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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.
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).
Here is a partial list of electrical dualities: voltage – current; parallel – series (circuits) resistance – conductance; voltage division – current division; impedance – admittance; capacitance – inductance; reactance – susceptance; short circuit – open circuit; Kirchhoff's current law – Kirchhoff's voltage law. KVL and KCL
The potential differences across the components are the same in magnitude, and they also have identical polarities. The same voltage is applied to all circuit components connected in parallel. The total current is the sum of the currents through the individual components, in accordance with Kirchhoff's current law.
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
The name "harmonic balance" is descriptive of the method, which starts with Kirchhoff's Current Law written in the frequency domain and a chosen number of harmonics. A sinusoidal signal applied to a nonlinear component in a system will generate harmonics of the fundamental frequency. Effectively the method assumes a linear combination of ...
The modern method is simply to create a set of conditions from the above Kirchhoff laws (junctions and head-loss criteria). Then, use a Root-finding algorithm to find Q values that satisfy all the equations. The literal friction loss equations use a term called Q 2, but we want to preserve any changes in direction.