Chapter 9 T9 Note 2

Status
Not open for further replies.
PaulMmn said:
Finally, a diagram showing the relation between a helix (a circle moving through time) and the sin / cos functions:

View attachment 2551636
Click to expand...

That's interesting. In school, I could understand trigonometry. It all made sense, like the first diagram you posted. And I could understand real and imaginary numbers and how they mapped onto the complex plane.

But I never had any idea where Euler's Formula came from, or how anyone ever managed to mentally relate trig functions and imaginary numbers together. I just had to memorize the formula, and then just accept it was true.

I don't completely understand it yet, but that diagram does seem to show the connection.

I had an entire class on something very similar - Laplace Transforms. I could do the homework, but I could never really understand how or why it worked.
 
steve66 said:
That's interesting. In school, I could understand trigonometry. It all made sense, like the first diagram you posted. And I could understand real and imaginary numbers and how they mapped onto the complex plane.

But I never had any idea where Euler's Formula came from, or how anyone ever managed to mentally relate trig functions and imaginary numbers together. I just had to memorize the formula, and then just accept it was true.
Click to expand...
There was a Feynman lecture that showed how Euler's formula was connected to trigonometry, algebra, and geometry. Euler's formula comes together at the end of the lecture at:

A short audio exerpt of the original lecture is at:

Feynman on Algebra – Richard Feynman

Happy Feynman’s Birthday! I hope this day finds you as excited as ever about the wonders of the world that surround us every day. In Feynman’s honor, I’ve strung three 90-second excerpts together to show what passion Feynman brought to the subject of elementary algebra.
www.feynman.com www.feynman.com
 
synchro said:
There was a Feynman lecture that showed how Euler's formula was connected to trigonometry, algebra, and geometry. Euler's formula comes together at the end of the lecture at:

A short audio exerpt of the original lecture is at:

Feynman on Algebra – Richard Feynman

Happy Feynman’s Birthday! I hope this day finds you as excited as ever about the wonders of the world that surround us every day. In Feynman’s honor, I’ve strung three 90-second excerpts together to show what passion Feynman brought to the subject of elementary algebra.
www.feynman.com www.feynman.com
Click to expand...

I'm going to have to read that as soon as I get time.
 
synchro said:
There was a Feynman lecture that showed how Euler's formula was connected to trigonometry, algebra, and geometry. Euler's formula comes together at the end of the lecture at:
Click to expand...

Wow, that is amazing. I'm not sure i will ever completely understand it. I've had access to a scientific calculator since I was in grade school. I've never had to use logs to do square roots and exponents.

Now that everyone has access to calculators and computers to do all the hard work, I wonder if there will ever be anyone as smart as those guys like Feynman and Einstein were again.
 
charlie b said:
You lost me here: What has led you to believe that the K value changes with power factor? It does not. There are different values for copper versus aluminum wires. The K factor is based on the properties of the materials and varies with the assumed ambient temperature.

The influence that power factor has on voltage drop comes into play with the value of current you use in the formula. If you started by only knowing the "real power" value, the "kW" value, then you are not ready to calculate VD. You need to also know the PF, in order to calculate the "apparent power," or "kVA." From that value, and also knowing the voltage and whether this is a single phase or three phase circuit, you calculate the current. Then and only then do you apply the formula you cited in your original post.
Click to expand...
the reason I ask is because I was watching mikes DVD on voltage drop and he used a power factor in replace of the K value
his formula looked like

1.732x6.91ohmsx404A (locked rotor current)x150FT divided by a Cmil value of 52,620
he went on to explain that 6.91 was came up with by the power factor of the motor.
 
I GIVE UP LOL :LOL: I feel the concept is at the tips of my fingers but I don't have enough education about electrical engineering to understand this in great detail. I may be able to figure the formula out to get the answer, however the pictures of the three phase worm hole ,makes me want to throw the towel in. Im done😂
 
steve66 said:
But I never had any idea where Euler's Formula came from, or how anyone ever managed to mentally relate trig functions and imaginary numbers together. I just had to memorize the formula, and then just accept it was true.

I don't completely understand it yet, but that diagram does seem to show the connection.
Click to expand...

One example of where you can see the reason for Euler's formula relating trig to imaginary exponents, is the differential equation governing a mass on a spring. Experimentally, you can show that it is a sine wave shape, and your intuition of what a vibration is, would agree.

It takes following form, where the " indicates second derivative, and m and k are the mass and spring constant:
m*x" + k*x = 0

The method that works to solve the solution, involves setting up x as an exponential function of time, x = C*e^(r*t), where r and C are constants, and e is Euler's number. You'll end up with a quadratic equation that has two imaginary numbers as solutions. The real life meaning of that, ends up being that the solution is a sinusoidal function of time.
 
anthonysolino said:
I GIVE UP LOL :LOL: I feel the concept is at the tips of my fingers but I don't have enough education about electrical engineering to understand this in great detail. I may be able to figure the formula out to get the answer, however the pictures of the three phase worm hole ,makes me want to throw the towel in. Im done😂
Click to expand...


Sorry, sometimes we get a little sidetracked here. I don't think you have to understand Euler's formula and all the diagrams that have been posted just to do a voltage drop calc.

So back to your first question: There are so many different ways to write or approx. the voltage drop formula, that I'm not familiar with the one you posted. And I don't have time to really dig into it and see how it works. But I do see Mike has posted some simpler formulas that don't include the power factor:

MH VOltage Drop Calcs

I'd suggest working through those first. Then looking at the formula that includes power factor again. If I get some time, I'll do the same, but I can't make any guarantees.

But please don't give up.
 
Status
Not open for further replies.
Top