# R.M.S

#### zaidqais

Joined Feb 14, 2009
16
Hi
can i found the R.M.S of the the function

Rich (BB code):
10sin(wt)+20
by divide it by the root of 2 ?

Thank you

#### PRS

Joined Aug 24, 2008
989
If the peak voltage is 10v then the rms voltage is 10/sqrt(2). You're right. The function still has the same frequency and phase angle.

#### SawabyPlus

Joined Feb 27, 2009
14
The r.m.s. of any function of DC and harmonics is given by the formula
X r.m.s = sqrt(x0^2 + x1^2/2 + x2^2/2 + ... )
where :
x0 is the DC value.
x1,x2,.. are the amplitude of the harmonics.

so the answer to ur question is
X r.m.s = sqrt( 20^2 + 10^2/2) = 21.213

this can be driven from the definition of the r.m.s.

#### zaidqais

Joined Feb 14, 2009
16
First thank you all for your help

#### PRS

Joined Aug 24, 2008
989
I see that sawabyplus understood the function to have a dc value. I assumed that you had put the second parenthesis in the wrong place so that we have
10sin(wt+20) volts or amps, whatever -- you didn't specify.

If sawabyplus is right in assuming V = 20 + 10sin(wt), then we need the value of omega and t to solve for the instantaneous rms voltage. You did not provide this information so we cannot compute the rms voltage as it varies sinusoidally.

However, if my hunch is right, then we can write V = 7.07sin(wt + 20)

#### SawabyPlus

Joined Feb 27, 2009
14
you are right PRS, it might have been a mistake.
but what's meant by the instantaneous rms value ?, isn't the root mean square a constant that describes the function better than the simple average in average power calculations? what would be the idea behind mean if instantaneous?
and the most important, when to use that instantaneous expression? and what is physics behind it?

#### zaidqais

Joined Feb 14, 2009
16
things are mixed up a little bit with me

if my function was

Rich (BB code):
10sin(wt+30)+20
R.M.S = 21.213 and σ =30 degree ?

#### PRS

Joined Aug 24, 2008
989
Sawabyplus, instantaneous value of the voltage was meant, not instantaneous rms value. You're right the latter makes no sense.

#### PRS

Joined Aug 24, 2008
989
zaidquis, dc voltage is constant, not changing. I may be wrong but I think that only sinewaves are expressed as rms voltages or currents.