Finding R2 current using Kirchoff's loop rule

[Sastronaut]

Homework Statement

Compute the current through R2 of the circuit in the figure.

Homework Equations

kirchoff's loop rule
V=IR

The Attempt at a Solution

Junction: I1+I2=I3

Alpha loop: V1-I3R3-I5R5=0
I1=(V1-I5R5)/R3=?

Beta loop: V2-I8R8-I5R5=0

*without one of the currents provided I am not exactly sure where to proceed from here...any help would be greatly appreciated! Anything that is a different color than black in the figure is what I added to the circuit diagram! Thank You PF!

 

[Pythagorean]

You have two of the currents (in terms of other variables) so you can find the third.

 

[Sastronaut]

I have been trying to figure out the algebra but I am always left with two variable (grouping of I1, I2, or I3). I am not sure how I can get it down to just one variable for current...

 

[Pythagorean]

start here:

I3 = I1 + I2

and you know what I1 and I2 are, yeah? So...

I3 = ?

 

[Sastronaut]

I3=(-5v+(5ΩI8))/-8Ω

?

 

[Pythagorean]

I'm not sure what you did there... I1 and I2 will be in terms of I3 and your knowns.

Actually, I'm not quite sure what you did for your alpha/beta loops either. There is no I5 or R5 or I8/R8. Don't try to plug in your values yet, just use the names of the constants.

 

[Sastronaut]

I think I figured it out I have a value of 1.076A through R2. really appreciate the help :)