Node Rule

claimed by Shannon Gerhard

Definition

The node rule is one of Kirchhoff's laws regarding circuits and current. This law states that at any junction in an electrical circuit, the amount of current flowing into the junction is equal to the amount of current flowing out of the junction. This law is also referred to as Kirchhoff's junction rule, Kirchhoff's nodal rule, Kirchhoff's current law, and Kirchhoff's first law. This rule is an application of the conservation of electric charge, basically that charge within a circuit cannot be created or destroyed.

Mathematically, the Node Rule states ∑ I = 0, where I stands for the current of the individual parts or wires in a circuit.

Kirchhoff's Laws

Kirchhoff developed two very important rules that allow us to "solve" simple circuits, or find out different values for the different components involved in the circuit. The node rule is Kirchhoff's first rule, but there is one more, called the loop rule or Kirchhoff's Voltage Law. The loop rule states that, going around in a loop within a circuit, one will find that the voltages around the loop will sum to 0. Because voltage is just energy per unit charge, and both energy and charge are conserved, this is basically stating that no charge or energy is lost or created within the circuit. Both of Kirchhoff's Laws are very important to solving circuits and you can click here to learn more about the loop rule.

Limitations

Time-Varying Currents

Kirchhoff's law is based off the conservation of charge along with the nature of conductors. This law assumes that current will immediately flow from one end of the conductor to the other, which may not be true for time-varying currents, especially with higher frequencies.

Regions vs Circuits

Throughout a region, the charge can vary and be non-uniform, unlike in a wire. According to the law of conservation of charge, the only way to have a non-uniform charge density is if there is a net flow of current in or out of the region, which clearly violates the Node Rule. Therefore the node rule cannot be applied to regions with non-uniform charge densities. When looking at a junction in an electric circuit, we are looking at a point and therefore the point (which is infinitesimally small) must have a uniform charge distribution. In general, wires should have a uniform charge distribution across their length, because they are conductors and allow for the movement of charge.

Other Topics

History

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See Also

Further Reading

Node Rule

External Links

https://www.boundless.com/physics/textbooks/boundless-physics-textbook/circuits-and-direct-currents-20/kirchhoff-s-rules-152/the-junction-rule-539-6331/

https://en.wikipedia.org/wiki/Kirchhoff%27s_circuit_laws#Kirchhoff.27s

References

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