Transformer Formula

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 the voltage of alternating current by using two coils wound around 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?

Solution

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

Answer

V_s = 1200 \text{ V}
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} to 220 \text{ V}. If the secondary current is 50 \text{ A}, what is 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.
  • Forgetting that power is conserved: if the secondary voltage is higher, the secondary current must be lower, not the same.
  • Mixing up primary and secondary — the primary coil is connected to the input (source), the secondary to the output (load).

Why This Formula Matters

Transformers make long-distance power transmission efficient by stepping voltage up (reducing current and heat losses).

Frequently Asked Questions

What is the Transformer formula?

A device that changes the voltage of alternating current by using two coils wound around 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?

Transformers make long-distance power transmission efficient by stepping voltage up (reducing current and heat losses).

What do students get wrong about Transformer?

A transformer doesn't create energy — if voltage goes up, current goes down proportionally (power is conserved).

What should I learn before the Transformer formula?

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

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Related Concepts

Faraday's LawGenerator

Related Formulas

Faraday's Law Formula