Why is mains voltage a sine wave?
Generators produce voltage that rises and falls sinusoidally: v(t) = V·sin(2πft + φ), where V is the peak, f the frequency, and φ the phase.
// maths › Electronics
AC Circuit Voltage
Find the instantaneous voltage of an AC supply with v(t) = V·sin(2πft + φ), with the phase angle in degrees or radians.
v(t) = V·sin(2πft + φ)
Angle unit
Frequently asked questions
What is the frequency in Australia?
50 Hz — fifty full cycles per second, so the period is T = 1/50 = 0.02 s.
Can you show a worked example?
With V = 325 V and f = 50 Hz, a quarter-period in (t = 0.005 s) reaches the peak: v ≈ 325 V.
Why is 230 V quoted, not 325 V?
230 V is the RMS (effective) value; the peak is V = 230×√2 ≈ 325 V. RMS is what determines heating and power.
Does phase use radians?
The phase φ can be entered in degrees or radians; the toggle converts it. Internally the 2πft term is always in radians.