Meaning and mechanism
A symmetrical sine wave will generate heat in a resistor, even if the average voltage over one cycle is 0. This is because power is related to the square of the voltage, not the sign of the voltage.
RMS calculates by squaring the values, then averaging them, and taking the square root. This method compares the amplitudes of both positive and negative cycles to contribute to energy transfer.
Relationships and conditions
For a sine wave, Vrms=V₀/√2, and average power in an ideal resistor is Vrms²/R. V₀ is the magnitude of one peak, not the peak-to-peak voltage.
V₀/√2 applies to a sine wave. For an arbitrary waveform, the RMS value must be calculated from its definition; real power in a load with a phase difference also requires the power factor.
What to observe in the simulation
For a sine wave RMS is peak/√2, and mean power is Vrms²/R.
The load is an ideal resistor, so current and voltage have no phase difference. Experiment on screen; do not reproduce this with real power supplies, outlets or high voltage.
Key relationships and symbols
Vrms = V₀/√2 · Pavg = V₀²/(2R)
| Symbol | Meaning | Unit |
|---|---|---|
| V₀ | Peak voltage of a sine wave | V |
| Vrms | RMS voltage | V |
| P_average | Average power consumption | W |
Worked example
What is the mean power of a 6 V peak sine wave across 20 Ω?
0.9 W
Common misconceptions
- The average AC voltage of 0 does not necessarily result in an average consumption power of 0.