# what is root mean square voltage? and why is there a root mean square voltage and a peak voltage? for instance, 120v ac has an RMS voltage of 120v and has a peak voltage of 170 volts

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what is root mean square voltage? and why is there a root mean square voltage and a peak voltage? for instance, 120v ac has an RMS voltage of 120v and has a peak voltage of 170 volts

In: Physics

It is the equivalent voltage of alternating current that delivers the same amount of energy as direct current at that voltage.

Alternating currents in the power grid are sine waves that form from plus to minus peak voltage. in the shape of a sine wave. DC and AC look like https://www.matsusada.com/column/uploads/dc_vs_ac_img_dcac.png

If you look at how a load like a simple resistive heater is heated. For DC it is simple Power = voltage * current.

But with AC the voltage and current constantly change and are sometimes zero. If you just take the peek value and multiply them you get a to high value. What you can do is take the voltage and current at each moment in time and multiply them. If the times steps are identical you can calculate the average power as the sum of all of them divided by the number of steps. This is really quite impractical.

If you look at the maths and how electricity works you will notice that we can drive what DC voltage provides the same power. Why it just is the RMS (root mean square) is not that relevant to what matters if we have found a way to get this voltage?

For sine waves RMS voltage is Peek voltage / square root of 2. The square root of two is approximately 1.41. for 120V the result is 120*1.41 = 169.2V. It is rounded to 170V. Grid voltages have an allowed range, it is +-5% in the US so 114 V to 126 V, so a tiny 0.8V rounding do not matter.

So the RMS voltage and current is the useful values for AC current because it you can use it as a DC voltage and current would be used, at least for resistive loads.

It is quite similar to how if you drive in a city 5 km with lots of other traffic and, so the speed varies. The top speed is not relevant if you look at travel time, it is the average speed that matters. The average speed is like the RMS voltage and the top speed is like the peak voltage.

The top speed can be relevant too like if a cop gives you a speeding ticket because it was to high. For the same reason, peek voltage is relevant for some design parameters of devices like distance to separate the high and low voltage side of a device. But as a usage of the power grid just RMS is enough.