ELC-35

Kirchhoff current law

Σ Ik = 0 at a node. Charge is conserved.

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CircuitsKirchhoff 1845

Governing equation

\sum_k I_k=0

where

I_1: In 1 (A)
I_2: In 2 (A)
I_3: In 3 (A)
I_{\mathrm{out}}: Leaving current (A)

Lecture brief

Historical brief

Ohm (1827), Kirchhoff (1845) and Maxwell’s circuit reduction still run every board: RLC transients, transformers, skin effect and three-phase power. The sheets are those network laws, not a SPICE deck. This sheet (ELC-35 — Kirchhoff current law) is the form associated with Kirchhoff 1845. Working symbols: $I_1$ , $I_2$ , $I_3$ $\rightarrow$ $I_{\mathrm{out}}$ . The algebraic sum of currents into a node vanishes because charge cannot accumulate on a lumped node.

Purpose

Purpose: compute

I_{\mathrm{out}}

from

I_1

I_2

I_3

in Electrical via

\sum_k I_k=0

Σ Ik = 0 at a node. Charge is conserved. Use it when a real electrical question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

I_1 = 4.000\,\mathrm{A}

I_2 = 2.500\,\mathrm{A}

I_3 = -1.200\,\mathrm{A}

, the governing relation

\sum_k I_k=0

yields

I_{\mathrm{out}} = 5.300\,\mathrm{A}

. A node, three incoming arrows, one outgoing. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

In 1 I_14 AIn 2 I_22.5 AIn 3 I_3-1.2 A

Outputs

Leaving current I_{\mathrm{out}}5.300 A

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Narration of this film

A node, three incoming arrows, one outgoing.

The algebraic sum of currents into a node vanishes because charge cannot accumulate on a lumped node.

Reading speed

Watch on YouTube