Finding current in circuit using Kirchoff's Rules

  • Thread starter Zorba
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Homework Statement


[URL]http://img25.imageshack.us/i/circuitj.jpg[/URL]
(Image won't show up, here's the link http://img25.imageshack.us/i/circuitj.jpg/)

Homework Equations


Kirchoff's Junction & Potential rules.

The Attempt at a Solution


[URL]http://img29.imageshack.us/i/circuit2.jpg[/URL]
(Image won't show up, here's the link http://img29.imageshack.us/i/circuit2.jpg/)
Equations I get are:
(Loop1) [tex]-7I_2+4I_3 = 5[/tex]
(Loop2) [tex]-4I_2 - 2I_2 +2I_3 - 2I_4 = 8[/tex]
(Loop3) [tex]-6I_2 + 7.5I_3 - 2I_4 = 8[/tex]
(Loop4) [tex]-3I_2 - 4I_1 - 1.5I_3 = 5[/tex]

I made a matrix out of these then and row reduce them but, I don't have enough equations becuase I get a row of zeroes... which doesn't make sense to me, 4 equations, 4 unknowns and I don't see why applying Kirchoffs rules would make me end up with something like that... so I need to get another equation, but I was wondering if I've done wrong with the equations.
 
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Answers and Replies

  • #2
tiny-tim
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I made a matrix out of these then and row reduce them but, I don't have enough equations becuase I get a row of zeroes... which doesn't make sense to me, 4 equations, 4 unknowns and I don't see why applying Kirchoffs rules would make me end up with something like that... so I need to get another equation, but I was wondering if I've done wrong with the equations.
Hi Zorba! :smile:

There are 4 loops in your circuit, but only 3 of them are independent

so inevitably Kirchhoff (note the extra "h" :wink:) for one will be a linear sum of the others, which eventually reduces the matrix to zero! :biggrin:

Hint: yes you do need an extra equation, and you can get it from one of the junctions. :wink:
 
  • #3
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Hi Zorba! :smile:

There are 4 loops in your circuit, but only 3 of them are independent

so inevitably Kirchhoff (note the extra "h" :wink:) for one will be a linear sum of the others, which eventually reduces the matrix to zero! :biggrin:

Hint: yes you do need an extra equation, and you can get it from one of the junctions. :wink:
Thanks, makes sense.

One last question, the current on either side of the batteries, can I equate them? Or can I only do this when there is only one battery in the circuit.
 
  • #4
tiny-tim
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One last question, the current on either side of the batteries, can I equate them? Or can I only do this when there is only one battery in the circuit.
Hi Zorba! :smile:

Yes, you can do this across any component …

basically it's because of conservation of charge … like water, the amount flowing in must equal the amount flowing out …

in terms of Kirchhoff's Rules you can look at a battery as a junction, with only two lines … the total current in those two lines must be the same! :biggrin:
 

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