Art of Electronics 1.17

Discussion in 'Math' started by Sparky49, Dec 6, 2012.

1. Sparky49 Thread Starter Well-Known Member

Jul 16, 2011
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421
Hi all,

I'm re-reading The Art of Electronics (before, I would read as much as I could, and skipped most of the exercises with hardcore maths).

Now I am trying to get every exercise done.

But I#ve only got 33 pages in before I need some help guys. :/

Page 33, Exercise 1.17:

Show that if A=BC, then A=BC, where A,B, and C are magnitudes. Hint: Represent each complex number in polar form, ie., A=Ae^(iθ).

Now, I haven't had much formal education on complex numbers (about three lessons, and some lunch-time help with something), so all other things I have learnt have been on the internet.

I have no idea where to start with this. I am not sure what is meant with the bold characters?

I've tried looking back, but alas, to no avail.

Would someone mind helping me get there?

Many thanks,

Sparky

P.S. I'd just like to say that I am not a uni student, just someone doing this for fun! I have given it a shot, but nothing which has made any real sense.

2. MrChips Moderator

Oct 2, 2009
18,155
5,700
btw, my edition is 1980 and Exercise 1.17 is on page 28, same exercise.
I have never read "The Art" but I can figure out the exercise by reading the context. You have to read the section just before the exercise.

Bold A is a vector where as A is a scalar.
What does this mean?
It means that A contains both amplitude and phase information,
where as A is the amplitude only.

The exercise is saying the current I = V/Z if I = V/Z.

3. thatoneguy AAC Fanatic!

Feb 19, 2009
6,349
731
If you are working your way through it, I'd suggest the companion book:

"Student Manual for The Art of Electronics - Horowitz, Hayes",
ISBN 0 521 37709 9, Cambridge University Press.

Not cheap, but the physical versions are handy to have aroud, though I'd like PDFs, I haven't seen them.

4. Sparky49 Thread Starter Well-Known Member

Jul 16, 2011
822
421
Thanks guys.

Mr Chips, I must admit, I am still a little thrown.

First i, then j, then i... (in the book)

I don't get what the book is saying with the current/capacitor example. It kind of makes a silly statement:

If:

A=B/C

then

A=B/C

I understand that the vector form has the direction as well as the magnitude - but I don't see just re-writing it as proof.

The stuff with j notation has thrown me.

Sparky

5. MrChips Moderator

Oct 2, 2009
18,155
5,700
$i$ and $j$ are the same thing.

$i = j = \sqrt{-1}$

Scientists use $i$.
Electrical engineers already use $i$ to represent current. So we use $j$ instead of $i$.

A = $Ae^{j\omega}$

You have to do the multiplication or division on the vectors.

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6. Sparky49 Thread Starter Well-Known Member

Jul 16, 2011
822
421
Ah - it's that simple?

Thanks!

7. Sparky49 Thread Starter Well-Known Member

Jul 16, 2011
822
421
Just thinking about it, I remember my maths teacher making jokes about engineers who use "j - because they are wierd like that".

8. Clay Member

Feb 12, 2010
21
8
Scientists say vectors have magnitude, and direction.

Engineers say vectors have magnitude, and direction, and

point of application.

/Clay

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