What is the formula for Instantaneous AC Voltage?

The Instantaneous AC Voltage formula is v = Vmax × sin(θ) (θ = ωt), where v—Instantaneous voltage (V); Vmax—Peak amplitude (V); θ—Phase angle ωt (degrees).

What does v mean in the Instantaneous AC Voltage formula?

v is Instantaneous voltage (V).

Instantaneous AC Voltage

Q: How do you calculate Instantaneous AC Voltage?

Use the formula v = Vmax × sin(θ) (θ = ωt). The instantaneous value of a sinusoidal voltage at any point in its cycle is the peak amplitude times the sine of the phase angle. Enter the values you know in the calculator above and it solves for the remaining variable.

v = Vmax · sin(θ)

Calculator

Instantaneous Voltage

Peak Voltage

Phase Angle

Result

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Formula

v = Vmax × sin(θ) (θ = ωt)

Description

The instantaneous value of a sinusoidal voltage at any point in its cycle is the peak amplitude times the sine of the phase angle. This is the fundamental description of an AC waveform from which RMS, average, and power values are derived. Evaluating it at a given angle (or time, since θ = ωt) gives the actual voltage at that instant.

Variables

v — Instantaneous voltage (V)
Vmax — Peak amplitude (V)
θ — Phase angle ωt (degrees)

Practical Notes

At θ = 90° the voltage is at its peak; at 0° and 180° it crosses zero. Replace θ with ωt = 2πft to get the time-domain waveform.

Related Concepts

All AC Circuits formulas →

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