carlj0nes
  • carlj0nes
By using a Scaled phasor Diagram determine the resultant force when the following currents are added. (I will attach a picture in the comment). What I need is from the method I have used clearly explain the method/technique used and to validate the solution/ method by using an alternative mathematical method.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
carlj0nes
  • carlj0nes
Michele_Laino
  • Michele_Laino
here we can try to develop your formulas
Michele_Laino
  • Michele_Laino
please wait I'm computing your sum...

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Michele_Laino
  • Michele_Laino
here are my steps:
Michele_Laino
  • Michele_Laino
\[\begin{gathered} 20\cos \left( {60\pi t} \right)\cos \left( {\pi /4} \right) - 20\sin \left( {60\pi t} \right)\sin \left( {\pi /4} \right) + \hfill \\ \hfill \\ + 30\cos \left( {60\pi t} \right)\cos \left( {\pi /10} \right) - 30\sin \left( {60\pi t} \right)\sin \left( {\pi /10} \right) = \hfill \\ \hfill \\ = \cos \left( {60\pi t} \right)\left\{ {20\cos \left( {\pi /4} \right) + 30\cos \left( {\pi /10} \right)} \right\} - \hfill \\ \hfill \\ - \sin \left( {60\pi t} \right)\left\{ {20\sin \left( {\pi /4} \right) + 30\sin \left( {\pi /10} \right)} \right\} \hfill \\ \end{gathered} \]
Michele_Laino
  • Michele_Laino
now, we can write: \[\left\{ \begin{gathered} 20\cos \left( {\pi /4} \right) + 30\cos \left( {\pi /10} \right) = A\cos \alpha \hfill \\ 20\sin \left( {\pi /4} \right) + 30\sin \left( {\pi /10} \right) = A\sin \alpha \hfill \\ \end{gathered} \right.\]
Michele_Laino
  • Michele_Laino
using the subsequent values: \[\cos \left( {\pi /4} \right) = \sin \left( {\pi /4} \right) = \frac{1}{{\sqrt 2 }}\]
Michele_Laino
  • Michele_Laino
and:
Michele_Laino
  • Michele_Laino
\[\begin{gathered} \cos \left( {\pi /10} \right) = \frac{{\sqrt {10 + \sqrt {20} } }}{4}, \hfill \\ \hfill \\ \sin \left( {\pi /10} \right) = \frac{{\sqrt 5 - 1}}{4} \hfill \\ \end{gathered} \]
Michele_Laino
  • Michele_Laino
I rewrite those values:\[\begin{gathered} \cos \left( {\pi /10} \right) = \frac{{\sqrt {10 + \sqrt {20} } }}{4}, \hfill \\ \hfill \\ \sin \left( {\pi /10} \right) = \frac{{\sqrt 5 - 1}}{4} \hfill \\ \end{gathered} \]
Michele_Laino
  • Michele_Laino
\[\begin{gathered} \sin \left( {\pi /10} \right) = \frac{{\sqrt 5 - 1}}{4} \hfill \\ \cos \left( {\pi /10} \right) = \frac{{\sqrt {10 + \sqrt {20} } }}{4}, \hfill \\ \end{gathered} \]
Michele_Laino
  • Michele_Laino
\[\Large \begin{gathered} \sin \left( {\pi /10} \right) = \frac{{\sqrt 5 - 1}}{4} \hfill \\ \hfill \\ \cos \left( {\pi /10} \right) = \frac{{\sqrt {10 + \sqrt {20} } }}{4}, \hfill \\ \end{gathered} \]
Michele_Laino
  • Michele_Laino
I hope you see them correctly
Michele_Laino
  • Michele_Laino
we can rewrite those equations as below: \[\Large \left\{ \begin{gathered} \frac{{20}}{{\sqrt 2 }} + 30\frac{{\sqrt {10 + \sqrt {20} } }}{4} = A\cos \alpha \hfill \\ \hfill \\ \frac{{20}}{{\sqrt 2 }} + 30\frac{{\sqrt 5 - 1}}{4} = A\sin \alpha \hfill \\ \end{gathered} \right.\]
Michele_Laino
  • Michele_Laino
then we square both of those equations and we add them together, so we can write: \[\large {A^2} = {\left( {\frac{{20}}{{\sqrt 2 }} + 30\frac{{\sqrt {10 + \sqrt {20} } }}{4}} \right)^2} + {\left( {\frac{{20}}{{\sqrt 2 }} + 30\frac{{\sqrt 5 - 1}}{4}} \right)^2}\]
Michele_Laino
  • Michele_Laino
whereas divding side by side those equations, we find: \[\Large \tan \alpha = \frac{{A\sin \alpha }}{{A\cos \alpha }} = \frac{{\frac{{20}}{{\sqrt 2 }} + 30\frac{{\sqrt 5 - 1}}{4}}}{{\frac{{20}}{{\sqrt 2 }} + 30\frac{{\sqrt {10 + \sqrt {20} } }}{4}}}\]
carlj0nes
  • carlj0nes
@Michele_Laino thank you for your help. Sorry to be a pain but would you be able to hand write the first part for me and upload a picture just so i can try to understand some of the terminology of what you have put. e.g. hfill and \
Michele_Laino
  • Michele_Laino
no, I'm sorry I'm not able to hand write my answer, nevertheless I'm able to write a PDF file, and attach it using the "Attach FIle" button
Michele_Laino
  • Michele_Laino
from my preceding 2 formulas, you can find both the amplitude A, and the angle \alpha, so you can write your answer as follows: \[\Large {i_1} + {i_2} = A\cos \left( {60\pi t + \alpha } \right)\]
Michele_Laino
  • Michele_Laino
please wait, I'm doing that computation...
