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 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?

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 the entire electrical grid possible. Power stations step voltage up to 500,000 V for long-distance transmission (reducing current and I^2R heat losses by a factor of thousands), then substations step it back down for homes and businesses. Without transformers, electricity could only travel short distances efficiently.

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?

Transformers make the entire electrical grid possible. Power stations step voltage up to 500,000 V for long-distance transmission (reducing current and I^2R heat losses by a factor of thousands), then substations step it back down for homes and businesses. Without transformers, electricity could only travel short distances efficiently.

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