How to Calculate Current from a Circuit Using Voltage Division Law?

[-EquinoX-]

Homework Statement

http://img638.imageshack.us/img638/2416/64523221.jpg

Homework Equations

The Attempt at a Solution

My approach at this problem is using the voltage division law:

I first need to find the voltage at the 12 ohm, this can be done by the following using voltage division law.

Vb = (0.04 * 13)/ 41
Va = (0.04 * 28)/ 41

then we subtract the two, is this true?

 

[rl.bhat]

Let i branch out. i1 flows in upper loop and i2 flows in the lover loop.
Apply Kirchhoff law.
For upper loop
-12i -17i1 = 0...(1)
For lower loop
-12i - 24 i2 = 0...(2)
Similarly write down the equation for the left side loop which contains the voltage source and solve the equations to find i.

 

[-EquinoX-]

is the left side equal to:

40mV - 28i = 0

 

[rl.bhat]

is the left side equal to:

40mV - 28i = 0

No. i1 and i2 are in the opposite direction.
So it should be
40 mV = 16*i1 - 12*i2