AC Fundamentals — Why "230 V" Mains Actually Peaks at 325 V
The core idea
In direct current, voltage sits still: a steady push in one direction, like the DC circuits we started with. Alternating current instead swings sinusoidally — polarity reverses 50 times per second (50 Hz in Europe), and the instantaneous voltage is changing at every moment. So what does the "230 V" on a wall socket even mean?
It means RMS — root mean square. Take the sine wave, square it (making everything positive), average it, take the square root. The result is the DC voltage that would deliver exactly the same heating power in a resistor. RMS is the fair exchange rate between AC and DC. For a pure sine wave:
V_rms = V_peak / √2 ≈ 0.707 × V_peak
So 230 V RMS mains swings between +325 V and −325 V at its peaks. The same √2 relation holds for current (I_rms = I_peak/√2), and that is what makes AC calculations so convenient: as long as everything is in RMS, the familiar formulas survive untouched — P = V_rms × I_rms for a resistive load.
Real-world example
Take apart any phone charger or PC power supply. It rectifies the 230 V RMS mains and stores the result on a smoothing capacitor — which charges to the peak, about 325 V DC, not 230 V. That is exactly why the tiny capacitor inside a charger is rated 400 V, and why repair technicians bleed down that cap before poking around: the "little" device holds a potentially lethal 325 V charge even after unplugging. The same peak logic sets insulation rules everywhere — mains wiring is tested far above 325 V because the insulation never gets a moment off.
Common pitfall
Mixing value types in one calculation, or trusting a cheap meter's "RMS" label. A bargain multimeter measures the average of a rectified wave and applies the 0.707 factor — correct only for a pure sine. Feed it a dimmed lamp's chopped waveform or an inverter's square-ish output and the reading can be off by 10–30%. For anything non-sinusoidal you need a true-RMS meter. And in Ohm's-law work: use all-RMS or all-peak — never one of each.