Total voltage of 3 AC voltages

[Peter]

I have the following problem and I'm not sure if I did it correct:

Given v(t) =10 + 5 Sin (377t+30 degrees) - 7 Sin (377t-45 degrees)

Find VRMS


Putting them into rectangular form:



(7.07 + j 0) + (3.06 + j 1.77) - (3.5 - j 3.5)


now I add my reals and imaginaries and that's my answer? Or I can convert
that number into polar as well.

 

[sQuick]

I have the following problem and I'm not sure if I did it correct:

Given v(t) =10 + 5 Sin (377t+30 degrees) - 7 Sin (377t-45 degrees)

Find VRMS


Putting them into rectangular form:



(7.07 + j 0) + (3.06 + j 1.77) - (3.5 - j 3.5)


now I add my reals and imaginaries and that's my answer? Or I can convert
that number into polar as well.

sounds like homework to me sonny..

sQuick..

 

[Peter]

sounds like homework to me sonny..

sQuick..

and? I'm asking a question so I can understand it better. I've done half
the problem already!

 

[Mike Lamond]

and? I'm asking a question so I can understand it better. I've done half
the problem already!

You have also gotten the wrong results for that half. You may understand
the concept of polar to rectangular conversion, but your trigonometry math
is wrong. It helps to draw your vector, then the real and imaginary sides of
the triangle and do the math from there. Show all work. You have another
mistake but I'm not going to tell you what it is.

Back in high school trig (college prep track 1978-79), Mrs. Fliegel made
us memorize sine, cosine and tangent at 0, 30, 45, 60 and 90 degrees. We
also had to draw them freehand on trig graph paper. Calculators were not
allowed in that class!

Mike

 

[Figaro]

|I have the following problem and I'm not sure if I did it correct:
|
| Given v(t) =10 + 5 Sin (377t+30 degrees) - 7 Sin (377t-45 degrees)
|
| Find VRMS
|
|
| Putting them into rectangular form:
|
|
|
| (7.07 + j 0) + (3.06 + j 1.77) - (3.5 - j 3.5)
|
|
| now I add my reals and imaginaries and that's my answer? Or I can convert
| that number into polar as well.

You cannot use phasor since you have a DC component.

Recall that RMS = root-mean-square.

Therefore, to obtain Vrms first calculate the square of v(t), i.e. [
v(t) ]^2.
Then integrate the result over one cycle, i.e., from t=0 to t=1/(60),
and then divide the result by 1/(60) to obtain the mean.
Take the square-root of the result.
The answer is the Vrms.