Finding current using Kirchhoff's circuit rules

[slaufer]

Homework Statement

Homework Equations

Kirchhoff's loop rule and (maybe) Kirchhoff's current law

The Attempt at a Solution

So I attempted to apply Kirchhoff's loop rule to the circuit, and ended up with a system of linear equations:

24 - 6I$_{1}$ - 3I$_{3}$ = 0 $\rightarrow$ 2I$_{1}$ - I$_{3}$ = 8
36 - 6I$_{1}$ - 6I$_{2}$ = 0 $\rightarrow$ I$_{1}$ + I$_{2}$ = 6
12 - 3I$_{3}$ - 6I$_{2}$ = 0 $\rightarrow$ 2I$_{2}$ + I$_{3}$ = 4

but every time I try to solve it, I end up with everything dropping out. I'm not sure what I'm missing here, but I've been banging my head against this one for about 4 hours now, so any help would be appreciated!

 

[ehild]

Homework Statement

Homework Equations

Kirchhoff's loop rule and (maybe) Kirchhoff's current law

The Attempt at a Solution

So I attempted to apply Kirchhoff's loop rule to the circuit, and ended up with a system of linear equations:

24 - 6I$_{1}$ - 3I$_{3}$ = 0 $\rightarrow$ 2I$_{1}$ - I$_{3}$ = 8 wrong
36 - 6I$_{1}$ - 6I$_{2}$ = 0 $\rightarrow$ I$_{1}$ + I$_{2}$ = 6
12 - 3I$_{3}$ - 6I$_{2}$ = 0 wrong$\rightarrow$ 2I$_{2}$ + I$_{3}$ = 4

but every time I try to solve it, I end up with everything dropping out. I'm not sure what I'm missing here, but I've been banging my head against this one for about 4 hours now, so any help would be appreciated!

Check the signs.
You also have a relation between the currents. (Nodal Law) Use that and two loop equations.

ehild

 

[slaufer]

Thanks, that makes more sense now.

I might have eventually realized that my system was cancelling out because it was using mutually derived equations, but I probably never would have realized that I was treating I$_{3}$ as if it were flowing in two directions at once.

Using two of the equations from the original system in the nodal rule equation I$_{1}$ = I$_{2}$+ I$_{3}$ made it all fall together though. I'm still not sure how I'd figure out what direction I$_{3}$ was flowing in if it weren't given in the problem, but at least I'm FINALLY done with this problem.

tl;dr you are the best, thanks

 

[ehild]

You need not find out the direction of the currents in advance. If you have not chosen the proper direction you would get negative value for the current.

ehild

 

[Nickie]

It seems like you have correctly applied Kirchhoff's loop rule to the circuit and obtained a system of linear equations. However, it is possible that there is a mistake in your calculations or in setting up the equations. I would recommend double checking your work and making sure all the signs and values are correct. It is also helpful to label the nodes and branches in the circuit to keep track of the variables. Additionally, you can try using Kirchhoff's current law to set up another set of equations and solve the system using simultaneous equations. If you are still having trouble, you can consult with a classmate or your instructor for further assistance. Remember to always double check your work and equations when solving circuit problems. Good luck!