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### Kurs: Fizyka - program rozszerzony I>Rozdział 11

Lekcja 3: Prawo Kirchhoffa o sumach natężeń prądów wpływających i wypływających z węzła obwodu elektrycznego

# Kirchhoff's junction rule review

Review the key terms and skills related to Kirchhoff's junction rule.

## Pojęcia kluczowe

### Junction

Intersection of three or more pathways in a circuit. Typically represented by a dot on a circuit diagram. Also called a node.

### Branch

A path connecting two junctions.

## Kirchhoff’s junction rule

Kirchhoff’s junction rule says that the total current into a junction equals the total current out of the junction. This is a statement of conservation of charge. It is also sometimes called Kirchhoff’s first law, Kirchhoff’s current law, the junction rule, or the node rule. Mathematically, we can write it as:
${I}_{\text{in}}={I}_{\text{out}}$
Junctions can’t store current, and current can’t just disappear into thin air because charge is conserved. Therefore, the total amount of current flowing through the circuit must be constant.
For the total current in Figure 3, we can write the relationship between the current going into and out of the node as:
$\begin{array}{rl}{I}_{\text{in}}& ={I}_{\text{out}}\\ \\ \\ {i}_{1}+{i}_{2}& ={i}_{3}+{i}_{4}\end{array}$
For example, in Figure 4, the current into the node equals the current out of the node.
The current into the node is $3\phantom{\rule{0.167em}{0ex}}\text{A}$. There are two branches out of the node. The current across resistor ${R}_{2}$ is $2\phantom{\rule{0.167em}{0ex}}\text{A}$ and the current across resistor ${R}_{3}$ is $1\phantom{\rule{0.167em}{0ex}}\text{A}$, so we can write:
$\begin{array}{rl}{i}_{\text{in}}& ={i}_{\text{out}}\\ \\ 3\phantom{\rule{0.167em}{0ex}}\text{A}& =1\phantom{\rule{0.167em}{0ex}}\text{A}+2\phantom{\rule{0.167em}{0ex}}\text{A}\\ \\ 3\phantom{\rule{0.167em}{0ex}}\text{A}& =3\phantom{\rule{0.167em}{0ex}}\text{A}←\text{yes!}\end{array}$

## Dowiedz się więcej

For deeper explanations, see our video on Kirchhoff's junction rule (or current law).
To check your understanding and work toward mastering Kirchhoff's junction rule, check out the Kirchhoff's junction rule exercise.

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