Can anyone break this down for me?

I've just looked in the book myself.  The answers given are clearly wrong:

The first one balances, but the second one clearly doesn't!   It's not unusual for a book with so many equations/examples to contain a few errors.

Thanks Alan, Confession time i made a mistake in what is posted. The first equation at the end should also have

0 - V2/15. Those denominators are all resistors in the circuit.

The actual answers in the book are V2 = 32.34v  V3 = 40.14v though in my novice state with combining equations i can't get those answers.

The first way you wrote out the second equation is exactly the way the author has written it in the book. The second one is out because i forgot to include that part of the equation in my rush to post it!

Thanks for replying.

Like this?

Still don't get the same values as you quote!

Thanks Alan yeah the way you've written them at the top is the way the problem appears in the book.

This is from a book called 'Electronics: A Systems Approach' by a guy called Neil Storey who works at Warwick University here in the UK. I emailed him to help me, but he's on holiday!!

I don't know why the numbers don't match.

Thanks for taking the time to write all that out! Appreciate it.

I'll send him a message saying he's got a mistake in the book for future editions and see what he says.

You're right sometimes there are mistakes when so much data is being put on paper.

I'm principally interested in this because i'm into amplifiers and there's a lot of calculations for gain stages,

rectification and all the rest of it. Anyway in reading a couple of my textbooks i came across some sums that i

looked at from every angle and they just didn't make sense! So i contacted the author and he said i was right

that the book had a typo in there! So it might very well be that.

Thanks for helping me.

You're welcome!

I've looked more carefully in the book at the equations and the diagram from which they are derived, and I can see that the second equation has a misprint (in the book). The term (100 - V2)/30 should be (100 - V3)/30.  

With this change the solutions given for V2 and V3 in the book are correct.

Trying to follow all the steps Alan you wrote out in the second answer you gave. Forgetting about the mistake

in the book in the printing in the book for a second.

In the first rearrangement of the first equation: where are you getting the 5 from? are you just dividing the 50

 by the 10 in the denominator? I've been off maths so long and i'm so rusty! I thought that in that case that

would

cancel out the denominator and you couldn't use it further on.

Same with the bit where  we have 5 - 13/60 where is the 13/60 coming from?

Man i wish i was good at Maths!

Thanks Alan.

In the first rearrangement of the first equation: where are you getting the 5 from? 

(50-V2)/10 + (V3-V2)/20 + (0-V2)/15 = 0 This can be written as:

50/10 - V2/10 +V3/20 - V2/20 +0/15 - V2/15 = 0

The first term above is just 50/10 = 5; so that's where the 5 comes from.

Same with the bit where  we have 5 - 13/60 where is the 13/60 coming from?

Collect all the terms involving V2:  -V2/10 - V2/20 - V2/15  Factor out -V2 to get:

-V2*(1/10 + 1/20 + 1/15)  Collect the fractions together as a single fraction.  To do this we need to find a common multiple of 10, 20 and 15.  Any multiple will do, but often life is easier if we use the lowest common multiple.  In this case that is 60, so we can express the individual fractions as:

1/10 = 6/60

1/20 = 3/60

1/15 = 4/60

So now the sum can be written as 6/60 + 3/60 + 4/60, and because they are all over the same number we can write  6/60 + 3/60 + 4/60 = (6 + 3 + 4)/60 = 13/60.

Hope that helps!

Alan you're the best! That answers my questions, as i've forgotten so much about maths!

I bought one of those Algebra for dummies books to go right back to basics again and do the remedial work i need.

Really i only need to know enough to be able to do the math for circuits like the ones in the book we have by

Neil Storey and stuff related to that.

I got back into doing this because i'm a guitar player and love working on amps replacing capacitors and

resistors and the likes and stuff so am always studying amp schematics. Most of those things can

be worked out by using Ohm's Law which is pretty simple. But when you get to more advanced

problems/circuits like

we're discussing then that's where my lack of maths knowledge really gets me!

I have two amp textbooks by a guy called Merlin Blencowe. He has a Preamp one and a Power Amp one. In

those he also has quite a lot of maths in places. Some very easy involving Ohm's law and it's variants. But

others quite complex. So that has been another reason for me to try to learn more about all this. It becomes

very interesting to me after a while.

You'd understand everything that Merlin writes in the books regarding equations. But some of it i struggle

with. I learnt a lot of good stuff from chapter 2 in Neil Storey's book about phase angles and sine waves that

helped me deciphering stuff from Merlin's books 

Thanks very much Alan this has helped me a lot.

 Gary

Glad to have been of assistance.  

My own knowledge of electricity and electronics doesn't extend much beyond Ohm's law and Kirchoff's laws, but as long as there are some mathematical equations in there somewhere I'm happy!

Glad to note that you are making an effort to learn algebra.  A little effort goes a long way! 

Hi Alan,

Yeah i'm wanting to expand my knowledge enough that i can get around these calculations for circuits for working out voltages and currents. 

I also need to learn how to work with matrices. The problem like we discussed on here i think may be able to be solved by a matrix. Maybe your way is the best though for the type of equation we've talked about. The matrices seem like a lot more work. Maybe that's just because i don't know about them yet though.

I'm going to include a link to a video i've been watching on YT on nodal analysis. The guy get's two equations, re-arranges them and then instead of solving them by elimination or substitution he puts them through a matrix and gets the result.

Again i'm a total beginner again so don't have a clue whether that's the best way to approach these things or not. I'm just at the flailing around in the dark stage with anything complicated!

Have a look and see what you think. I know Neil Storey's book go's into matrices a bit further in than where i am at the moment. That's a bit complex for me at the moment though.

https://www.youtube.com/watch?v=fHcnMyFJjD4&list=LLHvr2s59Qp1Vs127pg7lLfA&index=2

Ok, I watched the video.  It was very clear for the most part (though a little puzzling that he said he wasn't going to use Kirchoff's laws and then proceeded to use Kirchoff's current law to set up his equations!  I guess he meant he wasn't going to use both laws together.).

However, if you don't understand how to use matrices, the last part, where he gets the voltages by producing results obtained with a calculator, must seem like black magic!  With just two simultaneous equations it's not too difficult to solve the matrix equations by hand (though a little tedious, which is why he just used a calculator).  It is worth taking the time to understand enough about matrices so that you don't think it's black magic, even if you do eventually use a calculator or computer software to do the number crunching.

As long as you only deal with two simultaneous equations, it doesn't much matter which approach you take.  However, the more simultaneous equations you have to solve, the better it is to adopt a matrix approach (though, inevitably, computer software using advanced numerical solution algorithms are required to do the number crunching for large matrices), so it's worth learning the principles of how to do this with just two. 

The following site might help with learning how to solve simultaneous equations using matrices: http://www.mathsisfun.com/algebra/systems-linear-equations-matrices.html 

Ha! You must have read my mind Alan! That's exactly what happened at the end bit where he talks about

getting the results through multiplying the different matrices.

I tried to muck around with it using the online calculator but not really knowing what i was doing i didn't get any

results!!  It said something about 'No inverse' in red warning letters and i was obviously doing it all wrong. Too

advanced for me at this point so i'll stick to just doing the equations.

Yeah the bit in the beginning about Kirchoff's law confused me as well because he was talking about the current

flowing into and out of the node which is what the law is about so i kinda scratched my head at that point.

Thanks for the link i'll be sure to study up on it.

Gary