What is the unit of the rms value
To explain the effective value, imagine two identical half-waves (amplitude and length) as in the diagram. Identified as positive peak voltage û_spos and negative peak voltage û_sneg. That corresponds to a period.
Let us assume that in the positive and in the negative half-wave a consumer consumes 1 ampere each. The electricity is converted into heat in a lamp. The mean value of the heat work converted within the period results in an output of one watt. A direct current of 1 ampere would also achieve this output.
This means that the rms value of the alternating current is the current that would convert the same power with a direct voltage. In other words, an alternating current of 1 A (rms value) produces the same heat output in a resistor as a direct current of 1 A.
From a mathematical point of view, the effective value U_eff is approx. 70.7% of the peak voltage û_s. AC voltage values are usually given as effective values.
The r.m.s. value is such as B. the rectification value is a root mean square and must therefore be designated with a capital letter as a formula symbol.
Why do we need the rms value?
Historically, direct current and alternating current have competed with each other. In the beginning it was common to use direct current for the power supply. Unfortunately, the line losses were very high here, which is why at some point the decision was made to use alternating current. Only direct current was not the same as alternating current (current value). In order to get the same luminosity with a lamp for alternating current as with a lamp for direct current, the peak-to-peak value of the alternating current had to be higher. The basis of this was the effective value.
Today, alternating voltage is named after the rms value. The 230 V of our local energy supply (sockets in the apartment or in the house) are the effective value of 325 V.
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