How to Use Nodal Analysis to Find Voltages in a Circuit?

[grekin]

Homework Statement

Use the node-voltage method to find v1 in the circuit(Figure 1) if i1 = 6.2A and i2 = 1.5A .
Use the node-voltage method to find v2 in the circuit.

Homework Equations

G = 1/R

The Attempt at a Solution

Top side going from left to right, I assigned each node as 1, 3, then 2 (because of the way v_2 is assigned).

For Node 1, I had:
(v_1)/40 - (v_3)/8 = 6.2

Node 3:
-(v_1)/8 + (v_3)/80 = 0

Node 2:
(v_2)/120 = -1.5

Solving, I got v_1 = -5.06 V and v_2 = -180 V. These are wrong (obviously). Any assistance would be appreciated.

Moving image to bottom for visibility:

 

[BvU]

Hello G and welcome to PF. Clear story. Do you have a reason to assign node 3, or could you make do with just nodes 1 and 2 ?
Reason I ask is because V2 = V3 seems a reasonable assumption to me. (I will look up the thread where I made a complete fool of myself by completely missing such a thing -- fortunately others put me right...)

Found it -- don't laugh!

 

[grekin]

Hello G and welcome to PF. Clear story. Do you have a reason to assign node 3, or could you make do with just nodes 1 and 2 ?
Reason I ask is because V2 = V3 seems a reasonable assumption to me. (I will look up the thread where I made a complete fool of myself by completely missing such a thing -- fortunately others put me right...)

Found it -- don't laugh!

In that case where would I include the 80 Ohm resistor? Should it only be connected to v_2 on the equation?

If so,
Node 1:
6.2 = (v_1)/40 - (v_2)/8
-1.5 = (v_2)(1/80 + 1/120) - (v_1)/8

Solving, v_1 = 3.86 V and v_2 = -48.8 V. Which is still incorrect.

I'm out of attempts for solving for v_1, which I now know is 115 V.

 

[BvU]

Ah, I interpret the node a equation a little different: after all, the 8 ohm is also connected to node a !

 

[grekin]

Ah, I interpret the node a equation a little different: after all, the 8 ohm is also connected to node a !

Ah, I see now. I didn't realize I had to include the resistors between each node as also connected to it individually.

1:
6.2 = v_1 * (1/40+1/8) - v_2 / 8

2:
-1.5 = v_2 * (1/80 + 1/120 + 1/8) - v_1 / 8

Ended with v_1 = 114.7 and v_2 = 88 (which is correct). Thanks.

 

[BvU]

Always nice to have the answer at hand... I was still plodding
And: you're welcome!