Square root ~ 7

With more intervals the rms average turns out to be (* peak value* ) / √2 = * peak value* / = * peak value*

2 For those who are familiar with the graphs of sine and cosine functions, then the following algebraic method can be attempted.

* I* = * I o * sin * ωt* and * I* 2 = * I o * 2 sin 2 * ωt*

The heating effect depends on * I 2 R* , and so an average of * I 2 * is needed and not an average of * I* .

To find the rms value, you need the average value of sin 2 as time runs on and on.

The graph of sin* ωt* and the graph of cos* ωt* look the same, except for a shift of origin. Because they are the same pattern, sin 2 * ωt* and cos 2 * ωt* have the same average as time goes on.

But sin 2 * ωt* + cos 2 * ωt* = 1. Therefore the average values of either of them must be 1/2.

Therefore the rms value of * I o * sinω* t* must be * I o / √2*

The rms value is times the peak value, and the peak value is times the value the voltmeter shows. The peak value for 230 V mains is 325 V.

3 Alternatively: Plot a graph of sin 2 * θ* . Cut the graph in half and turn one half upside down, or copy onto a transparency and fit together. The two halves fit together exactly, showing that the mean value is 1/2.