# Kirchhoff's Laws help

• 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?

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

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

which I know is completely off.

If you can't understand my handwriting,

$V_a$ is the one w/ the 12 ohms.

$V_h$ is the 13 ohms one.

It is because of the direction of the currents?

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.