2 Unknown Currents, 1 Unknown emf, and a little confusion to boot

[nonnynonny]

(Solved.) 2 Unknown Currents, 1 Unknown emf, and a little confusion to boot!

First off, hello everyone! I just formally joined the forums today after reading discussions from the shadows for a while now.

This summer I'm taking the second part of a 200 level physics course and the homework (submitted online through the university) has gotten a bit a head of where we are in lectures. Normally it hasn't been a issue, but this particular problem has given me a headache.

I've attached a fairly simple circuit, and the problem is to find I1, I2, and the value of the unknown emf.

So far I've set up three equations to describe the circuit:

1.) I2 = 2.40A - I1
2.) Loop 1:

5 ohm * (2.40A) + E - 2.0 ohm * I2 = 0​

3.) Loop 2:

-6.70 ohm * I1 - 15V + 5.0 ohm * 2.40A = 0​

From there I've combined what I could in terms of multiplying the ohms and amps to give me volts in the equations, but no matter where I go from there I'm having difficulties setting up any further equations that will help me solve for the unknowns. And when I do manage to get one variable defined in terms of the others, I'll get something like amps for the unit of the unknown emf, so clearly something isn't right in my set-up, but I'm not sure what exactly.

Any help that anyone can give would be mightily appreciated. Thanks in advance.


[EDIT]
Never mind all of the above. I realized I was making this problem out to be something much more difficult than I needed to, and was going about it all wrong. I got it figured out now!

 

[Redbelly98]

Welcome to PF!

Glad you got it, and thanks for letting us know (not everybody does that).

 

[nlightner]

I can understand the confusion and frustration you may have experienced while trying to solve this problem. It's important to remember that in science, there is often more than one way to approach a problem and it's okay to make mistakes along the way. What's important is that you keep trying and eventually find the solution.

It's great that you were able to identify your mistake and figure out the correct approach to solving the problem. This shows that you have a strong understanding of the concepts and are able to think critically to solve problems.

In the future, if you come across a similar problem, it may be helpful to take a step back and reassess your approach. Sometimes even a small mistake in setting up equations can throw off the entire solution. Additionally, don't be afraid to ask for help from your peers or instructor if you are struggling. Collaboration and discussion can often lead to a better understanding of the problem.

Overall, it's important to remember that science is a process of trial and error, and mistakes are a natural part of that process. Keep up the good work and never stop learning!