Super Node Analysis: Find V1,V2,V3,I1,I2,I3

[jdawg]

Homework Statement

Find V1,V2,V3,I1,I2,I3

Homework Equations

The Attempt at a Solution

Analysis at super node:
V3-V1=40 (equation 1)

(V1/40)+(V1-V2/40)+(V3-V2/20)=0
2V1 - 3V2 +2V3 = 0
After substituting in equation 1:
4V1-3V2 = -80

Analysis at V2

(V1-V1/40)+(V2/20)+(V2-V3/20)=0
After substituting in equation 1:
-3V1+5V2 = 80

But I think I'm doing something wrong, I don't feel like the voltages should be zero...

 

[gneill]

For your supernode equation, you left out the term for the 20 Ω resistor between V3 and the reference node.

 

[jdawg]

Oh ok, I fixed that part and now I have these equations:

6V1-3V2=-160 and -3V1+5V2=80

When I solve for V2, I get zero. And for V1 I get -26.7. Is it ok for one of the voltages to be zero?

 

[gneill]

Oh ok, I fixed that part and now I have these equations:

6V1-3V2=-160 and -3V1+5V2=80

When I solve for V2, I get zero. And for V1 I get -26.7. Is it ok for one of the voltages to be zero?

I question the sign of your V1. Since it's directly connected to the + terminal of the only voltage source I would expect it to have a positive potential. Check your math.

Zero is a perfectly good value for a potential for V2. In fact, it looks correct to me

 

[jdawg]

Thanks so much! :)