ELC-04

Ideal transformer ratio

Vs/Vp = Ns/Np = Ip/Is.

Reading speed

MachinesFaradayIEC 60076

Governing equation

\dfrac{V_s}{V_p}=\dfrac{N_s}{N_p}=\dfrac{I_p}{I_s}

$N_s \in \left[1, 5000\right]$

where

V_p: Primary voltage (V)
N_p: Primary turns (turns)
N_s: Secondary turns (turns)
I_p: Primary current (A)
V_s: Secondary voltage (V)
I_s: Secondary 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.

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①

Governing law — red

\dfrac{V_s}{V_p}=\dfrac{N_s}{N_p}=\dfrac{I_p}{I_s}

$N_s \in \left[1, 5000\right]$

$N_s = 1$ $V_s = 0.46$

Along the curve

②

Domain of the variable — blue

N_s_{\min} = 1,\quad N_s_{\max} = 5000

$N_s \in \left[1, 5000\right]$

$N_s = 1$ $N_s = 1$

Along the curve

③

Response curve — green

\dfrac{V_s}{V_p}=\dfrac{N_s}{N_p}=\dfrac{I_p}{I_s}

$N_s \in \left[1, 5000\right]$

$N_s = 1$ $V_s = 0.46$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}V_s}{\mathrm{d}N_s}

$N_s \in \left[1, 5000\right]$

$N_s = 32.44$ $V_s^{\prime} = 0.46$

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-04 — Ideal transformer ratio) is the form associated with Faraday · IEC 60076. Working symbols: $V_p$ , $N_p$ , $N_s$ , $I_p$ $\rightarrow$ $V_s$ , $I_s$ . Faraday's law on two windings that share flux gives voltages in the turn ratio; power conservation inverts the currents.

Purpose

Purpose: compute

V_s

I_s

from

V_p

N_p

N_s

I_p

in Electrical via

\dfrac{V_s}{V_p}=\dfrac{N_s}{N_p}=\dfrac{I_p}{I_s}

Vs/Vp = Ns/Np = Ip/Is. 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_p = 230.000\,\mathrm{V}

N_p = 500.000\,\mathrm{turns}

N_s = 50.000\,\mathrm{turns}

I_p = 2.000\,\mathrm{A}

, the governing relation

\dfrac{V_s}{V_p}=\dfrac{N_s}{N_p}=\dfrac{I_p}{I_s}

yields

V_s = 23.000\,\mathrm{V}

I_s = 20.000\,\mathrm{A}

. Ideal, no leakage, no magnetising current. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Primary voltage V_p230 VPrimary turns N_p500 turnsSecondary turns N_s50 turnsPrimary current I_p2 A

Outputs

Secondary voltage V_s23.000 V
Secondary current I_s20.000 A

Reading speed

Watch on YouTube

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Narration of this film

Ideal, no leakage, no magnetising current.

Faraday's law on two windings that share flux gives voltages in the turn ratio; power conservation inverts the currents.

Reading speed

Watch on YouTube