> [!summary] Kirchhoff's current law relies on the conservation of charge. It states that the total current entering a junction equals the total current out of a junction. Abiding by the conservation of energy. > Kirchhoff's voltage law relies on the conservation of energy. It states that the voltage around a complete loop around a circuit must equal zero to abide by the conservation of energy. **Key equations:** > > Current Law: $\sum I_{in}=\sum I_{out}$ > Loop rule: $\sum V = 0$ >[!info]+ Read Time **⏱ 2 mins** # Definition Kirchhoff's laws are two principles that rely on the [[Conservation of Charge|conservation of charge]] and [[Conservation of Energy|conservation of energy]] in circuits. They are justified because they obey the two conventions. ## Current Law The current law relies on the [[Conservation of Charge|conservation of charges]] in a circuit. Imagine a [[Junction|junction]] where multiple wires meet. If 2 [[Amps|amps]] (A) of current flow into a [[Junction|junction]], and 1 A flows out of one of the paths. Then the leftover 1 A must flow through the third path. Otherwise, it would violate the [[Conservation of Charge|conservation of charge]]. > [!note]+ Junction Diagram ![[ki_1.png|350]] [^1] Example of junction rule, where current spilts (or can add up in reverse of this image) Mathematically, the total current in must equal our total current out of a junction. $\begin{array}{c} I_{before} = I_{after} \\ \text{Or} \\ \sum I_{in}=\sum I_{out} \end{array} $ ## Voltage Law The voltage law relies on the [[Conservation of Energy|conservation of energy]] in a circuit. Imagine a charge moving our a circuit any energy gained must be used up when it reaches back at its starting point. Otherwise, this would imply that the charge creates or destroys energy. Which would violate the [[Conservation of Energy|conservation of energy]] Mathematically this is saying any closed loop total [[Potential Difference|voltage]] must be zero. $ \sum V = 0 $ [!note] Voltage Rule Diagram >[!note] Explanation General rule for loop rules # Resources <iframe width="560" height="315" src="https://www.youtube.com/embed/affa61AME68?si=lrpfT3pvoV4KbHK1" title="YouTube video player" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share" referrerpolicy="strict-origin-when-cross-origin" allowfullscreen></iframe> --- > 📂 Want to see more structured notes like these? > Help grow the project by [starring Math & Matter on GitHub](https://github.com/rajeevphysics/Obsidian-MathMatter). --- [^1]: Taken from https://tikz.net/electric_circuit_resistor/ by Izaak Neutelings (February, 2020)