How a Transformer Moves Power Across an Air Gap With No Wires Touching

No moving parts, no physical contact

A transformer moves electrical energy from one circuit to another without any wire connecting them, using nothing but a changing magnetic field. A primary coil of N₁ turns is wound around one side of a shared iron core; a secondary coil of N₂ turns is wound around the other side. Alternating current in the primary creates a magnetic flux that oscillates in step with it, the iron core channels almost all of that flux through the secondary coil as well, and by Faraday's law of induction a changing flux through any coil induces an EMF in it — including the secondary, even though it shares no electrical connection with the primary at all.

Faraday's Law:  EMF = -N * (dPhi/dt)
// a changing magnetic flux Phi through N turns induces a voltage
// the core links (almost) the same Phi(t) through BOTH coils simultaneously

The turns ratio sets the voltage

Because the iron core forces both coils to share essentially the same time-varying flux Φ(t), Faraday's law applied to each coil separately gives V₁ = N₁(dΦ/dt) and V₂ = N₂(dΦ/dt) — same dΦ/dt, different turn counts. Dividing one equation by the other cancels dΦ/dt entirely and leaves a strikingly simple relationship that depends only on the ratio of turns:

V2 / V1 = N2 / N1        // voltage scales directly with turns ratio
I2 / I1 = N1 / N2        // current scales INVERSELY (ideal, lossless transformer)
N2 > N1  ->  step-up   (higher voltage, lower current on secondary)
N2 < N1  ->  step-down (lower voltage, higher current on secondary)

An ideal transformer with N₂/N₁ = 10 steps 120V up to 1200V on the secondary — but it does not create energy. Power in equals power out for an ideal, lossless transformer (P = VI is conserved), so the tenfold voltage increase is paired with a tenfold decrease in available current. This is precisely why power grids transmit at hundreds of kilovolts: for a fixed amount of power delivered, higher voltage means proportionally lower current, and resistive transmission-line losses scale with the square of current (P_loss = I²R) — so stepping voltage up before a long transmission run and back down before it reaches homes cuts line losses dramatically for the same delivered power.

Why transformers only work on AC

Faraday's law depends entirely on dΦ/dt — a changing flux. A steady DC current through the primary produces a constant flux, and a constant flux induces exactly zero EMF in the secondary once the initial transient has settled (you'd see one brief pulse when DC is first switched on or off, and nothing in between). This is the fundamental reason transformers are an AC-only device and why the entire architecture of long-distance power transmission is built on alternating current rather than direct current — despite DC ultimately being easier to reason about and, since the advent of power electronics, now used for the very-long-distance HVDC links where conversion losses are outweighed by other efficiencies.

Why the core is layered, not solid iron

The same changing flux that induces useful EMF in the secondary coil also induces eddy currents directly within the iron core itself — the core is a conductor sitting in a changing magnetic field, so Faraday's law applies to it too, driving circulating currents that dissipate energy as heat and contribute nothing useful. Real transformer cores are therefore built from thin, electrically-insulated laminations rather than solid iron, which breaks up the paths available to eddy currents and confines them to tiny loops within each thin sheet, cutting eddy-current losses dramatically compared to a solid core of the same total cross-section. A second loss mechanism, hysteresis loss — energy dissipated by repeatedly magnetising and demagnetising the core material through its B-H hysteresis loop every AC cycle — is minimised by choosing a core material (typically silicon steel) with a narrow hysteresis loop.

Real transformers: leakage flux and coupling

The V₂/V₁ = N₂/N₁ relationship assumes perfect coupling — every field line from the primary passes through the secondary. Real transformers leak a small fraction of flux that loops back without linking both coils, which is why practical transformer design invests heavily in core geometry (E-I cores, toroidal cores, interleaved windings) to maximise the coupling coefficient k, defined so that k = 1 is perfect coupling and k = 0 is no coupling at all. Combined with winding resistance (ordinary I²R loss in the copper), core losses, and leakage inductance, real transformers reach efficiencies of 95–99% at their rated load — remarkably high, which is exactly why the transformer, essentially unchanged in principle since the 1880s, remains the backbone of every power grid on Earth.

Frequently asked questions

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