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

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The discussion focuses on calculating current in a circuit using the voltage division law. The user applies the voltage division formula to find voltages at specific resistors and sets up equations based on Kirchhoff's laws for both the upper and lower loops of the circuit. They derive equations for the currents in each loop and clarify the direction of current flow, indicating that the left side of the equation should reflect the correct relationship between the currents. The user seeks confirmation on their approach and calculations. The conversation emphasizes the importance of accurately applying circuit laws to solve for unknown currents.
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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?
 
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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.
 
is the left side equal to:

40mV - 28i = 0
 
-EquinoX- said:
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
 

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