## carlj0nes one year ago 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.

1. carlj0nes

2. Michele_Laino

here we can try to develop your formulas

3. Michele_Laino

4. Michele_Laino

here are my steps:

5. Michele_Laino

$\begin{gathered} 20\cos \left( {60\pi t} \right)\cos \left( {\pi /4} \right) - 20\sin \left( {60\pi t} \right)\sin \left( {\pi /4} \right) + \hfill \\ \hfill \\ + 30\cos \left( {60\pi t} \right)\cos \left( {\pi /10} \right) - 30\sin \left( {60\pi t} \right)\sin \left( {\pi /10} \right) = \hfill \\ \hfill \\ = \cos \left( {60\pi t} \right)\left\{ {20\cos \left( {\pi /4} \right) + 30\cos \left( {\pi /10} \right)} \right\} - \hfill \\ \hfill \\ - \sin \left( {60\pi t} \right)\left\{ {20\sin \left( {\pi /4} \right) + 30\sin \left( {\pi /10} \right)} \right\} \hfill \\ \end{gathered}$

6. Michele_Laino

now, we can write: $\left\{ \begin{gathered} 20\cos \left( {\pi /4} \right) + 30\cos \left( {\pi /10} \right) = A\cos \alpha \hfill \\ 20\sin \left( {\pi /4} \right) + 30\sin \left( {\pi /10} \right) = A\sin \alpha \hfill \\ \end{gathered} \right.$

7. Michele_Laino

using the subsequent values: $\cos \left( {\pi /4} \right) = \sin \left( {\pi /4} \right) = \frac{1}{{\sqrt 2 }}$

8. Michele_Laino

and:

9. Michele_Laino

$\begin{gathered} \cos \left( {\pi /10} \right) = \frac{{\sqrt {10 + \sqrt {20} } }}{4}, \hfill \\ \hfill \\ \sin \left( {\pi /10} \right) = \frac{{\sqrt 5 - 1}}{4} \hfill \\ \end{gathered}$

10. Michele_Laino

I rewrite those values:$\begin{gathered} \cos \left( {\pi /10} \right) = \frac{{\sqrt {10 + \sqrt {20} } }}{4}, \hfill \\ \hfill \\ \sin \left( {\pi /10} \right) = \frac{{\sqrt 5 - 1}}{4} \hfill \\ \end{gathered}$

11. Michele_Laino

$\begin{gathered} \sin \left( {\pi /10} \right) = \frac{{\sqrt 5 - 1}}{4} \hfill \\ \cos \left( {\pi /10} \right) = \frac{{\sqrt {10 + \sqrt {20} } }}{4}, \hfill \\ \end{gathered}$

12. Michele_Laino

$\Large \begin{gathered} \sin \left( {\pi /10} \right) = \frac{{\sqrt 5 - 1}}{4} \hfill \\ \hfill \\ \cos \left( {\pi /10} \right) = \frac{{\sqrt {10 + \sqrt {20} } }}{4}, \hfill \\ \end{gathered}$

13. Michele_Laino

I hope you see them correctly

14. Michele_Laino

we can rewrite those equations as below: $\Large \left\{ \begin{gathered} \frac{{20}}{{\sqrt 2 }} + 30\frac{{\sqrt {10 + \sqrt {20} } }}{4} = A\cos \alpha \hfill \\ \hfill \\ \frac{{20}}{{\sqrt 2 }} + 30\frac{{\sqrt 5 - 1}}{4} = A\sin \alpha \hfill \\ \end{gathered} \right.$

15. Michele_Laino

then we square both of those equations and we add them together, so we can write: $\large {A^2} = {\left( {\frac{{20}}{{\sqrt 2 }} + 30\frac{{\sqrt {10 + \sqrt {20} } }}{4}} \right)^2} + {\left( {\frac{{20}}{{\sqrt 2 }} + 30\frac{{\sqrt 5 - 1}}{4}} \right)^2}$

16. Michele_Laino

whereas divding side by side those equations, we find: $\Large \tan \alpha = \frac{{A\sin \alpha }}{{A\cos \alpha }} = \frac{{\frac{{20}}{{\sqrt 2 }} + 30\frac{{\sqrt 5 - 1}}{4}}}{{\frac{{20}}{{\sqrt 2 }} + 30\frac{{\sqrt {10 + \sqrt {20} } }}{4}}}$

17. 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 \

18. 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

19. 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: $\Large {i_1} + {i_2} = A\cos \left( {60\pi t + \alpha } \right)$

20. Michele_Laino

please wait, I'm doing that computation...

21. Michele_Laino

I got: $\Large \begin{gathered} A = 48.67Amperes \hfill \\ \alpha = 0.5\;radians \hfill \\ \end{gathered}$

22. Michele_Laino

so we can write: $\Large {i_1} + {i_2} \cong 48.7\cos \left( {60\pi t + 0.5} \right)$

23. Michele_Laino

please note that we have the subsequent equivalence: $\Large 0.5\;{\text{radians}} = 28.75\;{\text{degrees}}$

24. 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.

25. UsukiDoll

@Michele_Laino you deserve more than 2 medals D:! All that Latex!

26. Michele_Laino

thanks! :) @UsukiDoll

27. carlj0nes

Michele does

28. Michele_Laino

@carlj0nes ok! I start to write your PDF file, please wait, it will take some time

29. UsukiDoll

texmaker and then use Latex --> PDF I think it was F5 . I forgot.

30. carlj0nes

just a note at the beginning should that of been 32 cos not 30 cos

31. Michele_Laino

That's right! I use TexMik with TeXnicCenter

32. Michele_Laino

33. carlj0nes

just a note at the beginning should that of been 32 cos not 30 cos

34. Michele_Laino

here is my PDF file:

35. Michele_Laino

what do you think about that file?

36. UsukiDoll

I saw "in order to that" @______@

37. Michele_Laino

is it correct? @UsukiDoll

38. UsukiDoll

doesn't sound right

39. Michele_Laino

why?

40. UsukiDoll

"In order to [do] that"

41. Michele_Laino

ok! thanks! I'm updating my file @UsukiDoll

42. UsukiDoll

A simple computation shows us...

43. UsukiDoll

[Therefore,] we can write

44. UsukiDoll

compute [the following] ratio

45. Michele_Laino

following the suggestions by @UsukiDoll I have rewritten my file, here is it:

46. UsukiDoll

[Then],

47. UsukiDoll

known angles [we have], [Next,] we get,

48. 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

49. 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!

50. UsukiDoll

I still see that comma splice

51. Michele_Laino

please what is a comma splice?

52. UsukiDoll

I'll take a screenshot and use paint to add my marks AHHAAHAHHAHAHA

53. Michele_Laino

ok!

54. UsukiDoll

comma splice is a comma between two complete sentences. It's the most aggravating error for English Professors to see on essays

55. Michele_Laino

ok! Please show where is the comma splice in my file

56. UsukiDoll

57. 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.

58. UsukiDoll

I have to sleep early. I have to help shop blah

59. UsukiDoll