Transformer Formula

Transformer is a device that changes AC voltage using electromagnetic induction between two coils on a shared iron core.

The Formula

\frac{V_s}{V_p} = \frac{N_s}{N_p}

where

V

is voltage and

N

is number of turns (s = secondary, p = primary).

When to use: A transformer trades voltage for current (or vice versa) — like a gear system trades speed for torque.

Quick Example

Power lines carry electricity at 500,000 V. A transformer near your house steps it down to 120 V (or 230 V) for safe use.

Notation

V_p

and

V_s

are the primary and secondary voltages in volts,

N_p

and

N_s

are the number of turns,

I_p

and

I_s

are the primary and secondary currents in amperes, and

\Phi

is the magnetic flux in webers (Wb).

What This Formula Means

A device that changes AC voltage using electromagnetic induction between two coils on a shared iron core.

A transformer trades voltage for current (or vice versa) — like a gear system trades speed for torque.

Formal View

For an ideal transformer, the voltage ratio equals the turns ratio:

V_s / V_p = N_s / N_p

, and power is conserved:

V_p I_p = V_s I_s

. The changing current in the primary creates a time-varying flux

\Phi

in the shared core, inducing an EMF in the secondary by Faraday's law.

Worked Examples

Example 1

easy

A step-up transformer has

100

turns on the primary coil and

500

turns on the secondary coil. If the input voltage is

240 \text{ V}

, what is the output voltage?

Answer

V_s = 1200 \text{ V}

First step

Transformer equation:

\frac{V_s}{V_p} = \frac{N_s}{N_p}

Full solution

2
$V_s = V_p \times \frac{N_s}{N_p} = 240 \times \frac{500}{100} = 240 \times 5 = 1200 \text{ V}$
3
The turns ratio is $5:1$ , so the voltage is stepped up by a factor of $5$ .

A transformer changes AC voltage using electromagnetic induction between two coils. A step-up transformer has more secondary turns and increases voltage, while a step-down transformer decreases it.

Example 2

medium

An ideal transformer steps down

11{,}000 \text{ V}

220 \text{ V}

. If the secondary current is

50 \text{ A}

, what is the primary current?

Example 3

medium

An ideal transformer steps

230 \text{ V}

down to

46 \text{ V}

. The secondary load draws

5.0 \text{ A}

. Find the primary current.

Common Mistakes

Trying to use a transformer with direct current (DC) — transformers only work with alternating current because they rely on a changing magnetic flux. - Fix this by naming the system, checking "Am I using a field or potential to explain how one object influences another across space?", and attaching units or direction to the final statement.
Forgetting that power is conserved: if the secondary voltage is higher, the secondary current must be lower, not the same. - Fix this by naming the system, checking "Am I using a field or potential to explain how one object influences another across space?", and attaching units or direction to the final statement.
Mixing up primary and secondary — the primary coil is connected to the input (source), the secondary to the output (load). - Fix this by naming the system, checking "Am I using a field or potential to explain how one object influences another across space?", and attaching units or direction to the final statement.
Using transformer from a keyword alone - Signal words like field, charge, magnet only point to a possible model; the system must match too.

Why This Formula Matters

Transformer gives students a way to explain non-contact forces and energy changes. It connects electricity, magnetism, gravitation, induction, motors, generators, and orbital motion through a shared spatial model.

Frequently Asked Questions

What is the Transformer formula?

A device that changes AC voltage using electromagnetic induction between two coils on a shared iron core.

How do you use the Transformer formula?

A transformer trades voltage for current (or vice versa) — like a gear system trades speed for torque.

What do the symbols mean in the Transformer formula?

$V_p$ and $V_s$ are the primary and secondary voltages in volts, $N_p$ and $N_s$ are the number of turns, $I_p$ and $I_s$ are the primary and secondary currents in amperes, and $\Phi$ is the magnetic flux in webers (Wb).

Why is the Transformer formula important in Physics?

What do students get wrong about Transformer?

Students often know a formula related to transformer but skip the recognition step: Am I using a field or potential to explain how one object influences another across space? That leads to a correct-looking substitution attached to the wrong physical model.

What should I learn before the Transformer formula?

Before studying the Transformer formula, you should understand: faradays law, generator.

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Faraday's Law Generator

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