Impedance of a transformer is derived from both the resistance and reactance of the transformer, The resistance is derived from primarily the resistance of the wire and to some degree the silicone/steel laminate material. The reactance is a function of the turns of conductors around the core, and the size of the core material. As a Voltage is applied across the primary coil, the increasing EMF builds a magnetic field. Although current wants to flow through the Coil, the building magnetic field causes current to flow in the opposite direction from the excitation voltage with nearly the same force as that of the excitation voltage, effectively keeping the current at zero Amps through the first 90 degrees of the sine wave.
At peak voltage, the magnetic field has grown to it's maximum amplitude. As the excitation voltage falls off of peak, the magnetic field collapses, inducing a current into the coil, in the same direction as the excitation voltage. Current will flow in the same direction as the Excitation voltage intended, because of the collapsing magnetic field. As the Excitation voltage reverses direction, crossing zero, the magnetic field collapses faster, inducing peak current into the coil. If plotted, there would be zero current flow until the Sine wave reached peak voltage. As the voltage falls, the current will rise. As the voltage falls to zero, toward the opposite peak, the current peaks. As the Excitation voltage approaches peak, the magnetic field is nearly at it's maximum amplitude, the rate of change in the magnetic field causes the current to fall off, such that you have zero current at Peak Excitation Voltage again. As the Voltage falls off of the peak heading toward Zero, the Magnetic field collapses, again inducing current to flow in the direction that the Excitation Voltage intended. When the Excitation Voltage is at Zero, the Field collapses rapidly, causing current to peak again. As the Voltage rises toward the next peak, current falls off to zero.
This effectively causes the current to lag the voltage by ninety degrees, hence reactive. There is no tremendous inrush current because of the transformer. What current the transformer uses, is in the silicone steel laminated core of the transformer. In order for the magnetic field to build, the molecules of the laminate steel must align themselves magnetically north to south, as forced by the direction of the wire turns and by the Excitation Voltage. Saturation occurs when all the molecules that can align themselves have, a higher voltage will not increase the magnetic field. Heat is generated by the eddie currents of the silicone steel molecules as they move to align themselves, releasing their kinetic energy as they bump into one another. The steel is laminated to reduce this effect. Because the molecules align themselves and are nearly fluid with respect to their movement, the magnetic lines developing in the core are not necessarily straight and do in fact bend through the steel following the path of least reluctance created by those molecules that have or more nearly have aligned themselves.
For the purposes of this discussion, I'll go no deeper. E-mail me should reluctance be an issue in your design.
The mathematical models offered by another poster are just that, models. I particularly like his harmonics model, however his inrush model would only fit a switching power supply.
This day and age, most electronic office equipment, such as copiers, computers, UPS's and even the T-8 light fixtures all use switching power supplies. It is these connected devices that cause high inrush currents and outlandish harmonics effecting power quality.
The clear majority of these devices charge capacitors. A number 18 AWG Stranded TW conductor will see current spikes as high as 60 to 90 Amps of extremely short duration, considering power in the USA is 60 Hz. Many of these switching supplies operate around 5,000 Hz. To a power system, that can put unusual currents on the neutral. The National Electrical Code over the last few years has limited the System Neutral Reduction. Experience has dictated that in some instances the, Neutral is larger than the supply conductors. Now even though the switching currents are extremely high, they are normally of such short duration that the average heat generated within the conductors is well within range of the conductors and terminations. It is only the multiwire branch circuits that Neutral Conductor Harmonic currents become a concern. Steve4444
