Find voltage across resistor using mesh current analysis

[vizakenjack]

I'd like to find V_th by mesh current analysis.

Mesh A and B share a current source, so they're treated as one supermesh.

What's the equation for this supermesh? Also, do I ignore the loop with the open circuit? Since there's no current flowing there...

2A = i_b - i_a

Anyway, is this the right equation:

+12V + i_a(6Ω) + i_b(6Ω + 4Ω) = 0?

if yes, then my i_a ends up being -32V/(4Ω) = - 8A

i_b = 2A + 8A = 10A

And the Voltage across 4Ω (V_th) = i_b * 4Ω = 40 V!

But that's not correct, V_th should be 6V!

 

[NascentOxygen]

+12V + ia(6Ω) + ib(6Ω + 4Ω) = 0?

With currents marked clockwise, the voltages across all resistors here sum clockwise as voltage falls, and you could pencil in a small + and - sign on each resistor as a reminder.

So summing in a clockwise path the voltage rises around the loop:
+12 - i_a(6) - i_b(6+4) = 0