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
Solving Circuits
In order to solve circuits, we must first define a couple characteristics of circuits.
- The voltage of a (perfect, or non-resistive) wire is equal to its length (in meters) times its electric field.
- The voltage of an ohmic resistor (including a resistive wire) is equal to current times resistance.
- The voltage of a capacitor is equal to the charge on the capacitor divided by its capacitance.
There are other characteristics and equations that may be useful, but these two are the most important and used. If you are confused by any of the components of circuits mentioned above, visit the "Components" page.
History
Gustav Kirchhoff was a German physicist who lived during the 19th century. There are many equations and laws named after him that he helped to discover, one of them being the node rule. His circuit laws (the node rule and loop rule) were the first laws that he conceived, and he actually did this during his years in school and later wrote his doctoral dissertation on them. He created these laws in a time where electricity was a fairly new and was not commonly used.
Connectedness
The Node Rule is connected to a lot of other topics in physics. The loop rule is the most important one, as the node rule and loop rule in conjunction allow us to solve circuits. The node rule is also connected to other concepts such as voltage, current and electricity. See the "Further Reading" section to read more on these topics.
See Also
Further Reading
External Links
https://en.wikipedia.org/wiki/Kirchhoff%27s_circuit_laws#Kirchhoff.27s
References
Matter & Interactions 4th Edition by Ruth W. Chabay & Bruce A. Sherwood