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Proof of the number of independent Kirchhoff equations in an electrical circuit

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2 Author(s)
Feldmann, P. ; AT&T Bell Lab., Murray Hill, NJ, USA ; Rohrer, R.A.

A compact inductive proof is presented that the number of linearly independent KCL (Kirchhoff's current law) node equations of b-branch n-node connected circuits is n-1 and the number of independent KVL (Kirchhoff's voltage law) loop equations is b-n+1. Because it is easily illustrated pictorially and does not rely on graph theoretic concepts it is suitable for presentation at an elementary level of circuit theoretic instruction

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Circuits and Systems, IEEE Transactions on  (Volume:38 ,  Issue: 7 )