• Pixel-art sticker of Nodella, personifying Kirchhoff's Current Law, with the caption “What Flows In Flows Out.”

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Nodella

Kirchhoff's Current Law Physics

\[\sum I_{\text{in}} = \sum I_{\text{out}}\]
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Meet Nodella, a wire junction where what flows in flows out: charge does not pile up there, so the total current flowing in equals the total current flowing out. With one wire in and two wires out, the two outputs share the input current between them. Pixel-art kiss-cut sticker in 2, 3, 4 and 6 inches; equation, symbols and sources in the physics panel below.

Size
Surface

Flat $6 shipping worldwideMade to order, ships in 2–5 business days

Details

Size3″ × 3″

3″ × 3″ kiss-cut sticker.

Shipping

Flat $6 shipping on every order, worldwide, whatever's in it.

Delivery times & where we ship

Returns & replacements21 days

Every item is printed to order, so we can’t accept returns or exchanges for change of mind, or if you ordered the wrong size or colour.

Print defect, misprint, damage or the wrong item? We’ll send a free replacement, or a refund if you prefer. Report it within 21 days of delivery with a photo; no need to send it back.

Full refund & replacement policy

The physics

Meet Nodella, a wire junction where every bit of current coming in has to go out again.

Electric charge is conserved, and in a steady circuit it does not pile up anywhere. So at any junction, or node, the total current flowing in equals the total flowing out. Gustav Kirchhoff stated this current law in 1845, together with a voltage law for loops. They are the basic rules of circuit analysis.

Example: 3 amperes flowing into a node that splits into two branches might divide into 2 A and 1 A, but the two must add to 3 A. How it splits depends on the branches' resistances: more current takes the easier path.

Every circuit simulator and every electrician's calculation uses this rule. It explains why adding appliances in parallel adds to the total current drawn from the supply, and why the main fuse must handle the sum of all the branches.

The law holds for steady currents and for circuits small compared with the wavelength of their signals. At very high frequencies, charge can build up on components, and a more careful treatment is needed.

Equations

\[\sum I_{\text{in}} = \sum I_{\text{out}}\]
Symbols
SymbolMeaningUnit
\(I_{\text{in}}\) a current flowing into the junction \(\mathrm{A}\)
\(I_{\text{out}}\) a current flowing out of the junction \(\mathrm{A}\)