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.
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)
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?