Solve Resistance Question w/Kirchhoff's Laws & Ohm's Law

[imagemania]

Homework Statement

http://img97.imageshack.us/f/scn0003.jpg/

Homework Equations

Kirchhoff's first, second law, ohm's law

The Attempt at a Solution

I’m ok on all the questions, just I am stuck on part a. I can work out R1 from P=I^2R and get R = 5.00 ohms. But, R2? I can't see how to deduce it without working out the current that goes through the 10ohms resistor, and deducing the voltage through the 5ohm. But the way the question is laid indicates you need not do that...

Any help would be great.

 

[rl.bhat]

Hi imagemania, welcome to PF.
Power W = V*I
So voltage across the parallel combination of resistance is 10 V.
Now you can find the remaining things.

 

[imagemania]

I see that bit now, but once you've done that, there is still an issue with the current. We're not told that the power through R2 is 20W, and we're not told the current. If we take kirchhoffs second law about a loop that misses out R2 then
0 = 10ohms x I - 5ohms x 2A
I = 1A (through 10 ohm).

So through R2 it would be I = 3.5-(2+1) = 0.5A

R2 = 10/0.5 = 20ohm.

Is there another way that this is suppose to be deduced, as if you look at part b, c it asks for the steps I've taken above, which inclines there's an easier method. ..

thanks

 

[rl.bhat]

I don't think so. Now three resistances are in parallel. Find equivalent resistance. Total Current is given. Find emf.