Nodal and Mesh mismatch...where am I going wrong

[DFrentzen]

Given the circuit diagram above, I am interested in finding the current ia. Using mesh analysis, I determined it to be 1.71mA, but nodal analysis results in a value of 2.25mA. Solution attempts provided below. I think the issue is in my nodal analysis approach.

Mesh Analysis..I1 is the left mesh, I2 the right mesh.

Nodal analysis attempt...current calculation at the bottom.

 

[gneill]

For the node equation, check your substitution for v1: Note that the 6 V source is connected through a resistor to the reference potential.

 

[DFrentzen]

I tried to take that into account on one of my attempts, the voltage v1 as 3-v provides the correct value for current. I was unsure if I'm on solid ground to do that.

 

[gneill]

You're on the right track. But how to justify your substitution?

Consider that you have a term in your node equation for the current that passes through the "v1" resistor. How would you express v1 in terms of that current?

 

[DFrentzen]

You're on the right track. But how to justify your substitution?

Consider that you have a term in your node equation for the current that passes through the "v1" resistor. How would you express v1 in terms of that current?

I see v1 given as

Which allows me to plug in and

 

[gneill]

Looks good.

 

[DFrentzen]

Thank you.