Kirchhoff’s Circuit laws are two approximate equalities that deal with the current and voltage in electrical circuits. These approximations were first described in 1845 by Gustav Kirchhoff [1]. This generalized the work of Georg Ohm and preceded the work of Maxwell. Both of Kirchhoff’s laws can be understood as corollaries of the Maxwell equations in the low-frequency limit. The laws were the first approximations for AC circuits.

Kirchhoff’s current law is often referred to as Kirchhoff’s junction rule or Kirchhoff’s point rule. The principle of conservation of electric charges states that at any junction in an electrical circuit, the sum of currents flowing into the node is equal to the sum of currents flowing out of that node, or the algebraic sum of currents in a network of conductors meeting at a point is zero.

∑ I_{K} = 0

KCL in its usual form is dependent on the assumption that current flows only in conductors and that whenever current flows into one end of a conductor it immediately flows out of the other end. This however is not a safe assumption for AC circuits. It is possibly to salvage the form of KCL by considering “parasitic capacitances” distributed along the conductors.

[1] Oldham, p.52