Help with this simple nodal analysis issue, please

[PainterGuy]

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

 

[gneill]

You may find it simpler to convert both current sources (and their parallel resistances) to voltage sources (i.e., convert Norton to Thevenin). Then you'll have a single loop with only resistances and voltage sources. Easy peasy.

By the way, using this method I see that the voltage across R3 is indeed 9.71V as your book indicates.

 

[PainterGuy]

gneill: Many thanks for the reply. Sorry I wasn't able to says thanks in timely manner. As a matter of fact, I have been busy with some stuff lately. I appreciate your help.

Cheers

 

[gneill]

gneill: Many thanks for the reply. Sorry I wasn't able to says thanks in timely manner. As a matter of fact, I have been busy with some stuff lately. I appreciate your help.

Cheers

No worries. Glad to help.

 

[rwisz]

Hi there,

Thank you for reaching out for help with your nodal analysis issue. Nodal analysis is a fundamental technique in circuit analysis and it can be challenging at times, so it's great that you are seeking clarification.

Looking at the circuit diagram and the solution provided, it seems that the book is using Kirchhoff's Voltage Law (KVL) to find the voltage across R3. KVL states that the sum of the voltage drops in a closed loop must equal the sum of the voltage rises in that same loop.

In this case, the closed loop includes V1, R3, and V2. The book is using KVL to set up the equation V1 + V_R3 - V2 = 0. This is because V1 is a voltage rise (positive) and V2 is a voltage drop (negative), so the total voltage in the loop must equal 0. Then, they rearrange the equation to solve for V_R3, which is the voltage across R3.

To find the magnitude and polarity of the voltage across R3, you can use Ohm's Law: V = IR. In this case, the current through R3 is I4 (which you correctly calculated as -3.7A). So, the voltage across R3 is V_R3 = (-3.7A)(4Ω) = -14.8V. The book's solution of 9.71V may be a typo or a different calculation, but based on the values given in the problem, -14.8V seems to be the correct answer.

I hope this helps clarify the steps and calculations involved in finding the voltage across R3. Keep up the good work with your circuit analysis! Let me know if you have any other questions or need further clarification.

Best,