(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The voltage across a resistor is given by:

[tex]

v(t) = 5 + 3 \cos{(t + 10^o)} + \cos{(2 t + 30^o)} V

[/tex]

Find the RMS value of the voltage

2. Relevant equations

For a periodic function, [tex]f(t)[/tex], the rms value is given by:

[tex]

f_{rms} (t) = \sqrt{\frac{1}{T} \int_{0}^{T} f(t)^2 dt}

[/tex]

Where T is the period.

3. The attempt at a solution

I know that the solution is given by:

[tex]

v_{rms} (t) = \sqrt{5^2 + (\frac{3}{\sqrt{2}})^2 + (\frac{1}{\sqrt{2}})^2} V

[/tex]

It seems that you take the sum of the squares of the respective RMS value of each piece of the original voltage. I can't figure out why you do this though. I don't think applying the equation given will easily give you this answer. It's hard to even find a period to integrate over from the original voltage equation. Any insight into why the sum of squares works would be helpful.

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# RMS (root mean square) of sums of functions

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