Current and Power in DC Circuits

[Flaneuse]

I have two problems that have been bothering me, which I just cannot seem to figure out. Both have to do with current in a DC circuit with multiple resistors.

The first one looks like this:
12 V 4 ohms
|------:|:|-----\/\/\-----|
| |
| 18 V 12 ohms |
a|------:|:|----\/\/\------|b
| 8 ohms |
|-----------\/\/\---------|

I am trying to find the current through the 4 ohm resistor, but I am not quite sure how to go about doing so. I tried subtracting the voltages since they are in parallel and finding the equivalent resistance and then using Ohm's Law, but that was unsuccessful. I have a feeling it might intend for me to use Kirchoff's rules, so I then tried doing so from junction a to junction b. I got V_ab=16-4I₁=18-12I₂=8(I₁-I₂ (I₁ is from b to a around the top, where the 16 V and 4 ohm resistor is, I₂ is from b to a directly across the middle, and I₃ is from b to a along the bottom, where the 8 ohm resistor is), but just didn't know where to go from there. Would the current be I₁, or something else?


The second problem is quite similar. In this one, I am trying to find the power given off my one of the 10 ohm resistors; I think my problem here is again the current, as power=I^2 * R.
It looks like this:
12 V
|-----:|:|-------------|
| |
| |
| 2 ohms |--\/\----| <----20 ohms
|---\/\------|---\/\---| <----10 ohms
|---\/\---| <----10 ohms
So basically I am trying to find the current through one of the 10 ohm resistors so I can use it to find power, which is I^2 * R.

I would really appreciate some help on this, as I am studying for a test, and these two problems have been troubling me for much too long.

Thanks!

 

[Flaneuse]

Somehow those diagrams turned out horribly. I've attached some better ones; "Untitled" is corresponds to the first problem and "Untitled 2" corresponds to the second.

Thanks!