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    "title": "Kirchhoff: currents balance at junctions and around loops",
    "summary": "Kirchhoff states and derives steady-circuit junction and loop relations: current balances at a junction, and signed resistance drops around a closed path equal the electromotive forces on that path.\n\nA complicated circuit becomes manageable when every meeting point and every closed route supplies a simple equation. Kirchhoff uses the fact that steady charge cannot accumulate at a junction, together with the potential changes and sources along a loop. These local statements connect Ohm's wire relation to an entire network. His surrounding disk experiments show both where the theory agreed with observations and where the apparatus could not resolve a proposed test.",
    "boundary": "The assessed delta is the two relations on pages 513-514 of the 1845 paper, within its steady galvanic, resistive-wire and localized-source model. Junction balance uses absence of charge accumulation; loop balance uses the source and potential conventions stated in the original. It does not automatically cover arbitrary changing magnetic flux, distributed high-frequency circuits or all later component models. The preceding circular thin-disk theory is context, not a claim of a completely validated disk-resistance formula. Small contacts and approximate end conditions are explicit, and page 512 says the attempted total-resistance experiment was too uncertain to decide for or against theory. The unread 1846 supplement is a separate follow-up; later formulas are not absorbed here. Ohm and earlier balance constructions remain prior work.",
    "area": "Electrical network theory",
    "topic": "Engineering",
    "year": 1845,
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        "title": "Studiosus Kirchhoff, Ueber den Durchgang eines elektrischen Stromes durch eine Ebene, insbesondere durch eine kreisfoermige (1845), original facsimile",
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      "what_changed": "Kirchhoff states and derives steady-circuit junction and loop relations: current balances at a junction, and signed resistance drops around a closed path equal the electromotive forces on that path.",
      "scope": "Kirchhoff states and derives steady-circuit junction and loop relations: current balances at a junction, and signed resistance drops around a closed path equal the electromotive forces on that path. The assessed delta is the two relations on pages 513-514 of the 1845 paper, within its steady galvanic, resistive-wire and localized-source model. Junction balance uses absence of charge accumulation; loop balance uses the source and potential conventions stated in the original. It does not automatically cover arbitrary changing magnetic flux, distributed high-frequency circuits or all later component models. The preceding circular thin-disk theory is context, not a claim of a completely validated disk-resistance formula. Small contacts and approximate end conditions are explicit, and page 512 says the attempted total-resistance experiment was too uncertain to decide for or against theory. The unread 1846 supplement is a separate follow-up; later formulas are not absorbed here. Ohm and earlier balance constructions remain prior work.",
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        "description": "The assessed delta is the two relations on pages 513-514 of the 1845 paper, within its steady galvanic, resistive-wire and localized-source model. Junction balance uses absence of charge accumulation; loop balance uses the source and potential conventions stated in the original. It does not automatically cover arbitrary changing magnetic flux, distributed high-frequency circuits or all later component models. The preceding circular thin-disk theory is context, not a claim of a completely validated disk-resistance formula. Small contacts and approximate end conditions are explicit, and page 512 says the attempted total-resistance experiment was too uncertain to decide for or against theory. The unread 1846 supplement is a separate follow-up; later formulas are not absorbed here. Ohm and earlier balance constructions remain prior work.",
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          "citation": "Studiosus Kirchhoff, Ueber den Durchgang eines elektrischen Stromes durch eine Ebene, insbesondere durch eine kreisfoermige (1845), original facsimile",
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          "citation": "Wikisource author and work index for Gustav Robert Kirchhoff: the 1845, 1846 and 1847 electrical papers",
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      "statement": "# Kirchhoff: currents balance at junctions and around loops\n\nKirchhoff states and derives steady-circuit junction and loop relations: current balances at a junction, and signed resistance drops around a closed path equal the electromotive forces on that path.\n\nA complicated circuit becomes manageable when every meeting point and every closed route supplies a simple equation. Kirchhoff uses the fact that steady charge cannot accumulate at a junction, together with the potential changes and sources along a loop. These local statements connect Ohm's wire relation to an entire network. His surrounding disk experiments show both where the theory agreed with observations and where the apparatus could not resolve a proposed test.\n\n## Scientific scope\n\nThe assessed delta is the two relations on pages 513-514 of the 1845 paper, within its steady galvanic, resistive-wire and localized-source model. Junction balance uses absence of charge accumulation; loop balance uses the source and potential conventions stated in the original. It does not automatically cover arbitrary changing magnetic flux, distributed high-frequency circuits or all later component models. The preceding circular thin-disk theory is context, not a claim of a completely validated disk-resistance formula. Small contacts and approximate end conditions are explicit, and page 512 says the attempted total-resistance experiment was too uncertain to decide for or against theory. The unread 1846 supplement is a separate follow-up; later formulas are not absorbed here. Ohm and earlier balance constructions remain prior work.\n\n## People and systems\n\nGustav Robert Kirchhoff\n\n\n\n## Original sources\n\n- [Studiosus Kirchhoff, Ueber den Durchgang eines elektrischen Stromes durch eine Ebene, insbesondere durch eine kreisfoermige (1845), original facsimile](https://zenodo.org/records/2422851/files/article.pdf?download=1)\n- [Wikisource author and work index for Gustav Robert Kirchhoff: the 1845, 1846 and 1847 electrical papers](https://de.wikisource.org/wiki/Gustav_Robert_Kirchhoff)\n",
      "summary": "Kirchhoff states and derives steady-circuit junction and loop relations: current balances at a junction, and signed resistance drops around a closed path equal the electromotive forces on that path.\n\nA complicated circuit becomes manageable when every meeting point and every closed route supplies a simple equation. Kirchhoff uses the fact that steady charge cannot accumulate at a junction, together with the potential changes and sources along a loop. These local statements connect Ohm's wire relation to an entire network. His surrounding disk experiments show both where the theory agreed with observations and where the apparatus could not resolve a proposed test.",
      "title": "Kirchhoff: currents balance at junctions and around loops"
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    "title": "Kirchhoff: currents balance at junctions and around loops",
    "context": "Electrical network theory",
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    "what_changed": "Kirchhoff states and derives steady-circuit junction and loop relations: current balances at a junction, and signed resistance drops around a closed path equal the electromotive forces on that path.",
    "scope": "Kirchhoff states and derives steady-circuit junction and loop relations: current balances at a junction, and signed resistance drops around a closed path equal the electromotive forces on that path. The assessed delta is the two relations on pages 513-514 of the 1845 paper, within its steady galvanic, resistive-wire and localized-source model. Junction balance uses absence of charge accumulation; loop balance uses the source and potential conventions stated in the original. It does not automatically cover arbitrary changing magnetic flux, distributed high-frequency circuits or all later component models. The preceding circular thin-disk theory is context, not a claim of a completely validated disk-resistance formula. Small contacts and approximate end conditions are explicit, and page 512 says the attempted total-resistance experiment was too uncertain to decide for or against theory. The unread 1846 supplement is a separate follow-up; later formulas are not absorbed here. Ohm and earlier balance constructions remain prior work.",
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