Circuit with Two Batteries and Six Resistors

[Gee Wiz]

Homework Statement

A circuit is constructed with six resistors and two batteries as shown. The battery voltages are V1 = 18.0 V and V2 = 12.0 V. The positive terminals are indicated with a + sign, The values for the resistors are: R1 = R5 = 64.0 Ω, R2 = R6 = 157.0 Ω R3 = 53.0 Ω, and R4 = 65.0 Ω. The positive directions for the currents I1, I2 and I3 are indicated by the directions of the arrows.

https://www.smartphysics.com/Content/Media/Images/EM/10/h10_twoloop.png

Homework Equations

KCL and KVL

The Attempt at a Solution

So i tried to make equations, but I'm not getting it to work out.
I1+I3=I2
64I1=53I3+18

 

[CWatters]

It doesn't look like you have tried to simplify the circuit first?

You could replace R2+R6 with an R7.

18+53I3+157I2=12+R6I6

Personally I think it's better to write the equation so the voltages sum to zero. I haven't checked if your equation is correct but I note that I6 = I2

 

[Gee Wiz]

I summed them to zero initially, and then i moved them around so there weren't any negative signs. I also saw that I6=I2. I tried playing with that using I1+I3=I2 and I6+Iv(just assigned this to the v2)=I5(which i already solved from an earlier part)

 

[Gee Wiz]

nvm, just figured it out

 

[Gee Wiz]

thank you!

 

[riane]

are your origional equations correct?

 

[Gee Wiz]

nah, i messed up one of the loops.