Finding current in circuit using Kirchoff's Rules

[Zorba]

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) $$-7I_2+4I_3 = 5$$
(Loop2) $$-4I_2 - 2I_2 +2I_3 - 2I_4 = 8$$
(Loop3) $$-6I_2 + 7.5I_3 - 2I_4 = 8$$
(Loop4) $$-3I_2 - 4I_1 - 1.5I_3 = 5$$

I made a matrix out of these then and row reduce them but, I don't have enough equations because 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.

 

[tiny-tim]

I made a matrix out of these then and row reduce them but, I don't have enough equations because 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!

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

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

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

 

[Zorba]

Hi Zorba!

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

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

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

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.

 

[tiny-tim]

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!

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!