49-kirchhoff-circuit-laws

Both Kirchhoff’s current law and Kirchhoff’s voltage law can be directly derived from Maxwell’s equations. However, Kirchhoff’s circuit laws are simplified form of Maxwell’s equations designated for electric circuit analysis.

Kirchhoff’s current law known also as KCL, Kirchhoff’s first law or Kirchhoff’s junction rule is based upon conservation of charge law and says that is, the algebraic sum of all branch currents flowing into any node must be zero. Kirchhoff’s current law is valid for DC and AC stationary electric networks alike. For given electric circuit, number of independent equations according to Kirchhoff’s current law is N – 1, where N is the number of nodes.

kirch_eq01

Kirchhoff’s voltage law known also as KVL, Kirchhoff’s second law or Kirchhoff’s mesh rule is based upon energy conservation law and says that the algebraic sum of the products of the resistances of the conductors and the currents in them in a closed loop is equal to the total emf available in that loop. Kirchhoff’s voltage law is valid for DC and AC stationary electric networks alike. For given electric circuit, number of independent equations according to Kirchhoff’s voltage law is M, where M is the number of meshes.

kvl_a

Even though Kirchhoff’s circuit laws are simplified form of Maxwell’s equations, there are still very complex to be utilized directly for solving electric circuit. For example, if we need to solve circuit given in figure above we would need to write (and solve) six equations with six variables (three written according to Kirchhoff’s voltage law, having three meshes and three written according to Kirchhoff’s current law, having four nodes). It is more appropriate to solve electric circuit by writing smaller number of equations and smaller number of variables. This can be achieved by using one of the following solving methods:

All above mentioned methods and theorems are in accordance with Kirchhoff circuit laws yet less complex because lots of the magnitudes are already included into equations written.

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