Batteries, Machines and Electricity Systems
How Transformers Transfer Energy
Explain changing magnetic flux, turns ratio and practical losses.
You need to size or verify a real system using “How Transformers Transfer Energy”, with units, duty and limits that match the application.
Follow energy from one transformer winding to another through changing magnetic flux, apply the ideal turns-ratio model, and recognize the losses and operating limits that separate a real transformer from that model.
- Select or check first
- Flux is a field quantity, not a stream of particles. Copper does not cross from the primary to the secondary. Energy crosses through the electromagnetic field. The core provides a low-reluctance path that improves coupling, while insulation maintains the transformer's specified electrical separation.
- Controlling assumption
- Circuit state, waveform, source impedance, ratings, temperature and protection topology match the equipment being analysed.
- Top risk
- A mains-frequency transformer is not a DC converter. Constant DC does not maintain changing flux. After the switching transient, induced secondary voltage vanishes while primary current may become dangerously limited mainly by winding resistance and core saturation.
- Proof
- Check the exact manufacturer data, units and limits, then verify the result by calculation, measurement or a controlled acceptance test.
Start with the basics Optional foundation before “How Transformers Transfer Energy”
Electrical-engineering basics
Electrical behaviour becomes easier to reason about when every voltage has a reference and every current has a complete return path.
- Voltage
- Voltage is potential difference between two points. A voltage statement is incomplete unless both points or its reference are known.
- Current
- Current is charge flow through a path. It does not disappear after a component; in a complete circuit it returns to the source.
- Resistance and impedance
- Resistance opposes steady current. Impedance extends that idea to changing signals and can depend on frequency through capacitance and inductance.
- Power and heat
- Electrical power is the rate of energy transfer. Some becomes useful output and some becomes heat that must stay within component and enclosure limits.
- Rating versus operating point
- A rating is a limit or qualified condition, not a target. The operating point must remain inside all relevant voltage, current, power, temperature and timing limits.
How to use this article: Draw the source, load, reference and return path before calculating. Treat exposed or stored electrical energy as hazardous until isolation is proved.
On this page
A transformer transfers electrical energy between windings by a shared, time-varying magnetic field. An alternating primary voltage drives magnetizing current and changing core flux. That flux links the secondary winding and induces voltage there. When a secondary circuit is closed through a load, secondary current flows and the primary draws the additional current needed to supply the load plus losses. The windings can be electrically separate even though they are magnetically coupled.
Only changing linked flux sustains transformer voltage
Diagram description
The photograph is illustrative. The sinusoid represents AC excitation, and the equation shows that induced voltage depends on winding turns and the rate of change of linked magnetic flux.
Faraday's law for a winding
e(t) = −N·dΦ/dt
The minus sign expresses Lenz's law: the induced effect opposes the change that creates it. N is the effective series turns and Φ is the flux linking each turn in the simplified model. If flux becomes constant, dΦ/dt becomes zero and sustained secondary voltage disappears.
- e(t)
- instantaneous induced electromotive force, V
- N
- effective number of series turns
- Φ
- linked magnetic flux, Wb
- t
- time, s
Doubling the turns while preserving the same flux waveform doubles the induced voltage. Doubling frequency at the same peak flux also doubles the induced-voltage scale.
Turns ratio sets voltage ratio in the ideal common-flux model
Diagram description
The plate explicitly limits the equations to ideal magnitudes with the same linked flux and neglects magnetizing current, leakage and losses.
Ideal transformer relationships
Vₚ/Vₛ = Nₚ/Nₛ; Iₚ/Iₛ = Nₛ/Nₚ; VₚIₚ = VₛIₛ
These RMS-magnitude relations assume sinusoidal steady operation, nearly all flux linking both windings, negligible winding and core loss, and negligible magnetizing current. They predict direction and scale, not exact terminal voltage under load.
