Why voltage and current don't always peak at the same instant in an AC circuit — and how a phasor diagram makes that phase relationship visible at a glance instead of buried in a sine equation.
In a DC circuit, voltage and current are simple numbers. In an AC circuit, both are constantly changing sine waves, and — critically — they don't always reach their peak at the same instant. A phasor diagram is a way of representing that relationship as two rotating arrows (vectors) whose angle to each other captures the phase difference, without having to read it off a waveform equation. Adjust the interactive controls above to see how resistive, inductive, and capacitive circuits shift that relationship differently.
In a purely resistive circuit, current and voltage rise and fall together — Ohm's Law (V = IR) holds at every instant, with no time delay between them. Inductors and capacitors change this: an inductor resists a change in current, so current lags behind voltage in an inductive circuit; a capacitor resists a change in voltage, so current leads voltage in a capacitive circuit. This lag or lead, measured as a phase angle, is what a phasor diagram makes visually immediate — the angle between the voltage and current arrows is the phase difference.
Each phasor is a rotating vector whose length represents the signal's amplitude and whose angle (relative to a reference, usually the voltage) represents its phase. Both arrows spin together at the circuit's operating frequency, so their relative angle stays constant even as both rotate — that's the whole value of the phasor representation: it turns a moving, time-varying relationship into a fixed angle you can read at a glance, rather than having to compare two full sine waves point by point.
The phase angle between voltage and current directly determines power factor (cos of the phase angle) — a purely resistive load has a power factor of 1 (all delivered power does useful work), while a heavily reactive load has a lower power factor, meaning some of the current flowing doesn't contribute to real power delivered, just circulates reactive power back and forth. This is why utilities and electrical designers care about phase angle beyond pure circuit theory — it has a direct, billable consequence in real power systems.
A phasor is a way of representing a sinusoidal AC signal (voltage or current) as a fixed-length rotating arrow, capturing its amplitude and phase angle without having to track its continuously changing instantaneous value. Two phasors rotating together at the same frequency keep a constant angle between them, which is the phase difference.
An inductor opposes a change in current (via induced back-EMF), so current physically can't change instantaneously — it lags the voltage that's driving it. A capacitor opposes a change in voltage instead, so its current (which depends on how fast voltage is changing) actually leads the voltage waveform. These are fundamental, opposite behaviors of the two component types.
Related but not identical — power factor is the cosine of the phase angle between voltage and current. A phase angle of 0° gives a power factor of 1 (unity, best case); a phase angle of 90° (purely reactive) gives a power factor of 0 (no real power delivered despite current flowing).
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