Abstract: The basic concept of ＂independent circuit＂ in KVL was defined incorrectly by some authors previously. This paper points out clearly the problem and suggests a more accurate definition. Further, with ＂independent circuit＂ defined in the new way, the paper proves the independence of Kirchhoffs equations and the uniqueness of solutions to those equations by using some methods of linear algebra, geometry and topology.

Key words: circuit theory, KVL, independent circuit, linear independence