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The Junction Rule
Kirchhoff's junction rule states that at any circuit junction, the sum of the currents flowing into and out of that junction are equal.
Learning Objectives

Describe limitations of the Kirchhoff's junction rule

Formulate the Kirchhoff's junction rule
Key Points
 Kirchhoff's junction rule is an application of the principle of conservation of electric charge: current is flow of charge per time, and if current is constant, that which flows into a point in a circuit must equal that which flows out of it.
 The mathematical representation of Kirchhoff's law is:
$\sum_{k=1}^{n} I_k=0$ where I_{k} is the current of k, and n is the total number of wires flowing into and out of a junction in consideration.  Kirchhoff's junction law is limited in its applicability over regions, in which charge density may not be constant. Because charge is conserved, the only way this is possible is if there is a flow of charge across the boundary of the region. This flow would be a current, thus violating the law.
Terms

electric charge
A quantum number that determines the electromagnetic interactions of some subatomic particles; by convention, the electron has an electric charge of 1 and the proton +1, and quarks have fractional charge.

current
The time rate of flow of electric charge.
Full Text
Kirchhoff's junction rule, also known as Kirchhoff's current law (KCL), Kirchoff's first law, Kirchhoff's point rule, and Kirchhoff's nodal rule, is an application of the principle of conservation of electric charge.
Kirchhoff's junction rule states that at any junction (node) in an electrical circuit, the sum of the currents flowing into that junction is equal to the sum of the currents flowing out of that junction. In other words, given that a current will be positive or negative depending on whether it is flowing towards or away from a junction, the algebraic sum of currents in a network of conductors meeting at a point is equal to zero. A visual representation can be seen in .
Kirchhoff's Junction Law
Kirchhoff's Junction Law illustrated as currents flowing into and out of a junction.
Thus, Kirchoff's junction rule can be stated mathematically as a sum of currents (I):
where n is the total number of branches carrying current towards or away from the node.
This law is founded on the conservation of charge (measured in coulombs), which is the product of current (amperes) and time (seconds).
Limitation
Kirchhoff's junction law is limited in its applicability. It holds for all cases in which total electric charge (Q) is constant in the region in consideration. Practically, this is always true so long as the law is applied for a specific point. Over a region, however, charge density may not be constant. Because charge is conserved, the only way this is possible is if there is a flow of charge across the boundary of the region. This flow would be a current, thus violating Kirchhoff's junction law.
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Key Term Reference
 Law
 Appears in these related concepts: Newton and His Laws, Mechanical Work and Electrical Energy, and Models, Theories, and Laws
 application
 Appears in these related concepts: What is Potential Energy?, Work Done by a Variable Force, and Physics and Other Fields
 circuit
 Appears in these related concepts: Driven Oscillations and Resonance, Power, and Combinations of Capacitors: Series and Parallel
 conductor
 Appears in these related concepts: Wireless Communication, ParallelPlate Capacitor, and Conductors and Insulators
 conservation
 Appears in these related concepts: Conservation of Mechanical Energy, Museums and Private Collections, and Linear Momentum
 electrical circuit
 Appears in these related concepts: Safety Precautions in the Household, Photon Energies of the EM Spectrum, and Different Types of Currents
 node
 Appears in these related concepts: Sound Production: Vibrating String and Air Columns, Standing Waves in Air Columns, and Functions of Stems
Sources
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Cite This Source
Source: Boundless. “The Junction Rule.” Boundless Physics. Boundless, 21 Jul. 2015. Retrieved 13 Feb. 2016 from https://www.boundless.com/physics/textbooks/boundlessphysicstextbook/circuitsanddirectcurrents20/kirchhoffsrules152/thejunctionrule5396331/