Linked from
The 9 pages that link to Kirchhoff's current law, each with the reason it gives.
Gustav KirchhoffBroader topic: It expresses charge conservation at circuit junctions.
Flow conservationCompared with: It is a physical instance of the same vertex-balance principle.
Nodal analysisRelated: This current-balance rule supplies the equations at each nonreference node.
Current sourceRelated: It determines how source current divides among connected branches.
Miller theoremRelated: Node-current equations provide a direct way to verify the equivalent circuit.