[SOLVED] Kirchoff's Laws 1. The problem statement, all variables and given/known data A link to the problem statement is provided here: http://img231.imageshack.us/img231/5305/kirchoffry1.png [Broken] (with one modification: the question should read find the current in the .75 ohm resistor) 2. Relevant equations Ohm's Law: R=delta(V)/I loop rule: sum(changes in potentials) = 0 (for closed loop) junction rule: because of conservation of charge, the currents follow such that: I_1 + I_2 = I_3 3. The attempt at a solution I am supposed to solve a set of simultaneous linear equations. The first one is simply the node equation I_1+I_2=I_3. Then by looking at the top loop, I have: 2.25 - (I_2)*(3) - (I_3) * (4.2) = 0 The next part is what I am somewhat confused about. I can either make one of two loops for the final equations: the bottom one with the middle wire included, or the top and bottom one as a whole. For just the bottom loop, I get: 4.75 - (I_1)*(.75) + 1 - (I_1)*(1.2) + (I_2)*(3) +2.25 = 0 I am not sure if this is right because I don't know if it is appropriate to add the voltages 1 and 4.75 when they have the resistor between them. Perhaps I am supposed to use their potential difference? But then in that case, the .75 ohms would be internal resistance and I don't have any emf. And, I think it is probably incorrect to assume that the current going through the 1.2 ohm resistor is the same as I_1. For the whole loop (the biggest one which does not include the middle wire), I get: 4.75 - (I_1)*(.75) + 1 - (I_1)*(1.2) - (I_3)*(4.2) = 0 When I solve this simultaneously with the first two equations, I get a different answer from when I solve the first three simultaneously.