# E-book CorrectionPossible error in Vol. 1, Ch. 10, Mesh Circuit Method and Analysis

#### mdesena77

Joined Jun 12, 2019
7
Hello,

I believe there is an error in the eBook pertaining to the labeling of the direction of current. I am referencing the unbalanced Wheatstone Bridge example. In the circuit diagram the direction of mesh current I3 appears to disagree with the labeled resistor voltage drop polarities. The resistor polarities are oriented opposite of the voltage source but the arrows showing the direction of current infer the resistors are backwards. If the arrows in I3 were reversed it would appear to be correct. This error also affects the latter diagram showing the final direction of currents across each resistor.

Let me know if I am see this right or if it's a misunderstanding on my end.

Diagrams I am referencing are attached.

Thanks.

#### Attachments

• 23.9 KB Views: 7
• 67.3 KB Views: 7

#### mdesena77

Joined Jun 12, 2019
7
The direction of current I1 doesn't appear to have been switched after obtaining a negative value for its current.

#### MrChips

Joined Oct 2, 2009
27,116
In KVL and KCL analysis, the original choice of the current direction does not matter. If the calculated result turns out to be negative then the current flows in the opposite direction.

AAC eTutorials use the electron flow model.

Since the charge of the electron by convention is accepted as being a negative charge, this is consistent with conventional current flow where current flows from a higher to lower potential.

#### mdesena77

Joined Jun 12, 2019
7
Then why isn't I1 flipped?

#### mdesena77

Joined Jun 12, 2019
7
The textbook states that it uses conventional flow.

#### Attachments

• 451 KB Views: 4

#### MrChips

Joined Oct 2, 2009
27,116
I do not understand the question.

You can choose the initial direction of the current.
You maintain the same direction in the illustration even if you discover that the result is negative.

#### MrChips

Joined Oct 2, 2009
27,116
As I said, it does not matter which current model you choose.
The KVL and KCL is still valid as long as you be consistent in your model.

#### mdesena77

Joined Jun 12, 2019
7
Sorry for being unclear. I do understand that the direction of current is arbitrary. I guess my first question would be, assuming conventional flow, why aren't the resistor polarities on the I3 side oriented against the current? They are for I1 and I2.

#### Attachments

• 46.5 KB Views: 3

#### mdesena77

Joined Jun 12, 2019
7

My question is why isn't this the case in the diagram below?

#### mdesena77

Joined Jun 12, 2019
7
Either I'm really not understanding this or it seems that the text is contradicting the diagram its referring to.

"since both I1 and I3 go from bottom to top through that resistor, and thus work together to generate its voltage drop."

It looks to me like I3 goes from bottom to top and I1 goes from top to bottom.

Please let me know if I am incorrect.

#### WBahn

Joined Mar 31, 2012
27,392
Hello,

I believe there is an error in the eBook pertaining to the labeling of the direction of current. I am referencing the unbalanced Wheatstone Bridge example. In the circuit diagram the direction of mesh current I3 appears to disagree with the labeled resistor voltage drop polarities. The resistor polarities are oriented opposite of the voltage source but the arrows showing the direction of current infer the resistors are backwards. If the arrows in I3 were reversed it would appear to be correct. This error also affects the latter diagram showing the final direction of currents across each resistor.

Let me know if I am see this right or if it's a misunderstanding on my end.

Diagrams I am referencing are attached.

Thanks.
There appear to be a couple of inconsistencies. The first one:

has the problem you pointed out, namely that the polarities of the I3 side of the voltages on R1 and R4 are reversed. This could be a simple case of the author intending for I3 to go the other way.

Once thing that the author does that is against generally accepted best practices is to have some loop currents (I1 and I3) go counterclock wise while the rest go clockwise. This is a recipe for disaster -- and may well have played a role in this mistake. But from a bigger picture perspective, using consistent loop current directions results in the voltage relationships being standardized and so if (or rather when) you do make a mistake, it is much more likely to make you feel like something is out-of-kilter and let you catch it more easily.

The second diagram:

The diagram as far as the polarities and such is just fine -- though it violates that best practices mentioned earlier.

I have no idea what the I1 > I2 > I3 is referring to. Using the values from the work below it, they are claiming that I1 = 93.8 mA, I2 = 77.2 mA, and I3 = 136.1 mA. So if they really mean that I1 is greater than I2 is greater than I3, their results clearly don't agree with that claim.

Note from their answers (assuming they are correct) that they are clearly using electron flow since they claim that all of the branch currents (Ir3 doesn't matter for this point) are going from lower potential to higher potential.

Looking at the equations below the diagram we see that any equation involving I2 has the sign of I2 reversed relative to the definition in the diagram. The most obvious conclusion is that they intended to define I2 going counter clockwise (which would make it consistent with the other two).

My guess is that they worked the problem okay (at least the branch currents seem self-consistent) but, in preparing the diagrams for publication, messed them up.

#### WBahn

Joined Mar 31, 2012
27,392
The textbook states that it uses conventional flow.
The page that you pulled that from is self-contradictory. Earlier on the page it states, "You will find conventional flow notation followed by most electrical engineers, and illustrated in most engineering textbooks. Electron flow is most often seen in introductory textbooks (this one included) and in the writings of professional scientists, especially solid-state physicists who are concerned with the actual motion of electrons in substances."

Keep in mind that the E-book was not written by a single person and that it has been edited many times. The original author intended the use of electron flow throughout. Like nearly everyone that uses electron flow, they used it incorrectly.