An analogy
A transformer can be likened to a mechanical gearbox, which transfers mechanical energy from a high-speed, low torque shaft to a lower-speed, higher-torque shaft, but which is not a source of energy itself. A transformer transfers electrical energy from a high-current, low-voltage circuit to a lower-current, higher-voltage circuit.
 Coupling by mutual induction
The principles of the transformer are illustrated by consideration of a hypothetical ideal transformer. In this case, the core requires negligible magnemotive force to sustain flux, and all flux linking the primary winding also links the secondary winding. The hypothetical ideal transformer has no resistance in its coils. A simple transformer consists of two electrical conductors called the primary winding
and the secondary winding
. Energy is coupled between the windings by the time varying magnetic flux that passes through (links) both primary and secondary windings. Whenever the amount of current in a coil changes, a voltage is induced in the neighboring coil. The effect, called mutual inductance, is an example of electromagnetic induction.
An ideal step-down transformer showing flux in the core
If a time-varying voltage is applied to the primary winding of turns, a current will flow in it producing a magnetomotive force (MMF). Just as an electromotive force (EMF) drives current around an electric circuit, so MMF tries to drive magnetic flux through a magnetic circuit. The primary MMF produces a varying magnetic flux in the core, and, with an open circuit secondary winding, induces a back electromotive force (EMF) in opposition to . In accordance with Faraday''s law of induction, the voltage induced across the primary winding is proportional to the rate of change of flux:
are the voltages across the primary winding and secondary winding,
are the numbers of turns in the primary winding and secondary winding,
are the derivatives of the flux with respect to time of the primary and secondary windings.
In the hypothetical ideal transformer, the primary and secondary windings are perfectly coupled, or equivalently, . Substituting and solving for the voltages shows that:
are voltages across primary and secondary,
are the numbers of turns in the primary and secondary, respectively.
Hence in an ideal transformer, the ratio of the primary and secondary voltages is equal to the ratio of the number of turns in their windings, or alternatively, the voltage per turn is the same for both windings. The ratio of the currents in the primary and secondary circuits is inversely proportional to the turns ratio.
The EMF in the secondary winding will cause current to flow in a secondary circuit. The MMF produced by current in the secondary winding opposes the MMF of the primary winding and so tends to cancel the flux in the core. Since the reduced flux reduces the EMF induced in the primary winding, increased current flows in the primary circuit. The resulting increase in MMF due to the primary current offsets the effect of the opposing secondary MMF. In this way, the electrical energy fed into the primary winding is delivered to the secondary winding. In addition, the flux density will always stay the same as long as the primary voltage is steady.
For example, suppose a power of 50 watts is supplied to a resistive load from a transformer with a turns ratio of 25:2.
(power = electromotive force × current)
50 W = 2 V × 25 A in the primary circuit if the load is a resistive load. (See note 1)
Now with transformer change:
50 W = 25 V × 2 An the secondary circuit.
Since a direct current by definition does not change, it produces a steady MMF and so steady flux in the core; this quantity does not change and so cannot induce a voltage in the secondary winding. In a practical transformer, direct current applied to the winding will create only heat.
 The universal electromotive force (EMF) equation
If the flux in the core is sinusoidal, the relationship for either winding between its number of turns, voltage, magnetic flux density and core cross-sectional area is given by the universal emf equation (from Faraday''s law):
is the sinusoidal rms or root mean square voltage of the winding,
is the frequency in hertz,
is the number of turns of wire on the winding,
is the cross-sectional area of the core in square metres
is the peak magnetic flux density in teslas,
Other consistent systems of units can be used with the appropriate conversions in the equation.
 Operation at different frequencies
The equation shows that the EMF of a transformer at a given flux density increases with frequency. By operating at higher frequencies, transformers can be physically more compact without reaching saturation, and a given core is able to transfer more power. However, other properties of the transformer, such as losses within the core and skin-effect, also increase with frequency. Generally, operation of a transformer at its designed voltage but at a higher frequency than intended will lead to reduced magnetising (no load primary) current. At a frequency lower than the design value, with the rated voltage applied, the magnetising current may increase to an excessive level.
Operation of a power transformer at other than its design frequency may require assessment of voltages, losses, and cooling to establish if safe operation is practical. For example, transformers at hydroelectric generating stations may be equipped with over-excitation protection, so-called "volts per hertz" protection relays, to protect the transformer from overvoltage at higher-than-rated frequency which may occur if a generator loses its connected load.
Transformers are adapted to numerous engineering applications and may be classified in many ways:
By power level (from fraction of a volt-ampere(VA) to over a thousand MVA),
By application (power supply, impedance matching, circuit isolation),
By frequency range (power, audio, radio frequency(RF))
By voltage class (a few volts to about 750 kilovolts)
By cooling type (air cooled, oil filled, fan cooled, water cooled, etc.)
By purpose (distribution, rectifier, arc furnace, amplifier output, etc.).
By ratio of the number of turns in the coils
The secondary has more turns than the primary.
The secondary has fewer turns than the primary.
Intended to transform from one voltage to the same voltage. The two coils have approximately equal numbers of turns, although often there is a slight difference in the number of turns, in order to compensate for losses (otherwise the output voltage would be a little less than, rather than the same as, the input voltage).
The primary and secondary have an adjustable number of turns, which can be selected without reconnecting the transformer.
 Circuit symbols
Transformer with two windings and iron core.
Transformer with three windings.
The dots show the relative winding configuration of the windings.
Step-down or step-up transformer.
The symbol shows which winding has more turns,
but does not usually show the exact ratio.
Transformer with electrostatic screen,
which prevents capacitive coupling between the windings.
 Practical considerations
 Basic Impulse Insulation Levels (BIL)
Outdoor electrical distribut