Superposition method and proof

[schmiggy]

Homework Statement

Use the superposition method to find the magnitude and direction of the current flowing through the 10 ohm resistor. Then use any technique other than that used previously to check the validity of your answer

Homework Equations

The Attempt at a Solution

First I'd like to point out that I have a very basic understanding of the content being covered in class, I understand the theory but have a hard time actually putting it into practice.

First of all I simplified the circuit down to three resistors by finding the resistance total of the 5 ohm and 15 ohm in parallel then adding the 16 ohm in series.

A number of things confused me about this question. Firstly, every worked example in class has never included 2 of the same type sources; the circuits included either a single voltage source, a single current source, or one of each, never two of the same. So my first question is, does the same concept apply? Do I remove one source, calculate the current using V = IR by finding resistance total, and then do the same with the other source? Do I combine the sources, find Rtotal and use V=IR?

My attempt at superposition by taking out one of the sources and calculating I through the entire circuit yielded a different value than that found using mesh analysis - it was very close, however still different. I'm not confident at all in my calculations and as such am a little uncomfortable posting calculations (embarrassment, shame etc).

My mesh analysis calculations yielded 6.25Amps flowing through the 10 ohm resistor.
I designated two loops using the simplified diagram attached and using KVL I found..
Loop 1: 200 - (10+20)I1 + 20I2 = 0
Loop 2: -100 - (20+19.75)I2 + 20I1 = 0
I rearranged in terms of I1 and using simultaneous equations found I1 which is equal to the current flowing through the 10ohm resistor.

One more questions regarding superposition.. if using V = IR for the two different sources, is Rtotal different depending on the current flow? Ie will the 200V source experience resistance equal to (10||20)+19.75 and for the 100V (19.75||20)+10 for Rtotal?
As you can see I'm not very good at this!

Is anyone able to verify my calculation of I through the 10ohm, or point out where I'm going wrong.. any help is greatly appreciated!

 

[schmiggy]

Managed to figure it out after a lot of smashing my head against a brick wall, thanks anyway! :)