Determine current using Kirchoff's Junction/Loop Rule

[Renaldo]

Homework Statement

In the circuit shown in the figure, R1 = 6 Ω, R2 = 13 Ω, and R3 = 19 Ω, Vemf,1 = 10 V, and Vemf,2 = 15 V. Using Kirchhoff's Loop and Junction Rules, determine the currents i1, i2, and i3 flowing through R1, R2 and R3, respectively, in the direction indicated in the figure.

Homework Equations

i₁ + 1₂ = 1₃

V=IR

The Attempt at a Solution

i₁ + 1₂ = i₃

V₁ + I₃R₃ + I₁R₁ = 0

V₂ + I₂R₂ + I₃R₃ = 0

I₁ = (-V₁ - I₃R₃)/R₁

I₂ = (-V₂ - I₃R₃)/R₂

I₃ = (-V₁ - I₁R₁)/R₃

Does this look right?

 

[voko]

The last equation leads you nowhere. Instead, sum the two previous equations, that, together with the first equation, will give you an equation from which you will be able to find I3.

 

[Renaldo]

Thanks. I was able to solve it.