lesson
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If you plug a standard AC step-down transformer labeled 12 V into an outlet, it will instantly destroy a capacitor rated for exactly 12 V.
That happens because AC power labels show an effective average called RMS, while the alternating voltage actually swings to much higher peak values twice every cycle.
How does a transformer convert high wall-socket voltages into lower AC levels in the first place?
Stepping Down Mains AC
A mains transformer transfers electrical energy between two isolated coils of wire using a changing magnetic field inside an iron core.
In 1831, Michael Faraday discovered magnetic induction, which showed that a changing current in a primary coil induces an alternating voltage in an adjacent secondary coil.
The secondary voltage depends directly on the turns ratio, which is the ratio of primary coil turns (Npβ) to secondary coil turns (Nsβ):
\frac{V_s}{V_p} = rac{N_s}{N_p}
πA clean schematic diagram showing an iron-core step-down transformer. On the left, a primary coil with 10 loops labeled 'Primary (Np = 1000 turns)' connected to 'Mains AC: 120 V_RMS'. In the middle, laminated iron core bars. On the right, a secondary coil with 1 loop labeled 'Secondary (Ns = 100 turns)' connected to 'Secondary Output: 12 V_RMS'. Animated faint magnetic flux lines loop through the core between coils. Clear labels, high-contrast text on white card background, responsive layout.
A transformer changes the amplitude of an AC voltage, but how do we accurately quantify the continuous wave it creates?
Anatomy of an AC Sine Wave
The secondary winding outputs a smooth sinusoidal voltage that alternates continuously between positive and negative polarities.
The peak voltage (Vpβ or Vmaxβ) is the maximum instantaneous voltage measured from the zero-volt baseline to the highest crest of the waveform.