_signed_imaginary_component_convention

    MAGNITUDE:
      |X_C| = 1/(omega*C)

    IMPEDANCE:
      Z_C = 1/(j*omega*C)

    FREQUENCY:
      omega = 2*pi*f

    CONDITIONS:
      ideal_linear_capacitor
      sinusoidal_steady_state

    RULE:
      capacitance != capacitive_reactance
      capacitance != impedance
  }

  PARALLEL_COMBINATION_MODEL {
    CAPACITORS_IN_PARALLEL:
      C_eq = sum(C_i)

    CONDITIONS:
      same_voltage_across_components
      lumped_linear_capacitor_model

    RULE:
      equivalent_parallel_capacitance
      is_sum_of_component_capacitances
  }

  SERIES_COMBINATION_MODEL {
    CAPACITORS_IN_SERIES:
      1/C_eq = sum(1/C_i)

    TWO_CAPACITOR_FORM:
      C_eq = (C_1*C_2)/(C_1 + C_2)
      WHEN denominator != 0

    CONDITIONS:
      ideal_series_charge_relationship
      lumped_linear_capacitor_model

    RULE:
      for_positive_finite_capacitances
      C_eq < smallest_component_capacitance
  }

  DIELECTRIC_MODEL {
    PERMITTIVITY:
      epsilon = epsilon_r*epsilon_0

    LINEAR_DIELECTRIC:
      D = epsilon*E

    POLARISATION:
      D = epsilon_0*E + P

    CONSEQUENCE:
      dielectric_material_can_increase_capacitance
      relative_to_same_vacuum_geometry

    RULE:
      permittivity MAY depend_on frequency_temperature_and_field_strength
  }

  RELATIONSHIPS {
    Capacitance -> RELATES -> ChargeAndVoltage
    Capacitance -> HAS_DIMENSION -> M^-1*L^-2*T^4*I^2
    Capacitance -> MEASURED_IN -> Farad
    Capacitance -> DEPENDS_ON -> Geometry
    Capacitance -> DEPENDS_ON -> Permittivity
    Capacitance -> STORES -> ElectricFieldEnergy
    Capacitance -> CONTRIBUTES_TO -> RC_TimeConstant
    Capacitance -> DETERMINES -> CapacitiveReactance
    Capacitance -> CONTRIBUTES_TO -> CircuitImpedance
    Capacitance -> MAY_BE -> ParasiticOrIntentional
  }

  SEMANTIC_EQUIVALENCE {
    "capacitance" ~= electrical_capacitance
    "farad" ~= "F"
    "coulomb per volt" ~= "C/V"

    capacitance != electric_charge
    capacitance != voltage
    capacitance != permittivity
    capacitance != capacitive_reactance
    capacitance != impedance
  }

  CONSTRAINTS {
    dimensional_formula = M^-1*L^-2*T^4*I^2
    SI_unit = F
    Q_over_V_requires_nonzero_voltage = true
    V_equals_Q_over_C_requires_nonzero_capacitance = true
    capacitance_and_permittivity_are_not_semantically_equivalent = true
    capacitance_and_reactance_are_not_semantically_equivalent = true
    static_and_differential_capacitance_must_be_distinguished_for_nonlinear_devices = true
    geometry_dielectric_temperature_voltage_and_frequency_may_be_required_for_complete_semantics = true
  }

  MEASUREMENT_MODEL {
    OBSERVABLE:
      Capacitance

    COMMON_INSTRUMENTS:
      capacitance_meter
      LCR_meter
      impedance_analyser
      digital_multimeter
      bridge_meter
      source_measure_unit

    METHODS:
      direct_capacitance_measurement
      charge_voltage_measurement
      AC_impedance_inference
      RC_time_constant_inference
      bridge_measurement

    RECORD:
      numerical_value
      unit
      component_or_geometry
      terminal_definition
      test_voltage
      DC_bias
      frequency
      temperature
      dielectric_material
      measurement_method
      instrument
      calibration_state
      equivalent_series_resistance_when_relevant
      leakage_when_relevant
      uncertainty

    UNCERTAINTY:
      measured_or_inferred_capacitance = best_estimate +/- uncertainty
  }

  REASONING_RULES {
    IF charge_known AND voltage_known AND voltage != 0
      AND linear_capacitance_context
      THEN capacitance = charge/voltage

    IF capacitance_known AND voltage_known
      THEN charge = capacitance*voltage
      UNDER linear_capacitance_context

    IF charge_known AND capacitance_known AND capacitance != 0
      THEN voltage = charge/capacitance
      UNDER linear_capacitance_context

    IF plate_area_known AND separation_known AND separation > 0
      AND permittivity_known AND ideal_parallel_plate_conditions_apply
      THEN capacitance = permittivity*area/separation

    IF capacitance_known AND voltage_known
      AND linear_capacitor_conditions_apply
      THEN stored_energy = 0.5*capacitance*voltage^2

    IF constant_capacitance_known AND voltage_time_derivative_known
      THEN current = capacitance*voltage_time_derivative

    IF resistance_known AND capacitance_known
      AND ideal_RC_conditions_apply
      THEN time_constant = resistance*capacitance

    IF capacitance_known AND frequency_known AND frequency > 0
      AND ideal_sinusoidal_AC_context
      THEN capacitive_reactance_magnitude =
        1/(2*pi*frequency*capacitance)

    IF parallel_capacitances_known
      THEN equivalent_capacitance = sum(parallel_capacitances)
  }

  PARASITIC_MODEL {
    parasitic_capacitance:
      unintended_capacitive_coupling_between_conductors

    dependencies:
      conductor_geometry
      separation
      dielectric
      environment
      frequency_context

