Node-Voltage Method to Solve Circuit Problem

[ChocHeartz]

http://img106.imageshack.us/my.php?image=hahaxp4.jpg




I'm required to use the node-voltage method to obtain the branch currents at all the resistors. I already tried using the node-voltage method at the three middle nodes but I still couldn't get the currents as obtained using OrCAD. I got V1=V2=V3=0.

Maybe I made a mistake during the calculation, coz I'm not quite sure how to approach the 3 ohmn in the middle since it's connected between the 2 sources..

 

[berkeman]

V1 and V2 are the voltage sources, so don't use those labels for node voltages. Call them Va, Vb, etc. or something.

Show us the equations that you wrote for the 5 non-ground nodes in this circuit, and show us how you combined them to derive the node voltages and branch currents. We'll look to see where your math error is.

 

[ChocHeartz]

Actually I tried a few ways of calculation but this is one of them..

Node 1 : V1/2+(V1-V2)/8+(V1-V3)/16=0

Node 2 : (V2-V1)/8+V2/3+(V2-V3)/24=0

Node 3 : (V3-V2)/24+V3/3+(V3-V1)/16=0

Then I calculated it using the calculator and got V1=V2=V3=0.

Another way I tried, calculating using only two nodes :

Node 1 : (V1-110)/2+V1/8+(V1-V2)/16=0

Node 2 : (V2+110)/2+V2/24+(V2-V1)/16=0

The answer I got doesn't seem right.
Hope u understand the working I've shown u..

 

[mjsd]

not really sure what your v1, v2 and v3 are... you don't seem to have done things with respect to the same reference (ground). remember once you have assigned a ground node/reference, all voltages are expressed with respect to it.. otherwise your equations won't be consistent.

 

[VinnyCee]

OK, I made a slightly more readable circuit diagram and embedded it into the post (you can use the picture icon in the toolbar when you make a post to do this).

http://img133.imageshack.us/img133/1636/pfposthelpxg3.jpg Now, the next step is to assign variables to each node that is not ground to represent the node voltages.

http://img443.imageshack.us/img443/6580/pfposthelp2xi1.jpg

Notice that Node V_2 is larger than the others because it connects 3 circuit elements to each other that are further away from each other than the other 3 element nodes in the circuit.Now, you want to make some current arrows in the diagram to use KCL. The arrow directions are arbitrary, but you should use passive sign convention. Passive sign convention means that the current arrows always go into the positive side of the circuit element. However, don't worry too much about passive sign convention now, as the resistors can have either terminal being positive or negative.

http://img509.imageshack.us/img509/3485/pfposthelp3lw7.jpg

Notice that you cannot represent the current for the voltage sources.


Now, you start solving the circuit by representing the currents in terms of the node voltages using Ohm's Law (V = i R, or in this case i\,=\,\frac{V}{R}). Then when you have represented all of the currents using node voltages, you can use Kirchoff's Current Law to solve for the node voltages.

I will represent the current i_1 in terms of the node voltages for you:

i_1\,=\,\frac{V_1\,-\,V_2}{2\Omega}

Do this for the rest of the currents and try solving using KCL. You should get a system of equations.

 

[berkeman]

Nice post, Vinny. Very helpful and tutorial.