Root-Mean-Square Voltage - r-m-s voltage of AC


Root-Mean-Square Voltage in the UK

The root-mean-square value of a function, f(t), is calculated as follows:

r--m-s voltage

  1. Integrate the square of the function in the given range of the variable - from a to b in this case.
  2. Find the mean value of the above integral, dividing by the range of the variable - (b - a) in this case.
  3. Find the square root of the value that you get in step 2).
The AC voltage is a sine curve and it changes with time as follows:
v = 325 sin(t), where the peak value in the UK is about 325V.

The calculation is as follows:

r.m.s voltage calculation

The r.m.s value of the AC gives the same power given by
an equal DC through the same resistor.


If the resistor in question is 5Ω, peak voltage and r-m-s voltage are
325V and 230V respectively, 
Power = V2/R
Power = 2302/5, not 3252/5, which is the same as under 230V, DC through 5Ω resistor.

For interactive practise, here is the applet:


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