help with wikipedia explanatino of I_rms

[LordSnailz]

Probbably a simple question for all you math gurus --

I can't seem to understand why Irms = Ip/sqrt(2).
Why is it divide by sqrt(2)?

http://en.wikipedia.org/wiki/Root_mean_square

 

[franksta]

cosine, I think.

 

[JohnCU]

Take the function, square it, take the average (by integrating from 0 to T and then dividing by T), then take the square root. It works out in the integration.

 

[LordSnailz]

Originally posted by: JohnCU
Take the function, square it, take the average (by integrating from 0 to T and then dividing by T), then take the square root. It works out in the integration.

So this equation applies to any function? So if I have a sinusoidal equation(ot necessarily cos or sine) and I can blindly say that the rms value of the function is the peak/sqrt(2).

Any intuition on why it works out that way through the integral? I would think it depends on the period you're integrating through.

 

[JohnCU]

If it has a period T, then as long as you integrate over 1 complete period, you get the answer. The sqrt(2) factor only applies to cosines and sines I think, I know a triangle wave is like sqrt(3) I believe.

Use your Ti-89. Take the square root of (1/2*pi)* integral of sin(t)^2 with respect to t from 0 to 2*pi and you should get the answer.

 

[LordSnailz]

ah, got it. It's sqrt(2) because it's a sinusoidal wave, if it's a different function then the value will be different.

Cool, got it, thanks guys.