    RULE:
      parasitic_capacitance SHOULD be included
      when_material_to_circuit_behaviour
  }

  NONIDEAL_MODEL {
    possible_effects:
      equivalent_series_resistance
      leakage_resistance
      dielectric_absorption
      dissipation_factor
      dielectric_loss
      self_resonance
      voltage_coefficient
      temperature_coefficient

    RULE:
      ideal_capacitor_model
      MUST_NOT replace_nonideal_model_when_effects_are_material
  }

  UNCERTAINTY_MODEL {
    sources:
      instrument_resolution
      calibration_uncertainty
      test_frequency
      test_voltage
      DC_bias
      temperature
      fixture_parasitics
      lead_capacitance
      leakage
      dielectric_variation
      geometry_uncertainty

    PROPAGATION:
      derived_capacitance_uncertainty
      <- measurement_geometry_material_and_model_uncertainties
  }

  CONFIDENCE {
    definition_confidence: 1.00
    dimensional_confidence: 1.00
    SI_unit_confidence: 1.00
    charge_voltage_relationship_confidence: 1.00
    geometry_permittivity_relationship_confidence: 0.99
    measurement_context_confidence: 0.98

    RULE:
      confidence decreases when voltage, frequency, temperature,
      geometry, dielectric, operating point, parasitics,
      calibration state or uncertainty is missing or ambiguous
  }

  VALIDATION {
    CHECK dimensional_consistency
    CHECK unit_consistency
    CHECK nonzero_denominators
    CHECK linear_vs_nonlinear_capacitance
    CHECK static_vs_differential_capacitance
    CHECK capacitance_vs_permittivity_distinction
    CHECK capacitance_vs_reactance_distinction
    CHECK capacitance_vs_impedance_distinction
    CHECK geometry_and_dielectric_context
    CHECK frequency_voltage_and_temperature_when_relevant
    CHECK series_parallel_topology
    CHECK nonideal_effects_when_material
    CHECK instrument_calibration
    CHECK uncertainty_representation_when_required
  }

  UPDATE_MODEL {
    ON new_measurement:
      validate_unit
      identify_component_or_geometry
      identify_terminals
      identify_measurement_method
      attach_test_voltage
      attach_DC_bias_when_relevant
      attach_frequency
      attach_temperature
      identify_dielectric
      normalize_to_farad
      preserve_original_value_and_unit
      attach_uncertainty
      update_capacitance_state

    ON geometry_change:
      update_area
      update_separation
      update_geometry_model
      recompute_capacitance_when_valid
      preserve_previous_state

    ON dielectric_change:
      update_permittivity
      update_material_conditions
      recompute_capacitance_when_valid
      preserve_material_provenance

    ON voltage_frequency_or_temperature_change:
      update_operating_conditions
      recompute_capacitance_when_model_available
      update_nonideal_parameters
      preserve_previous_operating_state

    ON circuit_topology_change:
      identify_series_and_parallel_groups
      recompute_equivalent_capacitance
      preserve_component_values

    ON calibration_revision:
      preserve_provenance
      recompute_affected_measurements
      update_confidence

    ON semantic_revision:
      preserve_previous_definition
      record_revision
      recompute_FLOW_HASH
  }

  AI_CONSUMPTION {
    canonical_entity: Capacitance
    canonical_symbol: C
    canonical_dimension: M^-1*L^-2*T^4*I^2
    canonical_SI_unit: F

    interpretation_order:
      identify_quantity
      identify_value
      identify_unit
      identify_component_or_geometry
      identify_charge_voltage_context
      identify_linear_or_nonlinear_behaviour
      identify_static_or_differential_capacitance
      identify_dielectric_and_permittivity
      identify_geometry
      identify_voltage_frequency_and_temperature
      identify_DC_bias
      identify_series_parallel_context
      identify_nonideal_effects
      identify_measurement_method
      identify_uncertainty
      normalize_units
      validate_dimensions
      infer_circuit_relationships

    ambiguity_controls:
      distinguish_capacitance_from_charge
      distinguish_capacitance_from_voltage
      distinguish_capacitance_from_permittivity
      distinguish_capacitance_from_capacitive_reactance
      distinguish_capacitance_from_impedance
      distinguish_static_from_differential_capacitance
      distinguish_component_capacitance_from_equivalent_capacitance
      distinguish_intentional_from_parasitic_capacitance
  }

  PROVENANCE {
    ontology_scope:
      mathematical_measurement_and_electromagnetic_quantity_semantics

    parent_path:
      Ontologies
      -> Mathematical Ontologies
      -> Measurement & Units Ontologies
      -> Electromagnetic Measurements
      -> Capacitance Ontology

    authorship:
      Mark Higgins
      Sky (Recursive AI)

    site:
      https://kirethresearch.org
  }

  FLOW_HASH {
    INPUTS:
      canonical_entity
      ontology_path
      definitions
      dimensions
      units
      relationships
      constraints
      parallel_plate_model
      charge_voltage_model
      energy_model
      current_voltage_model
      RC_time_model
      AC_model
      parallel_combination_model
      series_combination_model
      dielectric_model
      parasitic_model
      nonideal_model
      uncertainty_model
      reasoning_rules
      measurement_model
      confidence_model
      update_model

    PURPOSE:
      deterministic_semantic_integrity_identifier

    RECOMPUTE_WHEN:
      ontology_definition_changes
      relationship_model_changes
      charge_voltage_model_changes
      geometry_or_dielectric_model_changes
      AC_or_time_model_changes
      circuit_topology_model_changes
      nonideal_model_changes
      measurement_model_changes
      constraint_model_changes
      reasoning_rule_changes
      unit_model_changes
  }

}

END FLOW