{
"node": {
"id": "term:kirchhoffs-laws",
"type": "Term",
"label": "Kirchhoff’s laws",
"properties": {
"id": "kirchhoffs-laws",
"name": "Kirchhoff’s laws",
"aka": [
"Kirchhoff’s current law",
"Kirchhoff’s voltage law",
"KCL",
"KVL"
],
"section": "topic-units",
"definition": "Two rules of circuit analysis: the currents flowing into any node sum to zero, and the voltages around any closed loop sum to zero. In a pack they explain why every cell in a series string carries the same current, and why cells in a parallel group share current unequally when their resistances differ.",
"formula": "ΣI = 0 at a node; ΣV = 0 around a loop",
"related": [
"series-parallel",
"ohms-law",
"current",
"voltage",
"internal-resistance",
"cell-to-cell-variation"
],
"example": {
"title": "Balance a parallel junction",
"text": "If 6 A enters a junction and 2 A leaves through one branch, 4 A must leave through the other branch in a steady circuit. Voltage differences around a closed loop must also sum to zero."
},
"url": "https://lemonergy.com/learn/glossary/kirchhoffs-laws/",
"mentions": [
"string"
]
}
},
"edges": [
{
"id": "edge:158",
"source": "term:kirchhoffs-laws",
"target": "workflow:ohm-circuit",
"type": "usedIn",
"properties": {
"sourceFile": "wiki-blocks.json"
}
},
{
"id": "edge:5659",
"source": "term:kirchhoffs-laws",
"target": "topic:topic-units",
"type": "belongsTo",
"properties": {
"sourceFile": "terms.json"
}
},
{
"id": "edge:5660",
"source": "term:kirchhoffs-laws",
"target": "term:series-parallel",
"type": "relatedTo",
"properties": {
"sourceFile": "terms.json",
"meaning": "Related context; not a causal claim"
}
},
{
"id": "edge:5661",
"source": "term:kirchhoffs-laws",
"target": "term:ohms-law",
"type": "relatedTo",
"properties": {
"sourceFile": "terms.json",
"meaning": "Related context; not a causal claim"
}
},
{
"id": "edge:5662",
"source": "term:kirchhoffs-laws",
"target": "term:current",
"type": "relatedTo",
"properties": {
"sourceFile": "terms.json",
"meaning": "Related context; not a causal claim"
}
},
{
"id": "edge:5663",
"source": "term:kirchhoffs-laws",
"target": "term:voltage",
"type": "relatedTo",
"properties": {
"sourceFile": "terms.json",
"meaning": "Related context; not a causal claim"
}
},
{
"id": "edge:5664",
"source": "term:kirchhoffs-laws",
"target": "term:internal-resistance",
"type": "relatedTo",
"properties": {
"sourceFile": "terms.json",
"meaning": "Related context; not a causal claim"
}
},
{
"id": "edge:5665",
"source": "term:kirchhoffs-laws",
"target": "term:cell-to-cell-variation",
"type": "relatedTo",
"properties": {
"sourceFile": "terms.json",
"meaning": "Related context; not a causal claim"
}
},
{
"id": "edge:mentions/kirchhoffs-laws/string",
"source": "term:kirchhoffs-laws",
"target": "term:string",
"type": "mentions",
"properties": {
"sourceFile": "terms.json",
"method": "build_glossary.mention_index + mentions",
"field": "definition",
"meaning": "Text mention; not a causal claim"
}
},
{
"id": "edge:5667",
"source": "term:kirchhoffs-laws",
"target": "visual:pack",
"type": "illustratedBy",
"properties": {
"sourceFile": "visual-pages.json"
}
}
],
"neighbors": [
{
"id": "workflow:ohm-circuit",
"type": "Workflow",
"label": "Relate current and voltage",
"properties": {
"id": "ohm-circuit",
"title": "Relate current and voltage",
"kind": "studio",
"summary": "Conserving components solve constitutive relations and node balance.",
"steps": [
"Inspect source and resistor in the RC example.",
"Compare branch current with resistor voltage."
