Question

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.

Answer 1

here we can try to develop your formulas

Answer 2

please wait I'm computing your sum...

Answer 3

here are my steps:

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

and:

Answer 8

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

Answer 9

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

Answer 10

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

Answer 11

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

Answer 12

I hope you see them correctly

Answer 13

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

Answer 14

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

Answer 15

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

Answer 16

@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 \

Answer 17

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

Answer 18

from my preceding 2 formulas, you can find both the amplitude A, and the angle \alpha, so you can write your answer as follows:
\[\Large {i_1} + {i_2} = A\cos \left( {60\pi t + \alpha } \right)\]

Answer 19

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

Answer 20

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

Answer 21

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

Answer 22

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

Answer 23

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.

Answer 24

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

Answer 25

thanks! :) @UsukiDoll

Answer 26

Michele does

Answer 27

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

Answer 28

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

Answer 29

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

Answer 30

That's right! I use TexMik with TeXnicCenter

Answer 31

ok! I update my answer with your value @carlj0nes

Answer 32

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

Answer 33

here is my PDF file:

Answer 34

what do you think about that file?

Answer 35

I saw "in order to that" @______@

Answer 36

is it correct? @UsukiDoll

Answer 37

doesn't sound right

Answer 38

why?

Answer 39

"In order to [do] that"

Answer 40

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

Answer 41

A simple computation shows us...

Answer 42

[Therefore,] we can write

Answer 43

compute [the following] ratio

Answer 44

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

Answer 45

[Then],

Answer 46

known angles [we have],

[Next,] we get,

Answer 47

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

Answer 48

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!

Answer 49

I still see that comma splice

Answer 50

please what is a comma splice?

Answer 51

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

Answer 52

ok!

Answer 53

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

Answer 54

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

Answer 55

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.

Answer 56

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