# 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.

#### 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 Ik 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

• The time rate of flow of 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.

#### Figures

1. ##### Kirchhoff's Junction Law

Kirchhoff's Junction Law illustrated as currents flowing into and out of a junction.

2. ##### Kirchhoff's Loop and Junction Rules Theory

We justify Kirchhoff's Rules from diarrhea and conservation of energy. Some people call 'em laws, but not me!

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 Figure 2 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 Figure 1.

Thus, Kirchoff's junction rule can be stated mathematically as a sum of currents (I):

$\sum_{k=1}^{n} I_k=0$

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.

#### Key Term Glossary

ampere
A unit of electrical current; the standard base unit in the International System of Units. Abbreviation: amp. Symbol: A.
##### Appears in these related concepts:
application
the act of putting something into operation
##### Appears in these related concepts:
circuit
A pathway of electric current composed of individual electronic components, such as resistors, transistors, capacitors, inductors and diodes, connected by conductive wires or traces through which electric current can flow. T
##### Appears in these related concepts:
conductor
A material which contains movable electric charges.
##### Appears in these related concepts:
conservation
A particular measurable property of an isolated physical system does not change as the system evolves.
##### Appears in these related concepts:
coulomb
In the International System of Units, the derived unit of electric charge; the amount of electric charge carried by a current of 1 ampere flowing for 1 second. Symbol: C
##### Appears in these related concepts:
current
The time rate of flow of electric charge.
##### Appears in these related concepts:
electrical circuit
An interconnection of electrical elements such as resistors, inductors, capacitors, transmission lines, voltage sources, current sources and switches that has a closed loop giving a return path for the current.
##### Appears in these related concepts:
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.
##### Appears in these related concepts:
Law
A concise description, usually in the form of a mathematical equation, used to describe a pattern in nature
##### Appears in these related concepts:
node
Point on a wave where there is no displacement.