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Electricity & Magnetism
Electricity & Magnetism

Kirchhoff's Current Law

∑Iin=∑Iout\sum I_{in} = \sum I_{out}

Sum of currents at a node is zero.

Variables

ΣI_in
Current in
Current entering node
A
ΣI_out
Current out
Current leaving node
A

Derivation

Conservation of charge at junction.

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Common questions

What is the Kirchhoff's Current Law formula?

Kirchhoff's Current Law is written ΣIᵢₙ = ΣIₒᵤₜ. Sum of currents at a node is zero. It belongs to Electricity & Magnetism, under Electric Circuits.

What are the units in ΣIᵢₙ = ΣIₒᵤₜ?

In SI units, ΣI_in is current in, measured in A; ΣI_out is current out, measured in A.

How is the Kirchhoff's Current Law formula derived?

Conservation of charge at junction. The result is ΣIᵢₙ = ΣIₒᵤₜ.