ELC-35

Kirchhoff current law

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

Reading speed

CircuitsKirchhoff 1845

Governing equation

\sum_k I_k=0

$I_1 \in \left[-20, 20\right]$

where

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

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

00:0 / 00:08

①

Governing law — red

\sum_k I_k=0

$I_1 \in \left[-20, 20\right]$

$I_1 = -20$ $I_{\mathrm{out}} = -18.7$

Along the curve

②

Domain of the variable — blue

I_1_{\min} = -20,\quad I_1_{\max} = 20

$I_1 \in \left[-20, 20\right]$

$I_1 = -20$ $I_1 = -20$

Along the curve

③

Response curve — green

\sum_k I_k=0

$I_1 \in \left[-20, 20\right]$

$I_1 = -20$ $I_{\mathrm{out}} = -18.7$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}I_{\mathrm{out}}}{\mathrm{d}I_1}

$I_1 \in \left[-20, 20\right]$

$I_1 = -19.75$ $I_{\mathrm{out}}^{\prime} = 1$

Along the curve

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

Reading speed

Watch on YouTube

Free library

Full library

Free PDF / open book

YouTube channels

00:0 / 00:08

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