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RMS Voltage and Current

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RMS — a useful AC number

An AC sine wave is constantly changing, so which voltage do we use when we say “120 volts AC”? For ordinary power work we normally mean the RMS value.

A useful first picture

RMS asks: “What DC voltage would produce the same heating effect in a resistor?” That lets us compare useful AC power with familiar DC values.

The sine-wave relationship

V_RMS ≈ 0.707 V_peak

V_peak ≈ 1.414 V_RMS

Worked example

120 V RMS household power has a peak near:

120 × 1.414 ≈ 170 V peak

That is why “120 volts AC” does not mean the waveform never exceeds 120 volts.

A little history

As AC systems developed, engineers needed a practical way to compare alternating quantities with DC effects. Root-mean-square mathematics provides that equivalent-value measure for periodic waveforms.

Try these yourself

For a sine wave, 120 V RMS has a peak voltage closest to: 85 V 120 V 170 V 240 V

Vpeak ≈ 1.414 × Vrms, so 120 V RMS is about 170 V peak.

Why is RMS useful? It gives an AC value comparable to DC heating/power effect in a resistor It makes frequency zero It removes resistance It is only a wire size

RMS expresses AC in terms of an equivalent DC heating effect for a resistive load.

For a sine wave, RMS voltage is approximately: 0.707 × peak peak × 2 peak ÷ 10 always equal to peak

Vrms = Vpeak/√2 ≈ 0.707 Vpeak.

A little deeper

RMS literally means root mean square: square the waveform, average those squared values, then take the square root. For a pure sine wave, that process gives the familiar factor 1/√2 ≈ 0.707.

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