- #1
Emspak
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Homework Statement
I want to use Kirchoff's current law to analyze the pictured curcuit and find the current drawn fro the voltage source between the positive terminal and node 1.
[PLAIN]http://s42.photobucket.com/user/Jemspak/media/circuitdiagram.jpg.html"
(i can't figure out how to get the image insert to work)
Homework Equations
I a using V=IR and I know that the current into any node has to be equal to the current out, so the algebraic sum is zero. I also know that at the other end of the circuit the current that re-enters the power source has to be the same as that which left it.
For our purposes [itex]V_0[/itex] is 24 V. Al the resistors are 10Ω.
The Attempt at a Solution
So here are the equations I am using. I am trying to find out if I set up the problem correctly, because I feel like I am getting an extra unknown.
At node 1:
[itex]I_{source}-\frac{V_0-V_2}{R_2}-\frac{V_0-V_1}{R_1}=0[/itex]
node 2:
[itex]\frac{V_0-V_2}{R_2}-\frac{V_2-V_4}{R_4}-\frac{V_2-V_3}{R_3}=0[/itex]
node 3:
[itex]\frac{V_0-V_1}{R_1}-\frac{V_1-V_3}{R_3}-\frac{V_3-V_6}{R_6}=0[/itex]
node 4:
[itex]\frac{V_2-V_4}{R_4}-\frac{V_4-V_5}{R_5}=0[/itex]
node 5:
[itex]\frac{V_1-V_6}{R_6}-\frac{V_4-V_5}{R_5}+I_{source}=0[/itex]
And assuming I set this up correctly I should get the following system of equations:
[itex]10I_{source}-V_1-V_2=48[/itex]
[itex]-3V_2-V_4-V_3=-24[/itex]
[itex]-3V_1-V_3-V_6=-24[/itex]
[itex]-V_2-V_5=0[/itex]
[itex]-V_1+V_4-V_5-V_6+10I_{source}=0[/itex]
I know that [itex]V_1+V_2+48 = 10I_{source}[/itex] so the last equation becomes
[itex]V_4-V_5-V_6+V_2=-48[/itex]
ANd the system now looks like this
[itex]10I_{source}-V_1-V_2=48[/itex]
[itex]-3V_2-V_4-V_3=-24[/itex]
[itex]-3V_1-V_3-V_6=-24[/itex]
[itex]-V_2-V_5-=0[/itex]
[itex]V_4-V_5-V_6+V_2=-48[/itex]
I notice that V5=-V2 and I can sub that into the last equation as well getting me V4-V6+2V2=-48.
Well and good, but i suspect I set this up wrong and that is why my system of equations is looking awfully complicated. So any help in seeing where I err is much appreciated.
this might end up double posting because I was trying to get the image to show.
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