I am a science teacher who usually works with match classes or computer courses. Next semester I will be teaching a high school physics course and while I knew how to do this "once upon a time" when I took physics, I no longer remember the details. I remember most of it, but I'm missing some important detail.
Taking this problem as an example I cretae three equations which are based on the junction rule at A and the loop rule at B and C.
After solving this system of equations I arrive at the solution I1=1A, I2=3/8A, and I3=5/8A. So now I can work out the voltage drop across each element.
Okay, here is the problem. I expected (perhaps incorrectly) that the total voltage drops across the resistors would equal the sum of the voltage sources. I intened that this be a check on the answers to ensure they were wrong. In this case (an many others) I am getting a mismatch. 5v+15v+25v=45v which is not equal to 20v+10v=30v. Sometimes this works, but most of the time I don't get equal answers.
It has been so long since I did this, I'm hoping someone will know what I have forgotten. Is there a pattern of behavior for the voltages which I should expect to see? Is there some test which the students can do to check their work?