The Ideal Transformer

In single-phase two-winding transformers, two windings are wrapped around a magnetic core having a cross-sectional area A and magnetic permeability µ. Phasor current i₁ enters the left winding, and i₂ leaves the right winding.

Ampere's law states that the magnetic field intensity's tangential component integrated along a closed path equals the net enclosed current. The mean length of the magnetic circuit is selected as the closed path, where the field intensity phasor is constant.

Substituting the magnetic flux density and core flux yields Ohm's law for magnetic circuits, where the net magnetomotive force equals the product of core reluctance and core flux.

For ideal transformers, core permeability is infinite, implying zero core reluctance. So, the phase currents are in phase.

Faraday's law defines the voltage induced by a time-varying flux. Assuming sinusoidal steady-state flux with constant frequency, confined entirely to the core, the induced voltages across windings and their relationship are determined.

Substituting the turn ratio in the primary relations helps calculate the complex power entering and leaving the windings, which are equal, implying no power loss.