How do I solve the current of this resistor using Maxwell's Current Theorem?

I've been trying to solve this using the method the prof. taught us, and I happen to know the answer but I can't reach it no matter how many times I've tried. The circuit in question is below:

I am asked to use Maxwell's circulating current theorem to find out the current at the $20 \Omega$ resistor. My method was to write out all the loop equations:

$20 = 15I_1 + 10I_2$

$10 = 15I_1 + 25I_2 + 15I_3$

$10 = 15I_2 + 35I_3$

then solve by method of elimination. My answers are as follows:

$I_1 = 2.44A$

$I_2 = -1.66A$

$I_3 = -0.43A$

The answer for $I_3$ is $-0.57$.

Am I on the right path? If not, can someone point out where I am going wrong and why? Thanks

As I understand the circulating current theorem, you're really missing the simplicity of the method. You don't assign each resistor its own current. Call the current through the small, rectangular loop on the far left $I_\ell$ ($\ell$ for left). Let that current be positive when it runs clockwise. Let the current in the central loop be $I_c$, and for the right loop be $I_r$. The loop equation for left-hand loop is then
$$20 = 5I_\ell + 10(I_\ell - I_c)$$
• As far as I can tell the three loops are: $$1) 20=5I1 + 10(I1-I2)$$ $$2) 10 = 10(I1-I2) + 15(I2+I3)$$ $$3) 20I3 + 15(I2 + I3)$$ What I am really stuck on is finding out the value of the current at the 20ohm resistor. – Christy McGrory Dec 14 '12 at 7:36