**1. The problem statement, all variables and given/known data**

I need to come up with a formula to solve for i

_{2}given the diagram of the circuit attached. I can identify 2 junctions and 3 loops.

**2. Relevant equations**

*The algebraic sum of the currents into any junction is 0. By convention the currents entering the junction are positive and the currents leaving the junction are negative.

*The algebraic sum of the potential differences in any loop must equal 0.

Junction B: i_{1}-i_{2}+i_{3}=0 (Eq.1)

Junction E: -i_{1}+i_{2}-i_{3}=0 (Eq.2)

Loop ABEF: ε_{1}-i_{1}R_{1}-i_{2}R_{2}=0 (Eq.3)

Loop BCDE: ε_{2}-i_{3}R_{3}-i_{2}R_{2}=0 (Eq.4)

Loop ACDF: ε_{1}-i_{1}R_{1}+i_{3}R_{3}-ε_{2}=0 (Eq.5)

**3. The attempt at a solution**

Here is where I run into trouble. I am having difficulty using the above equations to find a formula for i_{2}. I am not sure if the equations above have an error in them or if I am heading in the wrong direction. I need to get everything in terms of R_{1},R_{2},R_{3} and ε. In the experiment ε_{1} is a fixed power supply and ε_{2} is a variable power supply. I am assuming we can add and subtract them and get:

ε_{1}–_{1}R_{1}+i_{3}R_{3}-ε_{2}=0 → -i_{1}R_{1}+i_{3}R_{3}=0

But I cannot seem to work the equations well enough to get everything in terms of R_{x}, i_{2} and ε so like I said I think there is an error above. I am also not very comfortable working with systems of equations.

http://ift.tt/1nX3RqM