],
"example": "A 1 V drop across 2 Ω implies 0.5 A.",
"observe": "Topology sets individual element voltages.",
"limits": "The RC example includes a capacitor: transient current varies and source voltage is not always resistor voltage.",
"url": "https://design.lemonergy.com/cosim.html?example=physical-rc",
"label": "Open the electrical circuit",
"evidence": [
"js/physical-network.js",
"js/studio-examples.js"
]
}
},
{
"id": "topic:topic-units",
"type": "Topic",
"label": "Units and electrical basics",
"properties": {
"id": "topic-units",
"name": "Units and electrical basics",
"lede": "The quantities every datasheet is written in, and how they relate.",
"context": "Use consistent units and cell/pack basis.",
"example": "10 A for 30 min transfers 5 Ah. At constant 3.6 V this is 18 Wh; varying voltage requires integration.",
"lesson_url": "https://lemonergy.com/learn/fundamentals/capacity-and-c-rate/",
"lesson_label": "Open capacity and C-rate"
}
},
{
"id": "term:series-parallel",
"type": "Term",
"label": "Series and parallel connection",
"properties": {
"id": "series-parallel",
"name": "Series and parallel connection",
"aka": [
"xSyP"
],
"section": "topic-pack",
"definition": "Cells in series add their voltages; cells in parallel add their capacities and share current. A pack is described as, for example, 96s4p: 96 groups in series, each of 4 cells in parallel. Series strings need balancing; parallel groups self-balance through their shared terminals.",
"formula": "V = n_s·V_cell, Q = n_p·Q_cell",
"related": [
"module",
"cell-balancing",
"pack-voltage",
"volt",
"fuse"
],
"lesson": "fundamentals/battery-basics/#cell-module-pack",
"example": {
"title": "Assemble an ideal 4s2p pack",
"text": "Eight identical 3.6 V, 5 Ah cells arranged as four series groups with two cells in parallel give 14.4 V nominal, 10 Ah and 144 Wh. Interconnect losses, cell variation and usable voltage limits are additional constraints."
},
"url": "https://lemonergy.com/learn/glossary/series-parallel/",
"mentions": []
}
},
{
"id": "term:ohms-law",
"type": "Term",
"label": "Ohm’s law",
"properties": {
"id": "ohms-law",
"name": "Ohm’s law",
"section": "topic-units",
"definition": "Voltage across a resistance equals current times that resistance. Applied to a cell it predicts the voltage drop under load from the internal resistance, which is the first-order reason terminal voltage sags.",
"formula": "V = I × R",
"related": [
"internal-resistance",
"ir-drop",
"ohm",
"kirchhoffs-laws"
],
"example": {
"title": "Convert a resistance into a voltage drop",
"text": "A 10 A current through a 20 mΩ resistance produces 0.2 V of voltage drop. Use 0.020 Ω in V = IR; inserting the number 20 without converting milliohms would be wrong."
},
"url": "https://lemonergy.com/learn/glossary/ohms-law/",
"mentions": [
"voltage"
]
}
},
{
"id": "term:current",
"type": "Term",
"label": "Current",
"properties": {
"id": "current",
"name": "Current",
"section": "topic-units",
"definition": "The rate at which charge flows through the cell and its circuit, in amperes. Outside the cell it is carried by electrons; inside, by lithium ions moving through the electrolyte.",
"formula": "I = dQ/dt",
"unit": "A",
"related": [
"ampere",
"c-rate",
"ionic-path"
],
"lesson": "fundamentals/cell-anatomy/#discharge",
"example": {
"title": "Convert charge transfer to current",
"text": "If 120 C passes a point in 60 s at a steady rate, the current is 2 A. When the rate varies, integrate the current trace to recover the total charge."
