Calculating i_1, i_2, v_A, and v_H in a Ladder Network | Kirchhoff's Laws

[vaio911]

Homework Statement

Find i_1,i_2,v_A,\text{ and }v_H in the ladder network. Calculate the power dissipated in the 2\;\Omega resistor.

http://i.snag.gy/PIhxl.jpg

Homework Equations

Kirchhoff's Laws (i.e. current law, voltage law).

The Attempt at a Solution

Ok, I know that I can simplify the circuit down to one loop then use Ohm's law to calculate i_1, but then I have to do other things to get the other stuff.

I tried to make a system to solve this problem using the laws.
Can somebody tell me where I'm doing wrong here?

<br /> \begin{align}<br /> i_b&amp;=i_c+i_a\\<br /> i_c&amp;=i_e+i_d\\<br /> i_e&amp;=i_g+i_f\\<br /> 12i_a-28+8i_b&amp;=0\\<br /> 12i_a+6i_c+15i_d&amp;=0\\<br /> 4i_e+10i_f+15i_d&amp;=0\\<br /> 2i_g+13i_h+10i_f&amp;=0\\<br /> 4i_e+2i_g+13i_h+15i_d&amp;=0<br /> \end{align}

Getting me something like:
-\frac{7}{39},\frac{49}{13},\frac{154}{39},\dots

which I know is completely off.

 

[vaio911]

If you can't understand my handwriting,

V_a is the one w/ the 12 ohms.

V_h is the 13 ohms one.

 

[vaio911]

It is because of the direction of the currents?

 

[CWatters]

I'd probably just simplify it. If you keep your working for each step it will help when it comes to working out the voltages using the potential divider rule.