What is a phasor?
A vector whose length is a sine wave's amplitude and whose angle is its phase, rotating at the wave's frequency. The sine wave is the phasor's vertical projection — as the arrow goes round, its height traces the wave. That is the definition rather than an analogy, and it matters because adding two sine waves of the same frequency is awkward trigonometry while adding two vectors is not.
How do you convert RMS to peak voltage?
For a sine wave, peak = RMS × √2, so 230 V RMS peaks at about 325 V and 120 V RMS at about 170 V. That √2 is specific to sine waves. A square wave's RMS equals its peak, and a triangle wave's is peak ÷ √3 — using 0.707 on a non-sinusoidal supply is a common and expensive mistake.
What is RMS voltage, and why not just use the average?
Because the average of a sine wave over a complete cycle is exactly zero — it spends as long negative as positive. RMS is the root of the mean of the square, and it answers a more useful question: what DC voltage would heat the same resistor by the same amount? That is why every meter, rating plate and supply specification quotes RMS.
What does it mean for current to lead or lag voltage?
It means their peaks do not line up in time. In a capacitor the current leads, because i = C·dv/dt makes the current follow the rate of change of voltage, and a sine wave changes fastest where its value is zero — a quarter-cycle early. In an inductor, v = L·di/dt puts the voltage ahead instead, so the current lags. The reason is in those two equations, not in a mnemonic.
What is power factor?
The cosine of the angle between the voltage and current phasors, and equivalently the ratio of real power to apparent power. At unity, every amp the supply delivers does useful work. At 0.7, the cables and transformer carry about 40% more current than the work requires. That extra current still causes heating losses, which is why large consumers are billed for poor power factor.
What is the difference between real, reactive and apparent power?
They are the three sides of a right triangle: S² = P² + Q². Real power P, in watts, does work. Reactive power Q, in VAr, sloshes back and forth between the source and the load's reactance and does no net work at all. Apparent power S, in VA, is simply voltage times current — what the wiring has to be sized for regardless of how much of it is useful.
Why is average power zero in a purely reactive load?
Because the current is exactly 90° out of phase with the voltage, so for half of each cycle the product is positive and for the other half it is equally negative. The reactance takes energy in and gives every joule of it back. Current flows, the wires warm up, the supply has to provide it — and no net work is done.
What is crest factor?
Peak divided by RMS: √2 for a sine wave, 1 for a square wave, √3 for a triangle or sawtooth. It matters because a meter that measures the rectified average and multiplies by a fixed factor is assuming a sine wave. Show it a distorted waveform — as most switch-mode power supplies draw — and it will read wrong, sometimes badly.
Can you use phasors for non-sinusoidal waveforms?
Not directly. Phasor analysis depends on every quantity in the circuit sharing one frequency, which only holds for sinusoids. A square or distorted wave is a sum of harmonics, each of which needs its own phasor at its own frequency. That is why a single power factor figure is misleading for non-linear loads, and why harmonic distortion is measured separately.
How does phase angle relate to time?
One full cycle is 360°, so the fraction of a period is the fraction of 360°. At 50 Hz a cycle lasts 20 ms, so 30° is 1.67 ms and 90° is 5 ms. Converting to time is what makes a phase angle comparable with an oscilloscope measurement, which is why this calculator shows both.