Michele_Laino
  • Michele_Laino
I got: \[\Large \begin{gathered} A = 48.67Amperes \hfill \\ \alpha = 0.5\;radians \hfill \\ \end{gathered} \]
Michele_Laino
  • Michele_Laino
so we can write: \[\Large {i_1} + {i_2} \cong 48.7\cos \left( {60\pi t + 0.5} \right)\]
Michele_Laino
  • Michele_Laino
please note that we have the subsequent equivalence: \[\Large 0.5\;{\text{radians}} = 28.75\;{\text{degrees}}\]
carlj0nes
  • carlj0nes
That would be helpful if you could put it as a PDF as im not use to how this is laid out. I normally have to type it up in word and it takes ages (see attached). That was why I suggested handwritten as it what i find easiest. But we all have our preferences.
UsukiDoll
  • UsukiDoll
@Michele_Laino you deserve more than 2 medals D:! All that Latex!
Michele_Laino
  • Michele_Laino
thanks! :) @UsukiDoll
carlj0nes
  • carlj0nes
Michele does
Michele_Laino
  • Michele_Laino
@carlj0nes ok! I start to write your PDF file, please wait, it will take some time
UsukiDoll
  • UsukiDoll
texmaker and then use Latex --> PDF I think it was F5 . I forgot.
carlj0nes
  • carlj0nes
just a note at the beginning should that of been 32 cos not 30 cos
Michele_Laino
  • Michele_Laino
That's right! I use TexMik with TeXnicCenter
Michele_Laino
  • Michele_Laino
ok! I update my answer with your value @carlj0nes
carlj0nes
  • carlj0nes
just a note at the beginning should that of been 32 cos not 30 cos
Michele_Laino
  • Michele_Laino
here is my PDF file:
Michele_Laino
  • Michele_Laino
what do you think about that file?
UsukiDoll
  • UsukiDoll
I saw "in order to that" @______@
Michele_Laino
  • Michele_Laino
is it correct? @UsukiDoll
UsukiDoll
  • UsukiDoll
doesn't sound right
Michele_Laino
  • Michele_Laino
why?
UsukiDoll
  • UsukiDoll
"In order to [do] that"
Michele_Laino
  • Michele_Laino
ok! thanks! I'm updating my file @UsukiDoll
UsukiDoll
  • UsukiDoll
A simple computation shows us...
UsukiDoll
  • UsukiDoll
[Therefore,] we can write
UsukiDoll
  • UsukiDoll
compute [the following] ratio
Michele_Laino
  • Michele_Laino
following the suggestions by @UsukiDoll I have rewritten my file, here is it:
UsukiDoll
  • UsukiDoll
[Then],
UsukiDoll
  • UsukiDoll
known angles [we have], [Next,] we get,
UsukiDoll
  • UsukiDoll
comma splice! period after Amplitude A A simple computation (no s) Again, after a simple computation, we get: delete So. add[ As a result, ]the requested sum of the two currents is
Michele_Laino
  • Michele_Laino
here my new updated version of the preceding PDF file, I have to be grateful to @UsukiDoll for her suggestions and comments to my english grammar!
UsukiDoll
  • UsukiDoll
I still see that comma splice
Michele_Laino
  • Michele_Laino
please what is a comma splice?
UsukiDoll
  • UsukiDoll
I'll take a screenshot and use paint to add my marks AHHAAHAHHAHAHA
Michele_Laino
  • Michele_Laino
ok!
UsukiDoll
  • UsukiDoll
comma splice is a comma between two complete sentences. It's the most aggravating error for English Professors to see on essays
Michele_Laino
  • Michele_Laino
ok! Please show where is the comma splice in my file
UsukiDoll
  • UsukiDoll
carlj0nes
  • carlj0nes
Thank you for all you help it is much appreciated. I am about to post another question and i would like to invite both of you.
UsukiDoll
  • UsukiDoll
I have to sleep early. I have to help shop blah
UsukiDoll
  • UsukiDoll

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