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## Homework Statement

Use Kirchhoff's rules to determine the currents flowing through the two batteries in the following circuit:

[PLAIN]http://img217.imageshack.us/img217/2779/circt.jpg [Broken]

## Homework Equations

Kirchhoff's junction rule and loop rule.

## The Attempt at a Solution

The correct answers must be: I

_{12V}=2A, I

_{3V}=0.4A (right to left).

Here's how I labled the currents in the circuit:

[PLAIN]http://img84.imageshack.us/img84/6831/circtcurrents.jpg [Broken]

I think the current through the 12V battery is I

_{1}, and current through the 3V battery is I

_{4}. So here's four equations in four unknowns:

I

_{1}-1.379-I

_{3}=0

I

_{4}0.5-I

_{6}=0

3-4I

_{6}+4I

_{3}-12+3.723=0

11.274-4I

_{6}+4I

_{1}=0

I put the following equations in the calculator but got an error:

[itex]\left\{\begin{matrix}I_1-I_3=1.379 \\ I_4-I_6=0.5 \\ -I_6+I_3=1.32 \\ -I_6+I_1=-2.82\end{matrix}\right.[/itex]

So is there something wrong with my method or I just need to try solving the equations somehow?

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