RMS Voltage
Effective value of a sinusoidal voltage.
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Example
170V peak ⇒ 120V rms
How it works
RMS voltage is the DC-equivalent value of an AC voltage: it tells you what constant voltage would produce the same heating effect in a resistor. For a pure sine wave, the voltage changes smoothly over time, and the average power depends on the square of the voltage, so the root-mean-square value works out to V_peak/√2. That factor comes from averaging the square of a sine wave over one full cycle.
When to use it
Use this when analyzing mains AC voltage, AC circuits with resistive loads, or any situation where you need the effective voltage rather than the instantaneous or peak value. It is especially useful for comparing AC and DC power delivery.
Worked example, step by step
Given a sinusoidal voltage with peak value 24 V Use the RMS formula: V_rms = V_peak / √2 Substitute the numbers: V_rms = 24 / √2 Calculate: V_rms ≈ 24 / 1.414 Result: V_rms ≈ 16.97 V So the RMS voltage is about 17.0 V
Common mistakes to avoid
- Using the peak-to-peak voltage instead of the peak voltage
- Applying V_rms = V_peak/√2 to non-sinusoidal waveforms without checking the shape
- Rounding √2 too early and losing accuracy in the final answer
Did You Know?
Household "120 volts" is an RMS value; the actual peak voltage swings to about 170 volts.
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