# help with this simple nodal analysis issue, please

Discussion in 'Homework Help' started by PG1995, May 11, 2011.

1. ### PG1995 Thread Starter Well-Known Member

Apr 15, 2011
805
5
Hi,

1: http://img19.imageshack.us/img19/2256/nodaldiagram1.jpg (diagram of circuit and few other details)
2: http://img36.imageshack.us/img36/5405/nodaldiagram2.jpg (solution)

The book asks "Find the magnitude and polarity of the voltage across each resistor".

I was trying to find the magnitude and polarity across R3 in the circuit diagram (please have a look on the link #1).

The values for V1 and V2 are correct. V1 is -14.9v, and V2 is -12.7v. The magnitude for voltage across R3 I found was 14.8v, but the book says it's 9.71v.

I4 is -3.7A (the assumed direction by me was from left to right of screen as is shown in the scan).

The book also says: V_R3 = V1 + 12 -V2. I don't get this step. Is the book applying KVL here, then how. Please help me with this. Many thanks for the help.

Cheers

2. ### t_n_k AAC Fanatic!

Mar 6, 2009
5,448
784
If your circuit is correctly reproduced from the original then the correct values are

V1=-13.1V
V2=-7.33V

VR3=6.22 [positive on the left]

Did you correctly transcribe the circuit from the original question?

3. ### t_n_k AAC Fanatic!

Mar 6, 2009
5,448
784
Hi PG1995,

Just a comment on the matter of methodology in approaching a solution. I guess you are probably constrained by your teachers to adopt a particular way of solving a problem.

Notwithstanding such constraints, I try to look (time permitting) for a simple means of verifying answers without any constraints and then do the problem as required.

In this case you took the perfectly valid option of converting the 12V voltage source & resistor R3 to a Norton equivalent. In one sense this further increases the complexity of the problem.

My alternative approach was to convert element group [I1, R1||R4] to a Thevenin equivalent and group [I2,R2] to a Thevenin equivalent. You then end up with a very simple series circuit with 3 voltage sources and 3 resistors. V1, V2 and VR3 are readily found from that formulation. You don't even need to apply matrix algebra.

A bit of lateral thinking [other than "let me outta here!"] before launching into a solution might be productive in the long run.

4. ### PG1995 Thread Starter Well-Known Member

Apr 15, 2011
805
5
Thanks a lot for the reply, t_n_k.

Well, if the instructor says the sky is yellow, then it is. I and other students have to agree unless they want to fail the course. If the instructor says that your question is nonsense and doesn't merit a response, then you have to agree. Do you see the problem? The funny thing is he is a PhD. I don't think education does good to everyone!

I see you used the terms Norton and Thevenin. These are theorems, right. We haven't covered these theorems yet. By the way, I like one thing very much about this forums. The members here are really helpful without being arrogant and condescending. I know some forums where they think they are the gods!

Thanks a lot for helping me in such a good way.

Best regards
PG

5. ### t_n_k AAC Fanatic!

Mar 6, 2009
5,448
784
A former colleague who was studying to complete his PhD used to cheekily quip that PhD was an abbreviation for "Post hole Digger".

6. ### t_n_k AAC Fanatic!

Mar 6, 2009
5,448
784
Curious that you are applying Norton's Theorem without actually having studied it.

Well - good luck with your studies!

7. ### jegues Well-Known Member

Sep 13, 2010
735
44
Have you covered source transformations yet?

If so, these are similiar to both Thevenin's and Norton's theorem.

A source transformation allows us to replace a voltage source and series resistor by a current source and parallel resistor and vice versa. Doing so does not change the element current or voltage of any element of the circuit.

Thevenin's theorem allows us to replace part of a circuit by a voltage source and series resistor. Doing so does not change the element current or voltage of any element of the circuit.

Norton's theorem allows us to replace part of a circuit by a current source and parallel resistor. Doing so does not change the element current or voltage of any element of the circuit.

So a source transformation can be interpreted as the application of Thevenin's/Norton's theorem to only a specific part of a circuit. (i.e. a voltage source and series resistor or current source and parallel resistor)

Hopefully if you've covered source transformations this will give you some insight into what Thevenin's/Norton's theorem is about.

Last edited: May 12, 2011
8. ### PG1995 Thread Starter Well-Known Member

Apr 15, 2011
805
5
Hi t_n_k

Well, perhaps your colleague was a kind of humble person. Three of my instructors are PhDs (one doesn't torment us anymore because he is on leave). Well, as far as my experience goes most of PhDs suck because some of them start acting arrogant and play down students' questions (especially when the students are undergrads and little stupid like me!). Perhaps they stop trying to improve themselves and become a stagnant source of knowledge. One of my teacher who was just a graduate was one of the best teachers and many people agree on this because he was always there to help you in every possible way. There were occasions when he would simply down play his own teaching techniques or explanations.

jegues: Thanks a lot for the explanation. Yes, I have studies the source transformation. I'm happy Thevenin and Norton theorems are only fearful in names not in their application.

Best wishes
PG