- Vₚ, Vₛ
- primary and secondary RMS voltage magnitudes, V
- Nₚ, Nₛ
- primary and secondary series turns
- Iₚ, Iₛ
- primary and secondary RMS current magnitudes, A
An ideal 230:115 V transformer has Nₚ/Nₛ = 2. A 4 A secondary load corresponds to 2 A primary load current in the ideal power-transfer component; a real primary also draws magnetizing and loss current.
| Real effect | What it changes | Typical design response |
|---|---|---|
| Magnetizing current | Primary draws current even with an open secondary | Core material, geometry, turns and applied volt-seconds |
| Winding resistance | Load current creates I²R heating and voltage drop | Conductor size, cooling and temperature class |
| Leakage flux | Not all flux links both windings; regulation and transients change | Winding arrangement and leakage specification |
| Core nonlinearity | Excess volt-seconds can drive saturation and large current | Respect rated voltage, frequency and waveform |
| Parasitic capacitance | High-frequency coupling and common-mode current appear | Insulation, shielding and layout |
Real input power divides into output and losses
Diagram description
Thin insulated laminations restrict large eddy-current loops. The energized core can consume power even when the secondary has no load.
Power and efficiency accounting
P_in = P_out + P_copper + P_core + P_stray + …; η = P_out/P_in
Copper loss changes strongly with load current, approximately as I squared R at a given temperature. Core loss depends on flux density, frequency, waveform, material and construction, so no-load loss is not zero. Efficiency therefore belongs to a stated operating point.
- P_in
- input real power, W
- P_out
- delivered real power, W
- η
- efficiency as a ratio
If a transformer takes 105 W and delivers 100 W at a stated load, total loss is 5 W and efficiency is about 95.2% at that point—not at every load.
| Check | Reason |
|---|---|
| Primary voltage, frequency and waveform | Flux swing follows applied volt-seconds; wrong conditions can saturate the core |
| Secondary current or VA rating | Excess current overheats windings and worsens regulation |
| Insulation and isolation rating | A turns ratio alone says nothing about safe separation |
| Temperature rise and enclosure | Cooling conditions determine usable loading |
| Inrush and protection | Energization angle, remanent flux and source impedance affect transient current |
| Earthing, fusing and applicable standard | Fault protection must match the installation |
Why an unloaded transformer still draws current
The primary must establish alternating core flux, so it draws magnetizing current even with the secondary open. Real core hysteresis and eddy currents also consume power, and winding resistance adds a smaller no-load copper loss. This current can be nonsinusoidal because the core's magnetic response is nonlinear. It should not be mistaken for load power reflected from the secondary.
Review Inductors and Their Stored Magnetic Energy for the magnetic-field foundation, then use Follow Energy Through an Electrical System to place the transformer between source, protection, conversion and load.
One-minute questions
Questions to answer before you apply this lesson
What should I select or check first for How Transformers Transfer Energy?
Flux is a field quantity, not a stream of particles. Copper does not cross from the primary to the secondary. Energy crosses through the electromagnetic field. The core provides a low-reluctance path that improves coupling, while insulation maintains the transformer's specified electrical separation.
Which assumption can change the conclusion?
Circuit state, waveform, source impedance, ratings, temperature and protection topology match the equipment being analysed.
What can go wrong if I copy the example directly?
A mains-frequency transformer is not a DC converter. Constant DC does not maintain changing flux. After the switching transient, induced secondary voltage vanishes while primary current may become dangerously limited mainly by winding resistance and core saturation.
How do I verify the result in the real system?
Check the exact manufacturer data, units and limits, then verify the result by calculation, measurement or a controlled acceptance test.
Sources and further reading
- 15.6 Transformers — University Physics Volume 2OpenStax, Rice University · 2026-10-13Reviewed for Faraday-law coupling, ideal turns/current ratios and the explicit ideal assumptions about common flux and losses.
- Determination of the Ratio of Transformation and of the Phase Relations in TransformersNational Bureau of Standards (now NIST) · 2026-10-13Reviewed for why terminal ratio departs from turns ratio through winding drop, leakage flux, magnetizing current and saturation.