# Ideal Transformer Calculator

Created by Miłosz Panfil, PhD
Reviewed by Małgorzata Koperska, MD and Steven Wooding
Last updated: Dec 21, 2022

Omni's ideal transformer calculator is an easy tool that helps with a question: how does a transformer work?

Have you ever wondered how the electric current from the high voltage power lines turns into a familiar $\small 110\ \mathrm{V}$ (or $\small 220\ \mathrm{V}$) in the outlet socket? That's what electric transformers do via voltage regulation (we talk about this in our voltage regulation calculator).

The text below explains the workings of transformers. By reading it, you will also learn about special types of transformers, such as current and voltage transformers.

## How does a transformer work?

A transformer is essentially just two coils, primary and secondary, that are placed next to each other. The AC current running through the primary coil creates a varying magnetic field according to the rules we explored in the magnetic field of a wire calculator. This magnetic field induces a voltage difference — an electromotive force — in the secondary coil.

You can learn more about inductance by checking out the solenoid inductance calculator: it covers the physical principles behind this intriguing phenomenon.

Coming back to the transformer, essentially, the magnetic field transfers the energy from one circuit to the other. If you're surprised that a magnetic field can transfer energy, you might check the energy density equation calculator.

In an idealized picture, we disregard all potential losses and assume that all the magnetic field from the primary coil passes through the secondary coil. Then the only thing that matters is the ratio of the number of windings between the primary and secondary coil. This is because the strength of the magnetic field depends on the number of windings in the primary coil. The number of windings in the secondary coil determines the strength of the electromotive force.

## Ideal transformer calculator

The ideal transformer equation relates the primary and the secondary voltage as follows:

$V_{\mathrm{s}} = V_{\mathrm{p}} \cdot \frac{N_{\mathrm{s}}}{N_{\mathrm{p}}},$

where:

• $V_{\mathrm{s}}\ [\mathrm V]$ — Voltage at the secondary coil;
• $V_{\mathrm{p}}\ [\mathrm V]$ — Voltage at the primary coil;
• $N_{\mathrm{s}}$ — Number of windings of the primary coil; and
• $N_{\mathrm{p}}$ — Number of windings of the secondary coil.

There is a second equation that relates the primary and secondary currents:

$I_{\mathrm{s}} = I_{\mathrm{p}} \cdot \frac{N_{\mathrm{p}}}{N_{\mathrm{s}}},$

where:

• $I_{\mathrm{s}}\ [\mathrm{V}]$ — Voltage at the secondary coil; and
• $I_{\mathrm{p}}\ [\mathrm{V}]$ — Voltage at the primary coil.

It is educative to see that the calculated electrical power in the primary coil and secondary coil are the same:

$P = I_\mathrm{p}\cdot V_{\mathrm{p}} = I_\mathrm{s}\cdot V_{\mathrm{s}}$

This relationship is a sign of the conservation of energy. In a real transformer, due to losses, the power at the secondary coil will always be smaller than the power at the primary coil.

## Current transformer

Current transformers are used to provide a precise measurement of the current. In current transformers, there are more secondary windings than primary windings. Therefore, the secondary current is smaller than the primary current. This way, we can monitor or measure large currents using standard, small current measuring devices. We usually connect the current transformer in series.

## Voltage transformer

Voltage transformers are parallel connected, and their usual role is to decrease the voltage. The reduced voltage is useful for running household electrical items. Also, like in the case of current transformers, it allows for standard measuring devices to monitor high-voltage lines. In voltage transformers, there are more primary than secondary windings.

Miłosz Panfil, PhD
Primary windings
Secondary windings
Voltage
Primary voltage
V
Secondary voltage
V
Current
Primary current
A
Secondary current
A
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