- #1
roam
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Homework Statement
Use Kirchhoff's rules to find the currents I1, I2 and I3 shown in the circuit below:
[PLAIN]http://img811.imageshack.us/img811/3640/13608736.gif
The Attempt at a Solution
Kirchhoff's junction law gives: I1+I2-I3=0
I have calculated the voltage rise/drop in the left inner loop containing the 10-V battery:
10-10I1+20I2=0
Also in the right inner loop containing the 30-V battery:
30-20I2-20I3=0
So we have the 3 equations:
I1+I2-I3=0
-10I1+20I2=-10
-20I2-20I3=-30
We can pust this in a matrix to solve for the three currents:
[tex]\begin{pmatrix}1&1&-1&0\\-10&20&0&-10\\0&-20&-20&-30\end{pmatrix}[/tex]
which row reduces to
[tex]\begin{pmatrix}1&0&0&2.2\\0&1&0&-0.3\\0&0&1&1.8\end{pmatrix}[/tex]
So I1= 2.2, I2=-0.3 and I3=1.8, but this is wrong. The correct answer must be I1=4, I2=1.5, I3=5.5 Amps.
So, what's wrong with my calculations?
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