This looks very complicated for a very simple problem. Can you not just solve it in this fashion or am I missing something here:
Solve the parallel resistors (3) into one resistor value
Add the three resistors together for resistance total
Divide resistance total into voltage total for current total.
Figure out voltage drops across each resistor
Remove V1 and V5 to give you leftover voltage on parallel branches
Divide each resistor(branch) into leftover voltage to give you current on that branch.

Just a thought. Maybe fancy math works better?

 

I don't follow the approach you are describing. First, the three resistors aren't in parallel. I only get more confused from there when you start talking about removing voltage sources to get leftover voltage.

The OP appears to be working from a very introductory level. May not even have gotten to combining series and parallel combinations of resistors yet.

 

WBahn, my most humble apologies. You will note in my first line, I said, "Am I missing something here?" Clearly I was and it was the extra power source on the resistor on the second branch. Therefore my method will not work without some tweaking. I am incorrect. It would still appear to be a fairly straightforward problem but I will leave this in your more than capable hands and wish you and the OP well on solving it. Good luck and good day. Cheers!

 

WBahn, my most humble apologies. You will note in my first line, I said, "Am I missing something here?" Clearly I was and it was the extra power source on the resistor on the second branch. Therefore my method will not work without some tweaking. I am incorrect. It would still appear to be a fairly straightforward problem but I will leave this in your more than capable hands and wish you and the OP well on solving it. Good luck and good day. Cheers!

I'm still trying to understand your approach and I think I'm getting a handle on it.

Okay, so let's assume for the moment that the extra power source (V2 but which I'm assuming you were calling V5) isn't there. You then combine them in parallel and then in that in series with the other two. When you said to find the voltage across each resistor, I figured that that meant across each of the two series resistors and also across the parallel combination. At that point you would have the voltage you needed to find the current in each branch. But now I'm thinking that you only mean the voltage across the two series resistors. In your next line you are then intending to take the difference between the applied voltage and the voltage drops across the two series resistors to arrive at the voltage across the parallel combination. Does that sound like what you had in mind?

 

That's exactly what I had in mind although my theory blew apart when I noticed the second voltage source in the circuit. Opened mouth too soon.

 

In many problems such as the one at hand it is possible to propose a simpler approach or apply some obvious shortcuts. The challenge for those just getting to grips with these problems is that they often can't see the forest for the trees. They usually just want a technique that works every time and in every situation - if such a thing exists in practice. The ability to visualize simplifications or shortcuts is a skill that comes with a good deal of practice. Also students are often required by their teachers to use a particular approach on a problem to hone or test their skills in that method - notwithstanding the fact that another approach may be better suited to more readily solving the problem.

 

Most definitely.

I think one of the most useful things for someone to do is to take a problem, such as this one, and solve it with every technique they know but to first guess which one they think will be the easiest and which one will be the hardest and why and then, afterward, assess whether they were right or wrong and, if wrong, why they were wrong. I still do that on a fairly regular basis and sometimes gain a bit of insight either into something that has largely escaped me up to now or sometimes into an aspect of something that I've mostly been aware of but some detail of it comes more sharply into focus.

 

if ever in doubt just use SUPERPOSITION

 

http://www.allaboutcircuits.com/vol_1/chpt_10/7.html covers superposition.

 

if ever in doubt just use SUPERPOSITION

1) Superposition is fine, but it very often results in considerably more time and effort than other techniques.

2) Even if you use superposition, you are still left with a bunch of circuits that have to be analyzed each of which has a single source. How does the "if ever in doubt just use superposition" principle work out then?

3) The goal is to become proficient with multiple tools and develop the ability to choose the best tool for the job at hand. This is akin to telling a mechanic in trade school, "if ever in doubt, just use a hammer."