Circuit analysis - very nearly finished

[pat666]

Homework Statement

Find the value of N(1,2,3) in attached circuit

Homework Equations

The Attempt at a Solution

I've found i(1,2,3,4) from mesh analysis as:
$$i_1=1.44159mA,i_2=0.919142mA,i_3=0.396691mA,i_4=-0.08609047mA$$

now I am having trouble finding N_2 and N_3 from this.

Thanks for any help.

 

[Maru]

Don't let the schematic confuse you. It might help to redraw the circuit as below. Redrawing in this manner does not affect the nodes, since the voltage is the same across a wire. I assume that the four mesh currents you found are from redrawing as I did below. The voltage at Node 2 is the voltage across R5, which is, based on my diagram, (I3-I4)R5. The voltage at Node 3 is a simple voltage divider, and if we draw a path from ground to that node, we get: 5V + I4*R7 = Voltage at Node 3.

 

[pat666]

I did see that, what I have for N_2 is N_2=N_1-(1000i_3) but it doesn't work. I know my currents are right because I have checked in multisim. N_2 should equal 4.81V but I can't get this.

Thanks

 

[Maru]

Sorry, I edited my post. Reread what I had done. If you do what I said for Node 2 you will get the right answer:

Voltage at Node 2 = (I3-I4)R5 = (0.396691mA--0.08609047mA)*10000 = 4.83V

A bit off, perhaps a rounding error, but I believe this is correct. Just remember, when you are trying to find those node voltages, you must subtract the mesh currents as I did, i.e. I3-I4, since the current going down that branch is indeed I3-I4 based on the way I redrew the schematic. The same process follows for Node 3.

 

[pat666]

Thanks for your help Maru

 

[pat666]

I just did N_2 and it doesn't work, it gives me 48.27V?

 

[pat666]

sorry yes it does