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The current entering any junction is equal to the current leaving that junction. i 2 + i 3 = i 1 + i 4. This law, also called Kirchhoff's first law, or Kirchhoff's junction rule, states that, for any node (junction) in an electrical circuit, the sum of currents flowing into that node is equal to the sum of currents flowing out of that node; or equivalently:
Kirchhoff's current law is the basis of nodal analysis. In electric circuits analysis, nodal analysis, node-voltage analysis, or the branch current method is a method of determining the voltage (potential difference) between "nodes" (points where elements or branches connect) in an electrical circuit in terms of the branch currents.
Kirchhoff's Current Law: The sum of all currents entering a node is equal to the sum of all currents leaving the node, or the sum of total current at a junction is zero. Kirchhoff's voltage law: The directed sum of the electrical potential differences around a circuit must be zero.
Kirchhoff's laws, named after Gustav Kirchhoff, may refer to: Kirchhoff's circuit laws in electrical engineering; Kirchhoff's law of thermal radiation; Kirchhoff equations in fluid dynamics; Kirchhoff's three laws of spectroscopy; Kirchhoff's law of thermochemistry; Kirchhoff's theorem about the number of spanning trees in a graph
Gustav Robert Kirchhoff (German: [ˈgʊs.taf ˈkɪʁçhɔf]; 12 March 1824 – 17 October 1887) was a German physicist, mathematican and chemist who contributed to the fundamental understanding of electrical circuits, spectroscopy and the emission of black-body radiation by heated objects.
When faced with a new circuit, the software first tries to find a steady state solution wherein all the nodes conform to Kirchhoff's Current Law and the voltages across and through each element of the circuit conform to the voltage/current equations governing that element.
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From Kirchhoff's circuit laws the rules for combining conductance can be deducted. For two conductances and in parallel, the voltage across them is the same and from Kirchhoff's current law (KCL) the total current is = +.