What is recorded here?
Kirchhoff gives a combinatorial solution of steady linear wire-network currents using independent cycles, resistance products and sums of electromotive forces around the remaining cycles. The shape of a network helps organize its equations. Kirchhoff removes just enough wires to leave no closed route, then restores individual wires to obtain independent cycles. Products of resistances on the removed wires build a common denominator; source sums on the remaining cycles determine the currents. This links a physical circuit to a reusable combinatorial structure. It is the exact historical network solution, with modern tree terminology used only to explain its structure.
Source-linked catalogue note. A detailed explanatory guide has not yet been prepared for this entry.
Scientific scope
The graph-based solution concerns the stated linear electrical network, resistances and circuit constraints. Connectivity/uniqueness and exceptional parameter choices matter. It does not model arbitrary nonlinear/time-varying circuits or give a universal numerical conditioning guarantee. The 1845 current/loop laws and later general graph theorems remain separate contributions.
Read the original work
- G. Kirchhoff, Ueber die Aufloesung der Gleichungen, auf welche man bei der Untersuchung der linearen Vertheilung galvanischer Stroeme gefuehrt wird (1847), original facsimile
- Wikisource author and work index for Gustav Robert Kirchhoff: the 1845, 1846 and 1847 electrical papers
This English explanation is an editorial reading view. It does not replace the complete original work or certify its science.
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People and systems
Gustav Robert Kirchhoff
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English catalogue narrative
Kirchhoff: solving a network through its cycles and trees
Kirchhoff gives a combinatorial solution of steady linear wire-network currents using independent cycles, resistance products and sums of electromotive forces around the remaining cycles.
The shape of a network helps organize its equations. Kirchhoff removes just enough wires to leave no closed route, then restores individual wires to obtain independent cycles. Products of resistances on the removed wires build a common denominator; source sums on the remaining cycles determine the currents. This links a physical circuit to a reusable combinatorial structure. It is the exact historical network solution, with modern tree terminology used only to explain its structure.
Scientific scope
The graph-based solution concerns the stated linear electrical network, resistances and circuit constraints. Connectivity/uniqueness and exceptional parameter choices matter. It does not model arbitrary nonlinear/time-varying circuits or give a universal numerical conditioning guarantee. The 1845 current/loop laws and later general graph theorems remain separate contributions.
People and systems
Gustav Robert Kirchhoff