Hey guys I hope you can help me with this.
Im trying to find the resistance in R5, the rest are given and the emf's are given
R1=2Ω, R2=8Ω, R3=5Ω, R4=4Ω, R5=?, R6=2
E1=12V, E2=6V

This has been bugging me forever now. I attached a picture.

Hope someone can help me!

 

hi dynamix,

welcome to the forum, you should label circuit (nodes, loops). as stated there is no unique solution. you need one more piece of information (voltage or current for example)

 

To help build your intuition a bit so that you can spot the point that panic_mode is talking about before spending "forever" being bugged, consider the following:

Imagine I build up the circuit as shown except that I don't install R5. I use exactly the component values you've given. Now I turn my back and you install R5 and ask me what the value is that you just put in. You should be able to immediately realize that there is absolutely no way for me to do that because there was absolutely no constraint on the value of the resistor that you chose to put in. However, if you put in whatever value of resistor you want and then measure almost any thing in the circuit, such as the voltage across R3 or the current through R2, then I can run some numbers and tell you the value of the resistor you installed.

Now, note that I said "almost" anything. Whatever piece of additional information you give me has to be something that is dependent on the value of R5 in some way. In this particular circuit that is easy because all of the voltages and currents in all of the components, except the already given voltages across the two supplies, are dependent on R5.