How Do You Set Up Equations to Find Currents in a Circuit?

[theuniverse]

Homework Statement

Find currents I1-I6. I'm really looking only for the equations though...

Homework Equations

V=IR

The Attempt at a Solution

I tried to set up equations for the nodes and loops:
Node a:$$I_2-I_6-I_3=0$$
Node b: $$I_3+I_5-I_1=0$$
Node d: $$I_1-I_4-I_2=0$$

Loop 1: $$-V_1+I_1R_1+V_2+I_5R_2$$
Loop 2: $$-V_2+I_2R_5+I_6R_4$$
Loop 3: $$I_3R_6-I_5R_2-I_6R_4$$

I'm pretty sure that the above equations are not correct since I was not sure how to incorporate R3 and I am also a little bit confused about how to relate I1 and I2 and I4.

Thanks for the help!

 

[gneill]

Your node current equations look fine, except that you seem to have interchanged nodes a and d.

For your loops, they need to be in the form of equations (there should be an "=" in there somewhere). For loop 1, treat R3 as you did the other resistors; there's a voltage drop across R3 due to the loop current i1 flowing through it.

 

[theuniverse]

Yeah I meant to equal all the loops to 0. How about this:
Loop 1: $$-V_1+I_1(R_3+R_1)+V_2+I_5R_2=0$$
And you are right about the nodes a and d.. They are switched in my diagram on paper.. thanks!

 

[gneill]

Yeah I meant to equal all the loops to 0. How about this:
Loop 1: $$-V_1+I_1(R_3+R_1)+V_2+I_5R_2=0$$

Yup. That looks okay.

And you are right about the nodes a and d.. They are switched in my diagram on paper.. thanks!

You're welcome