Kirchhoff's Rules Physic Question Please help?

Question

given E1=4.0v E2=2.0V R1=1ohms R2= 2ohms R3=3ohms. determine the current in each branch.

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E1 R2 E2
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thanks

Answer 1

Since I had trouble with your diagram and you have two R2's, I have a drawing of what is the same structure
http://i142.photobucket.com/albums/r88/odu83/Circuit.jpg

Applying the current law at the bottom node
I1+I2+I3=0

Summing voltages at the left loop
R1*I1-R2*I2=E1

and the right loop
-R2*I2+I3*R3=E2

Multiply the first equation by -R3
The second equation by R3/R1
Gives the following three equations

-R3*I1-R3*I2-R3*I3=0
R3*I1-R3*R2*I2/R1=R3*E1/R1
-R2*I2+I3*R3=E2

add the three equations together
-I2*(R3+R3*R2/R1+R2)=
R3*E1/R1+E2

This can be solved for I2 and then the third equation for I3 and the second for I1 and check with the first.

j