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What is RMS simple?

Published in Electrical Engineering Basics 3 mins read

RMS, or Root Mean Square, simply represents a way to express the effective value of a fluctuating voltage or current. Think of it as the DC equivalent.

In other words, the RMS value of an AC voltage or current is the amount of DC voltage or current that would dissipate the same amount of power in a resistor. According to the reference, RMS is the "root mean square current/voltage of the alternating current/voltage represents the d.c. current/voltage that dissipates the same amount of power as the average power dissipated by the alternating current/voltage."

Understanding RMS

Here's a breakdown to make it easier to grasp:

  • Fluctuating Signal: Alternating current (AC) and voltage constantly change in magnitude and direction.
  • Effective Value: We need a way to compare AC to DC (direct current), which has a constant magnitude and direction. RMS provides this effective value.
  • Power Equivalence: The RMS value is chosen so that the AC source and a DC source with the same RMS value will deliver the same amount of power to a resistive load.

RMS Calculation

For a perfect sine wave, there's a simple relationship:

RMS Value = Peak Value / √2 (approximately Peak Value / 1.414)

For other waveforms (non-sinusoidal), a more complex calculation involving squaring the waveform, finding the average (mean) of the squared values, and then taking the square root is required. This is where the term "Root Mean Square" comes from:

  1. Square: Square all the values of the waveform.
  2. Mean: Calculate the average of these squared values.
  3. Root: Take the square root of the average.

Practical Implications

  • Measuring AC Voltage: When you use a multimeter to measure AC voltage in your home, the meter typically displays the RMS voltage.
  • Power Calculations: RMS values are used in power calculations for AC circuits (P = VRMS * IRMS).
  • Equipment Ratings: Electrical equipment is often rated in RMS values to indicate the continuous voltage or current it can handle.

Example

If the peak voltage of a sinusoidal AC signal is 170 volts, then the RMS voltage is approximately 170 / 1.414 = 120 volts. This means that a 120V DC source would deliver the same amount of power to a resistor as this AC source with a peak voltage of 170V.

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