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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:
This is because in current dividers, total energy expended is minimized, resulting in currents that go through paths of least impedance, hence the inverse relationship with impedance. Comparatively, voltage divider is used to satisfy Kirchhoff's voltage law (KVL). The voltage around a loop must sum up to zero, so the voltage drops must be ...
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 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
Kirchhoff's current law: The sum of all currents entering a node is equal to the sum of all currents leaving the node. Kirchhoff's voltage law: The directed sum of the electrical potential differences around a loop must be zero. Ohm's law: The voltage across a resistor is equal to the product of the resistance and the current flowing through it.
Gustav Robert Kirchhoff (German: [ˈgʊs.taːf ˈkɪʁç.hɔf]; 12 March 1824 – 17 October 1887) was a German chemist, mathematican and physicist who contributed to the fundamental understanding of electrical circuits, spectroscopy and the emission of black-body radiation by heated objects.
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 = +.
A dual of a relationship is formed by interchanging voltage and current in an expression. The dual expression thus produced is of the same form, and the reason that the dual is always a valid statement can be traced to the duality of electricity and magnetism. Here is a partial list of electrical dualities: voltage – current