ELC-22

Transformer EMF E=4.44 f N Φ

Erms = 4.44 f N Φmax for a sinusoidal flux.

Reading speed

PowerFaradayIEC 60076

Governing equation

E_{\mathrm{rms}}=4.44\,f N\Phi_{\max}

$N \in \left[10, 2000\right]$

where

f: Frequency (Hz)
N: Turns (—)
\Phi_{\max}: Peak flux (mWb)
E_{\mathrm{rms}}: Induced voltage (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

E_{\mathrm{rms}}=4.44\,f N\Phi_{\max}

$N \in \left[10, 2000\right]$

$N = 10$ $E_{\mathrm{rms}} = 8.88$

Along the curve

②

Domain of the variable — blue

N_{\min} = 10,\quad N_{\max} = 2000

$N \in \left[10, 2000\right]$

$N = 10$ $N = 10$

Along the curve

③

Response curve — green

E_{\mathrm{rms}}=4.44\,f N\Phi_{\max}

$N \in \left[10, 2000\right]$

$N = 10$ $E_{\mathrm{rms}} = 8.88$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}E_{\mathrm{rms}}}{\mathrm{d}N}

$N \in \left[10, 2000\right]$

$N = 22.52$ $E_{\mathrm{rms}}^{\prime} = 0.888$

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-22 — Transformer EMF E=4.44 f N Φ) is the form associated with Faraday · IEC 60076. Working symbols: $f$ , $N$ , $\Phi_{\max}$ $\rightarrow$ $E_{\mathrm{rms}}$ . e = N dΦ/dt with Φ = Φmax sin(2π f t) averages to 4.44 f N Φmax for the rms winding voltage.

Purpose

Purpose: compute

E_{\mathrm{rms}}

from

f

N

\Phi_{\max}

in Electrical via

E_{\mathrm{rms}}=4.44\,f N\Phi_{\max}

Erms = 4.44 f N Φmax for a sinusoidal 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

f = 50.000\,\mathrm{Hz}

N = 200.000\,\mathrm{—}

\Phi_{\max} = 4.000\,\mathrm{mWb}

, the governing relation

E_{\mathrm{rms}}=4.44\,f N\Phi_{\max}

yields

E_{\mathrm{rms}} = 177.60\,\mathrm{V}

. A core, a winding, a flux loop. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Frequency f50 HzTurns N200 —Peak flux \Phi_{\max}4 mWb

Outputs

Induced voltage E_{\mathrm{rms}}177.60 V

Reading speed

Watch on YouTube

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Narration of this film

A core, a winding, a flux loop.

e = N dΦ/dt with Φ = Φmax sin(2π f t) averages to 4.44 f N Φmax for the rms winding voltage.

Reading speed

Watch on YouTube