Superposition Circuit analysis

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zorro_phu

Joined Jun 14, 2018
20
I'm doing this question for practise from Engineerin g circuit analysis 8th edition. In chapter 5, question number five. I solved in the picture below
Screenshot_20180616-151749_1.jpg
but when i crossed checked with the answer solution, in the second part its divided by19 not 24 so it comes as -1.315 A but i got -1.04 A. My question is why 19 because 14 ohm and 5 ohm are in series and there is another 5 ohm?
 

ArakelTheDragon

Joined Nov 18, 2016
1,353
You have 3 resistors and 2 current generators, first one is parallel, second is serial and third is parallel.

The current passing through the resistors is the sum of both sources.

First you calculate the resistance of the first parallel resisote (14 ohms) with the first series resistor (5ohms). Then the result from those two you calculate with the third one.

The formula for parallel resistors is 1/(1/R1 +1/R2)
 

WBahn

Joined Mar 31, 2012
27,391
Don't just assume that the answer in the book is right and you are wrong. The people doing the solutions manual can and do make mistakes, no matter how careful they are.

Check your work to see if it is correct. This is a practice you need to get in the habit of since, in the real world, you won't find a solutions manual.

You have other solution techniques available to you, such as nodal analysis and mesh analysis. What do they yield?

You can also check your answer from the answer itself -- which is something that is the case more often than not, even in the real world.

Your answer is, presumably, ix = -2.78 A.

That means that 220 mA is flowing downward the 14 Ω combination making the voltage at the top left node (relative to the bottom node) 3.08 V.

It also means that 2.22 A is flowing upward through the 5 Ω resistor making the voltage at the top right node (relative to the bottom node) -11.10 V.

The means that the voltage across the top resistor (right side relative to left side to be consistent with the assigned direction of ix) is -14.18 V, which in turns means that ix is -2.84 A.

That's close -- the difference between the two is about 2% of the average of the two -- but I would expect it to be closer. It's close enough that I would suspect that you did it correctly, but that you introduced excessive roundoff error or something similar at some point.

Given the differential nature of the voltage across the top resistor, it would only take an error of about 1% in the current to cause that. So I'd recommend going back and redoing your computations and keeping at least four sig figs for the intermediate results.

If you DO determine that you are correct, I would then recommend checking the answer in the solutions manual in order to prove that it is NOT correct.
 

WBahn

Joined Mar 31, 2012
27,391
Did you find your math error?

Hint: It's something that you don't need a calculator for. If you simplify one of your expressions, you will find that the exact answer is slightly different than the one you have.
 
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