Calculate Current Through Resistor - Kirchhoff's Rules

[crimsonn]

Homework Statement

Calculate the current through the resistor of resistance for circuit B.

Express your answer in terms of EMF, R1, and R2.

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Homework Equations

Kirchhoff's Loop and junction rules

The Attempt at a Solution

So I have these equations that I've figured out using Kirchhoff's Rules:

There are two loops:

EMF = I1R1 + I3R2
EMF = I2R1 + I3R2
I1 + I2 = I3

I figured out pretty quickly that I1 = I2 by subtracting the top from the middle equation. I'm just not sure what to do next really...

The answer I'm supposed to get to is I3 = (2EMF) / (R1 +2R2)

I don't know why this is so confusing...but it is. So, assuming I did everything right, how do I get to the last (final) equation for I3?

 

[Doc Al]

I figured out pretty quickly that I1 = I2 by subtracting the top from the middle equation. I'm just not sure what to do next really...

Make use of that fact to eliminate I1 (or I2) from either of the first two equations. Express I1 (or I2) in terms of I3. (Use your third equation.)

 

[BruceW]

Simply use more substitution and rearranging to get the equation you want. You already have all the equations necessary, you don't even have to think about it anymore, just write out your equations (including your equation I1=I2), and then its just a problem of simultaneous equation solving.

 

[crimsonn]

I think I'm super sleep deprived because that was pretty simple.

Thanks you two :)