Root Mean Square (RMS)

Definition

RMS is defined as the square root of the mean square.

Why it’s useful

An understanding of root mean square (RMS) is necessary when delving deeper into the science of voltage and frequency. RMS, in regards to electronics, gives us an easy way to do calculations with AC current. It lets us treat AC as DC in many circumstances. For instance, the mains supply in many countries is 230 V. However, that’s not the peak voltage, it’s the RMS voltage. The peak voltage is about 325 V. It is now easier to calculate the power since we don’t need to take into account a shifting voltage and current. We can simply use 230 V in our calculations, and treat that as an average voltage.

The formula for the root mean square of a sinusoidal waveform is

Power

The dissipated power in the resistor is calculated with the following formula

This gives us a power of 25 mW. The power is dependent on voltage, and if the circuit was supplied with a sine wave instead, then the math would become more complex, as the voltage (and current) of a sine wave varies with time.

Power in AC circuits

We can simplify calculations and use RMS instead. Calculating the RMS of a sine wave will give us a constant DC voltage, as in the circuit above, which we can use the same power formula on. Given a sine wave with a peak voltage of 5 V, the power is calculated by combining the two above formulas and substituting the two variables.

The power is lower by a great deal, which makes sense considering 5 V is the peak, and not constant, as in the DC example.

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