How do you find the current going through a weird circuit?

[giantf]

Homework Statement

Homework Equations

at point C:
i₂ - i₃ - i₄
i₂ = i₃ + i₄[/B]

The Attempt at a Solution

I labeled all the currents going through each resistor in the picture[/B]

for loop ABC:
2000i₁ = 3000i₂ + 4000i₃

for loop BDC:
3000i₅ = 2000i₄ + 4000i₃

at point C:
i₂ - i₃ - i₄
i₂ = i₃ + i₄

at point B:
i₁ + i₃ - i₅
i₅ = i₁ + i₃

This is all I've been able to do so far for this problem. How would I solve for i2 and i5 which go through resistor 2? If I add the two loops (loop ABC and loop BDC) I would get a lot of variables and I'm wondering if I'm even doing this correctly

 

[phinds]

Google "delta-wye transform"

 

[giantf]

Google "delta-wye transform"

Would that help? We haven't learned anything about that, and it's nowhere in the textbook, not sure if I'm allowed to use things from outside the curriculum

 

[magoo]

Try ABCD for another loop.

Also check your signs for BCD. The currents are not in the same direction so one is negative.

 

[phinds]

Would that help? We haven't learned anything about that, and it's nowhere in the textbook, not sure if I'm allowed to use things from outside the curriculum

Yes, but if you study the DERIVATION of the delta-wye transform, it will show you how to attack your circuit.