ELC-21

Kirchhoff voltage law

Σ Vk = 0 around a closed loop. KVL is Faraday at zero flux.

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CircuitsKirchhoff 1845

Governing equation

\sum_k V_k=0

$V_1 \in \left[0, 200\right]$

where

V_s: Source (V)
V_1: Drop 1 (V)
V_2: Drop 2 (V)
V_3: Drop 3 (V)
\sum V: Loop sum (V)
\varepsilon: Residual (V)

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.

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①

Governing law — red

\sum_k V_k=0

$V_1 \in \left[0, 200\right]$

$V_1 = 0$ $\sum V = 5$

Along the curve

②

Domain of the variable — blue

V_1_{\min} = 0,\quad V_1_{\max} = 200

$V_1 \in \left[0, 200\right]$

$V_1 = 0$ $V_1 = 0$

Along the curve

③

Response curve — green

\sum_k V_k=0

$V_1 \in \left[0, 200\right]$

$V_1 = 0$ $\sum V = 5$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}\sum V}{\mathrm{d}V_1}

$V_1 \in \left[0, 200\right]$

$V_1 = 1.258$ $\sum V^{\prime} = -1$

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-21 — Kirchhoff voltage law) is the form associated with Kirchhoff 1845. Working symbols: $V_s$ , $V_1$ , $V_2$ , $V_3$ $\rightarrow$ $\sum V$ , $\varepsilon$ . The electrostatic field is conservative, so the line integral of E around a loop vanishes when dΦB/dt = 0.

Purpose

Purpose: compute

\sum V

\varepsilon

from

V_s

V_1

V_2

V_3

in Electrical via

\sum_k V_k=0

Σ Vk = 0 around a closed loop. KVL is Faraday at zero flux. Use it when a real electrical question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

V_s = 12.000\,\mathrm{V}

V_1 = 5.000\,\mathrm{V}

V_2 = 4.000\,\mathrm{V}

V_3 = 3.000\,\mathrm{V}

, the governing relation

\sum_k V_k=0

yields

\sum V = 12.000\,\mathrm{V}

\varepsilon = 0.000\,\mathrm{V}

. A loop, three drops, a source. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Source V_s12 VDrop 1 V_15 VDrop 2 V_24 VDrop 3 V_33 V

Outputs

Loop sum \sum V12.000 V
Residual \varepsilon0.000 V

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Narration of this film

A loop, three drops, a source.

The electrostatic field is conservative, so the line integral of E around a loop vanishes when dΦB/dt = 0.

Reading speed

Watch on YouTube