Finding the currents in this system

[Dell]

given the following:
http://lh6.ggpht.com/_H4Iz7SmBrbk/Sg04JIIg9vI/AAAAAAAAA-o/xDycbG90Gmc/s720/C.jpg

and given that

ε1=3V
ε2=2V
R1=1Ω
R2=2Ω
R3=3Ω

i am asked to find the current flowing throiught R1,R2, R3

what i did was

I₃=I₂+I₁
I₁R₁-I₂R₂=ε₁

but i am short of one equation to solve this, what i would like to do is somehow find R₁₂, as an the sum of R1 and R2, but my problem is that i have ε1 between them and i have no idea how to tackle this,

had ε1 noot been there i would have said R₁₂=(1/R₁+1/R_2)^-1 and then i could make a third equation using this.

how can i solve this?

 

[tiny-tim]

I₃=I₂+I₁
I₁R₁-I₂R₂=ε₁

but i am short of one equation to solve this, what i would like to do is somehow find R₁₂, as an the sum of R1 and R2, but my problem is that i have ε1 between them and i have no idea how to tackle this,

Hi Dell!

Stop trying to simplify it … it's simple enough already!

There are three loops, of which two are independent …

you've already applied Kirchhoff to the R1R2-loop, so now just apply it to the R2R3-loop.

 

[Dell]

thanks,.. for the second part of the question they ask what the difference in voltage is from pioint A which lies between R3 and ε2, and point B which is between R1 and ε1,

can i use kirchhoff here too, and igonre the part with R2 and R3, so I1R1=ε1-v
v=ε1-I1R1=2.8

?

 

[tiny-tim]

thanks,.. for the second part of the question they ask what the difference in voltage is from pioint A which lies between R3 and ε2, and point B which is between R1 and ε1,

can i use kirchhoff here too, and igonre the part with R2 and R3, so I1R1=ε1-v
v=ε1-I1R1=2.8

?

sorry, I don't understand that … and what happened to E2?

You need the potential difference across E2 and across R1 (or across E1 and across R3)

 

[Dell]

sorry meant to be v=ε2-I1R1=2-0.2=1.8,

but is it okay to just ignore the whole part that includes R2 and I2??

 

[tiny-tim]

sorry meant to be v=ε2-I1R1=2-0.2=1.8,

but is it okay to just ignore the whole part that includes R2 and I2??

Yup … Kirchhoff applies to only one loop at a time!