(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.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: RMS (root mean square) of sums of functions

**Physics Forums | Science Articles, Homework Help, Discussion**