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.

 

[rwisz]

Based on the information given in the image, we can use Kirchhoff's laws and Ohm's law to solve for the unknown resistance, R2.

Firstly, we can use Kirchhoff's first law, also known as the law of conservation of charge, to determine the total current in the circuit. This law states that the sum of the currents entering a node in a circuit must equal the sum of the currents leaving the node. In this circuit, the current entering the node is I1, and the currents leaving the node are I2 and I3. Therefore, we can write the equation:

I1 = I2 + I3

Next, we can use Ohm's law, which states that the current in a circuit is directly proportional to the voltage and inversely proportional to the resistance. We can use this law to write equations for the currents I1, I2, and I3 in terms of the voltage and resistance in each branch of the circuit:

I1 = V/R1
I2 = V/R2
I3 = V/R3

Now, we can substitute these equations into Kirchhoff's first law to get:

V/R1 = V/R2 + V/R3

We can then simplify this equation to get:

1/R1 = 1/R2 + 1/R3

We know the values for R1 and R3, so we can rearrange this equation to solve for R2:

1/R2 = 1/R1 - 1/R3

R2 = 1/(1/R1 - 1/R3)

Substituting in the values for R1 and R3, we get:

R2 = 1/(1/5 - 1/10) = 10 ohms

Therefore, the unknown resistance R2 has a value of 10 ohms.