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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:
The Tellegen theorem is applicable to a multitude of network systems. The basic assumptions for the systems are the conservation of flow of extensive quantities (Kirchhoff's current law, KCL) and the uniqueness of the potentials at the network nodes (Kirchhoff's voltage law, KVL).
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.
In principle, nodal analysis uses Kirchhoff's current law (KCL) at N-1 nodes to get N-1 independent equations. Since equations generated with KCL are in terms of currents going in and out of nodes, these currents, if their values are not known, need to be represented by the unknown variables (node voltages).
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
Mesh analysis and loop analysis both make systematic use of Kirchhoff’s voltage law to arrive at a set of equations guaranteed to be solvable if the circuit has a solution. [1] Mesh analysis is usually easier to use when the circuit is planar, compared to loop analysis.
Kirchhoff Institute of Physics, a research institute in Heidelberg, Germany; Kirchhoff's laws, a group of laws of physics (in thermodynamics, electrical circuits, spectroscopy, and fluid mechanics) named for Gustav Kirchhoff; Kirchhoff's theorem, in graph theory, a theorem concerning the number of "spanning trees" in a graph, named for Gustav ...
There is also a dual version of Miller theorem that is based on Kirchhoff's current law (Miller theorem for currents): if there is a branch in a circuit with impedance connecting a node, where two currents and converge to ground, we can replace this branch by two conducting the referred currents, with impedances respectively equal to (+) and ...