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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.
Figure 1. Two junctions represented by dots and the current pathways highlighted.

Branch

A path connecting two junctions.
Figure 2. Two branches in a circuit, each highlighted in a different color.

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, start subscript, start text, i, n, end text, end subscript, equals, I, start subscript, start text, o, u, t, end text, end subscript
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.
Figure 3: Kirchhoff’s junction rule says that the current flowing into the node, i, start subscript, 1, end subscript and i, start subscript, 2, end subscript, must be equal to the current flowing out of the node, i, start subscript, 3, end subscript and i, start subscript, 4, end subscript.
For the total current in Figure 3, we can write the relationship between the current going into and out of the node as:
Iin=Iouti1+i2=i3+i4\begin{aligned}I_\text {in} &= I_\text {out}\\ \\\\ i_1+i_2 &= i_3+i_4\end{aligned}
For example, in Figure 4, the current into the node equals the current out of the node.
Figure 4: The current into the node equals the current out of the node.
The current into the node is 3, start text, A, end text. There are two branches out of the node. The current across resistor R, start subscript, 2, end subscript is 2, start text, A, end text and the current across resistor R, start subscript, 3, end subscript is 1, start text, A, end text, so we can write:
iin=iout3A=1A+2A3A=3Ayes!\begin{aligned}i_\text{in} &= i_\text {out} \\\\ 3\,\text A &= 1 \,\text A + 2\,\text A\\\\ 3\,\text A &= 3\,\text A \goldD{\leftarrow \text {yes!}}\end{aligned}

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.