},
"url": "https://lemonergy.com/learn/glossary/current/",
"mentions": [
"electrolyte"
]
}
},
{
"id": "term:voltage",
"type": "Term",
"label": "Voltage",
"properties": {
"id": "voltage",
"name": "Voltage",
"aka": [
"terminal voltage"
],
"section": "topic-units",
"definition": "The potential difference between a cell’s two terminals. It comes from the chemical difference between the electrodes, moves with state of charge, and sags under load because of internal resistance.",
"unit": "V",
"related": [
"open-circuit-voltage",
"nominal-voltage",
"internal-resistance",
"ir-drop"
],
"lesson": "fundamentals/cell-anatomy/#voltage",
"url": "https://lemonergy.com/learn/glossary/voltage/",
"mentions": [
"state-of-charge"
]
}
},
{
"id": "term:internal-resistance",
"type": "Term",
"label": "Internal resistance",
"properties": {
"id": "internal-resistance",
"name": "Internal resistance",
"abbr": "IR",
"aka": [
"DC resistance",
"DCIR"
],
"section": "topic-units",
"definition": "The resistance a cell presents to current, from its foils, electrolyte, interfaces and the reactions themselves. It converts part of the delivered energy into heat, sets the voltage drop under load, and rises as the cell ages; a large automotive cell has about a milliohm, a small cylindrical cell tens.",
"unit": "mΩ",
"related": [
"ohms-law",
"ir-drop",
"impedance-rise",
"dcir",
"area-specific-resistance",
"resistance-capacity-product"
],
"lesson": "fundamentals/battery-basics/#datasheet",
"url": "https://lemonergy.com/learn/glossary/internal-resistance/",
"mentions": [
"electrolyte",
"cylindrical-cell"
]
}
},
{
"id": "term:cell-to-cell-variation",
"type": "Term",
"label": "Cell-to-cell variation",
"properties": {
"id": "cell-to-cell-variation",
"name": "Cell-to-cell variation",
"section": "topic-state",
"definition": "The spread in capacity, resistance and self-discharge between nominally identical cells, from manufacturing and from unequal temperatures in service. It is why packs need balancing and why grading matches cells before assembly.",
"related": [
"cell-balancing",
"grading",
"end-of-line-testing",
"thermal-management"
],
"url": "https://lemonergy.com/learn/glossary/cell-to-cell-variation/",
"mentions": [
"self-discharge"
]
}
},
{
"id": "term:string",
"type": "Term",
"label": "String",
"properties": {
"id": "string",
"name": "String",
"aka": [
"battery string",
"series string"
],
"section": "topic-pack",
"definition": "A chain of cells or modules connected in series to reach the system voltage, the basic electrical unit of a large battery. In stationary storage each rack is usually one string of about 1000–1500 V with its own contactors and BMS, and many strings are paralleled on a common DC bus.",
"related": [
"series-parallel",
"pack-voltage",
"stationary-storage",
"parallel-string-current-sharing",
"bms-architecture",
"contactor"
],
"url": "https://lemonergy.com/learn/glossary/string/",
"mentions": [
"bms"
]
}
},
{
"id": "visual:pack",
"type": "Visual",
"label": "Series voltage and parallel capacity",
"properties": {
"title": "Series voltage and parallel capacity",
"summary": "Count series and parallel connections separately.",
"readout": "4S2P: 8 cells, 14.8 V, 10 Ah, 148 Wh.",
"formula": "V_pack = Ns V_cell; Q_pack = Np Q_cell",
"note": "Identical 3.7 V, 5 Ah cells; ideal equal current sharing and no losses.",
"software": {
"status": "reference",
"label": "Reference concept",
"body": "Ideal pack ratings use V_pack = Ns V_cell and Q_pack = Np Q_cell. The core energy helper can multiply these ratings. Imbalance and current sharing require additional models.",
"href": "../fundamentals/capacity-and-c-rate/"
},
"html": "Voltage along one series string