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Peak and RMS values
Beginner
RMS equals peak over root two.
I_rms = I₀/√2The RMS value is the DC equivalent in heating: I_rms = I₀/√2 ≈ 0.707 I₀. Meters and mains ratings quote RMS.
A 10 A peak current has 7.07 A RMS.
Average of a full sine cycle is zero.
In more detail
The peak value is the maximum voltage or current in an AC cycle, while the RMS value is the steady DC value that gives the same heating effect. For a sinusoid, RMS equals peak divided by the square root of two.
Real-world uses
- Mains voltage is quoted as an RMS value, such as 230 V.
- Electrical appliances are rated using RMS values.
- A 230 V mains supply has a peak voltage of about 325 V, which is why insulation must be rated for the peak.
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Frequently asked questions
What is the peak of mains voltage?
About 325 volts, for a 230 volt RMS supply.
Why use RMS?
Because it gives the average power delivered to a resistor.
Why is the RMS value used?
It gives the same heating effect as a DC value, so it is the number that matters for power and appliance ratings.
Related topics in AC Circuits & EM Waves
Alternating current · Average power in AC · Phasors · Resistor in AC