### 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:

- Integrate the square of the function in the given range of the variable - from a to b in this case.
- Find the mean value of the above integral, dividing by the range of the variable - (b - a) in this case.
- 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:

The r.m.s value of the AC gives the same power given by

an equal DC through the same resistor.

E.g.

If the resistor in question is 5Ω, peak voltage and r-m-s voltage are

325V and 230V respectively,

Power = V

^{2}/RPower = 230

^{2}/5, not 325^{2}/5, which is the same as under 230V, DC through 5Ω resistor.For interactive practise, here is the applet:

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