{ "node": { "id": "term:rc-pair", "type": "Term", "label": "RC pair", "properties": { "id": "rc-pair", "name": "RC pair", "aka": [ "RC element", "RC branch" ], "section": "topic-transport", "definition": "A resistor and capacitor in parallel, the building block of an equivalent circuit model. Each pair reproduces one time constant of the cell’s voltage response, from the seconds of charge transfer to the minutes of diffusion.", "formula": "τ = R × C", "related": [ "equivalent-circuit-model", "relaxation", "charge-transfer" ], "example": { "title": "Calculate a response time", "text": "An illustrative 0.02 Ω resistance and 500 F capacitance have τ = RC = 10 s. A first-order step response reaches about 63% of its final change after one time constant." }, "url": "https://lemonergy.com/learn/glossary/rc-pair/", "mentions": [ "diffusion", "capacitor" ] } }, "edges": [ { "id": "edge:166", "source": "term:rc-pair", "target": "workflow:rc-response", "type": "usedIn", "properties": { "sourceFile": "wiki-blocks.json" } }, { "id": "edge:2151", "source": "term:rc-pair", "target": "topic:topic-transport", "type": "belongsTo", "properties": { "sourceFile": "terms.json" } }, { "id": "edge:2152", "source": "term:rc-pair", "target": "term:equivalent-circuit-model", "type": "relatedTo", "properties": { "sourceFile": "terms.json", "meaning": "Related context; not a causal claim" } }, { "id": "edge:2153", "source": "term:rc-pair", "target": "term:relaxation", "type": "relatedTo", "properties": { "sourceFile": "terms.json", "meaning": "Related context; not a causal claim" } }, { "id": "edge:2154", "source": "term:rc-pair", "target": "term:charge-transfer", "type": "relatedTo", "properties": { "sourceFile": "terms.json", "meaning": "Related context; not a causal claim" } }, { "id": "edge:mentions/rc-pair/diffusion", "source": "term:rc-pair", "target": "term:diffusion", "type": "mentions", "properties": { "sourceFile": "terms.json", "method": "build_glossary.mention_index + mentions", "field": "definition", "meaning": "Text mention; not a causal claim" } }, { "id": "edge:mentions/rc-pair/capacitor", "source": "term:rc-pair", "target": "term:capacitor", "type": "mentions", "properties": { "sourceFile": "terms.json", "method": "build_glossary.mention_index + mentions", "field": "definition", "meaning": "Text mention; not a causal claim" } }, { "id": "edge:2157", "source": "term:rc-pair", "target": "visual:rc", "type": "illustratedBy", "properties": { "sourceFile": "visual-pages.json" } }, { "id": "edge:2158", "source": "term:rc-pair", "target": "reference:plett-modeling", "type": "cites", "properties": { "sourceFile": "wiki-references.json", "scope": "direct technical reference" } } ], "neighbors": [ { "id": "workflow:rc-response", "type": "Workflow", "label": "Observe an RC time constant", "properties": { "id": "rc-response", "title": "Observe an RC time constant", "kind": "studio", "summary": "An RC circuit uses source, resistor, capacitor and reference blocks.", "steps": [ "Keep R = 1 Ω and C = 1 F.", "Inspect capacitor voltage after one and two time constants." ], "example": "From zero initial voltage with a 1 V step, ideal capacitor voltage is about 0.632 V at 1 s and 0.865 V at 2 s.", "observe": "Doubling resistance or capacitance doubles the time constant.", "limits": "This generic circuit does not identify cell parameters from measurements.", "url": "https://design.lemonergy.com/cosim.html?example=physical-rc", "label": "Open the RC example", "evidence": [ "js/physical-network.js", "js/studio-examples.js" ] } }, { "id": "topic:topic-transport", "type": "Topic", "label": "Transport and modelling", "properties": { "id": "topic-transport", "name": "Transport and modelling", "lede": "How ions move, and the equations and models that describe a cell.", "context": "Specify phase, direction and boundaries.", "example": "The same concentration difference across 10 μm gives ten times the gradient across 100 μm; at equal D, first-law flux magnitude is ten times greater.", "lesson_url": "https://lemonergy.com/learn/transport/ficks-first-law/", "lesson_label": "Open diffusion" } }, { "id": "term:equivalent-circuit-model", "type": "Term", "label": "Equivalent circuit model", "properties": { "id": "equivalent-circuit-model", "name": "Equivalent circuit model", "abbr": "ECM", "aka": [ "Thevenin model" ], "section": "topic-transport", "definition": "A cell model built from a voltage source for OCV, a series resistor and one or more RC pairs for the slower dynamics. Its few parameters are fitted from pulse tests, and it is what most battery management systems run in real time.", "related": [ "rc-pair", "open-circuit-voltage", "hppc", "kalman-filter", "single-particle-model" ], "url": "https://lemonergy.com/learn/glossary/equivalent-circuit-model/", "mentions": [] } }, { "id": "term:relaxation", "type": "Term", "label": "Relaxation", "properties": { "id": "relaxation", "name": "Relaxation", "aka": [ "rest" ], "section": "topic-charging", "definition": "The slow recovery of a cell’s voltage towards open-circuit voltage after current stops, as concentration gradients inside the electrodes level out. It takes minutes to hours, which is why OCV measurements need a rest period.", "related": [ "open-circuit-voltage", "polarization", "diffusion", "hppc", "voltage-relaxation-analysis" ], "url": "https://lemonergy.com/learn/glossary/relaxation/", "mentions": [] } }, { "id": "term:charge-transfer", "type": "Term", "label": "Charge transfer", "properties": { "id": "charge-transfer", "name": "Charge transfer", "section": "topic-electrochemistry", "definition": "The step in which an electron crosses the interface between electrode and electrolyte as an ion is inserted or removed. Its resistance appears as a semicircle in impedance spectra and grows as films thicken and the cell cools.", "related": [ "butler-volmer", "double-layer", "electrochemical-impedance-spectroscopy", "overpotential", "solvation" ], "url": "https://lemonergy.com/learn/glossary/charge-transfer/", "mentions": [ "impedance", "electrode", "electrolyte" ] } }, { "id": "term:diffusion", "type": "Term", "label": "Diffusion", "properties": { "id": "diffusion", "name": "Diffusion", "section": "topic-transport", "definition": "The net movement of a species from where it is concentrated to where it is scarce, driven by random thermal motion. In a cell lithium diffuses through the electrolyte in the pores and, far more slowly, through the solid particles themselves.", "related": [ "ficks-first-law", "diffusion-coefficient", "solid-state-diffusion", "concentration-gradient", "migration" ], "lesson": "transport/ficks-first-law/#in-a-cell", "url": "https://lemonergy.com/learn/glossary/diffusion/", "mentions": [ "electrolyte" ] } }, { "id": "term:capacitor", "type": "Term", "label": "Capacitor", "properties": { "id": "capacitor", "name": "Capacitor", "section": "topic-units", "definition": "A component that stores energy as charge on two conducting plates separated by an insulator; its voltage rises in proportion to the charge, unlike a battery’s nearly flat curve. The large DC-link capacitors at an inverter’s input draw a huge inrush current when connected to a pack, which is why a pre-charge circuit fills them first.", "formula": "Q = C·V; E = ½·C·V²", "unit": "F (farad)", "related": [ "pre-charge", "inverter", "supercapacitor", "double-layer", "contactor" ], "example": { "title": "Calculate stored charge and energy", "text": "An ideal 100 F capacitor charged to 2 V stores 200 C and 200 J. Doubling voltage quadruples its stored energy when capacitance remains constant." }, "url": "https://lemonergy.com/learn/glossary/capacitor/", "mentions": [ "inrush-current" ] } }, { "id": "visual:rc", "type": "Visual", "label": "Voltage response and relaxation", "properties": { "title": "Voltage response and relaxation", "summary": "One time constant completes about 63% of a first-order voltage change.", "readout": "At τ = 20 s, 63.2% of the step response is complete; a relaxation retains 36.8%.", "formula": "τ = RC; step response = 1 − e^(−t/τ)", "note": "Two separate analytical experiments; normalized voltage, not measured data.", "software": { "status": "reference", "label": "Reference concept", "body": "An analytical RC response explains polarization and relaxation. It is not an identified RC network or a native Studio battery capability.", "href": "../chapter-1/" }, "html": "
First-order voltage response
First-order voltage responseTime (s) versus Fraction of voltage change. Step response; Separate relaxation experiment. Interpretation follows the graphs.000.263450.525900.7881351.05180Time (s)Fraction of voltagechange
Step responseSeparate relaxation experiment (dashed)
" } }, { "id": "reference:plett-modeling", "type": "Reference", "label": "Extended Kalman filtering for battery management systems of LiPB-based HEV battery packs: Part 2. Modeling and identification", "properties": { "title": "Extended Kalman filtering for battery management systems of LiPB-based HEV battery packs: Part 2. Modeling and identification", "publisher": "Journal of Power Sources", "url": "https://doi.org/10.1016/j.jpowsour.2004.02.032", "type": "Research article", "scope": "Battery charge balance, open-circuit voltage, ohmic loss, polarization dynamics and model identification; parameters require cell-specific data.", "year": 2004, "authors": [ "Gregory L. Plett" ], "accessed": "2026-10-27" } } ] }