No indigestible maths: just the principle, in plain words. A transformer changes the voltage level of electricity through one simple phenomenon, electromagnetic induction.
A transformer is two windings wound around the same magnetic core. When an alternating current flows in the first winding, it creates a varying magnetic field in the core; that varying field in turn induces a voltage in the second winding. Electricity "passes" from one side to the other with no direct electrical link, purely through magnetism.
The magic lies in the number of turns of each winding. The voltage ratio equals the turns ratio:
U₁ / U₂ = N₁ / N₂
Alternating current is required because only a field that varies in time can induce a voltage: a constant direct current would produce nothing after the first instant. The core (stacked silicon-steel laminations) channels the magnetic field from one winding to the other so the transfer is efficient; its anatomy is detailed in core and windings.
A transformer creates no energy: it trades voltage against current. Idealising, input power equals output power:
U₁ × I₁ ≈ U₂ × I₂
So if the voltage rises, the current falls in the same proportion, and vice versa. That is the whole point for the grid: raise the voltage to transport energy with little current (hence little line loss), then lower it near the users.
No transformer is perfect. It dissipates a small share of the energy as heat, through two loss families: iron losses (in the core, present whenever it is energised) and copper losses (in the windings, growing with load). Reducing them is precisely the object of the European Tier 2 regulation.
Distribution mostly uses three-phase transformers: the same principle, but with three windings per side, connected according to a vector group (Dyn11 and friends). For the rest, the logic is identical to the above.
Simplified educational overview, meant to convey the general principle.
No. It needs alternating current, because only a varying magnetic field induces a voltage in the second winding. With constant direct current there would be no transfer.
Through the ratio of turns between the two windings: the voltage ratio equals the turns ratio. More turns on the secondary raises the voltage; fewer turns lowers it.
The magnetic core vibrates to the rhythm of the flux, at twice the network frequency plus harmonics. It is the machine's normal acoustic signature, present even at no load.
Into heat: iron losses in the core, present whenever the unit is energised, and copper losses in the windings, growing with load. Reducing them is precisely the object of the European Tier 2 regulation.