Finding Unknown quantities in a circuit

[Josh225]

Homework Statement

See attached photo

Homework Equations

Kirchhoff's current law[/B]

The Attempt at a Solution

So, I was solving for I3 and got the correct answer, but I want to be sure that I arrived at the right answer by using a reliable thought process. I don't want to get lucky!

So, I had already determied I1 and got 1A.

With that information I thought... It starts out with 2 A, and there are 2 identical resistors (R2 and R3). I3 = 1 A, so these 2 resistors must each have a current of .5 A going through it. From that I found that I3 = .5A

Is this a reliable thought process? What are some other ways to view this problem?

Thanks!

 

[cnh1995]

Your method is correct. I believe it is the only way to solve this problem.

 

[NascentOxygen]

Any solution is going to rely on Ohm's and Kirchoff's Laws.
But you could use the fact that R₁ is dissipating 30W to find $\left(\sf using~\color{blue}{power﹦\frac{E^2}R}\right)$ that E=30V

Then, with the battery delivering 30×2=60W, this means the R₂ R₃ combination is dissipating 30W. So R₂$\|$R₃ must be 30Ω, and so on ...