Calculating the current of a circuit- resistance and volatge known, see picture

[mmoadi]

Homework Statement

What current flows through the resistors R(1) = 1Ω, R(2) = 2 Ω and R(3) = 3 Ω, if the driving voltages are V(1) = 1V and V(2) = 2V?

Picture:
http://item.slide.com/r/1/151/i/lvtwIwH-0j8A8o-XAKDtPRQO1eHAb4Ik/

Homework Equations

V= RI → I= V/ R

The Attempt at a Solution

V(1)= I(2)R(2) + I(1)R(1)
V(2)= I(3)R(3) – I(2)R(2)
I(1)= I(2) + I(3)

- From what I stated above, I conclude three equations:

1) V(1) = I(2)R(2) + [(I(2) + I(3))*R(1)]
2) V(2)= I(3)R(3) - I(2)R(2)
3) V(1)= [I(2)*( R(1) + R(2))] + I(3)R(1)

- I combined the three equations and simplify for the current that goes through ALL resistors, which in our case is I(3):

I(2)= (I(3)R(3) - V(2))/ R(2)
V(1)R(2)= [(I(3)R(3) – V(2))/ R(2))*(R(2) + R(1))] + I(3)R(1)R(2)
(V(1)R(2))/ (R(2) + R(1))= (I(3)R(3)) + [I(3)R(1)R(2))/ (R(2) + R(1))]
I(3)*[R(3) + (R(1)R(2)/ (R(2) + R(1))]= [V(1)R(2)/ (R(2) + R(1))] + V(2)

I(3)= [(V(1)R(2)/ (R(2) + R(1)) + V(2)] / [R(3)* (R(1)R(2)/ (R(2) + R(1))]
I(3)= 1.37 A

Are my calculations correct?
Thank you for helping!

 

[diazona]

Homework Statement

What current flows through the resistors R(1) = 1Ω, R(2) = 2 Ω and R(3) = 3 Ω, if the driving voltages are V(1) = 1V and V(2) = 2V?

Picture:
http://item.slide.com/r/1/151/i/lvtwIwH-0j8A8o-XAKDtPRQO1eHAb4Ik/

Homework Equations

V= RI → I= V/ R

The Attempt at a Solution

V(1)= I(2)R(2) + I(1)R(1)
V(2)= I(3)R(3) – I(2)R(2)
I(1)= I(2) + I(3)

- From what I stated above, I conclude three equations:

1) V(1) = I(2)R(2) + [(I(2) + I(3))*R(1)]
2) V(2)= I(3)R(3) - I(2)R(2)
3) V(1)= [I(2)*( R(1) + R(2))] + I(3)R(1)

Equation #3 here is the same as equation #1, just written slightly differently... so you really have only two independent equations. I'd just start from the original three you had above.

- I combined the three equations and simplify for the current that goes through ALL resistors, which in our case is I(3):

I(2)= (I(3)R(3) - V(2))/ R(2)
V(1)R(2)= [(I(3)R(3) – V(2))/ R(2))*(R(2) + R(1))] + I(3)R(1)R(2)

I don't see where that last line comes from. The units are off, so something must be wrong in there.