The current in the 13.8 resistor = .780 A. Goal is to find the current in all resistors.
Parallel resistor law - R total = 1 / (1/R1 + 1/R2 + ...)
Series resistor law - R total = R1 + R2 + ...
KCL - sum of currents flowing into a node must be = to sum flowing out
KVL = directed sum of voltages in a closed circuit = 0
The Attempt at a Solution
Okay, quick preface... a friend randomly asked me if I had any idea how to do this. I haven't been to school in about 6 years, my only knowledge on the subject was what I taught myself way back then and I'm just interested in how this works for personal understanding as I honestly can't recall what's what and what I'm doing wrong and the writeups in Wiki/random tutorial sites are not helping me understand...
First, given the 13.8 resistor with .780 A, I figure out the voltage is 10.764. Applying this to the parallel resistor gives me .626 A. Using the parallel resistor law, I simplify the two to come up with a 7.66 resistor which I name R3. The two currents combined = 1.406 A or I3.
Now I add the other 15 and 12.5 resistors with the serial law for 27.5 or R1. I do the same for 8.45 and 4.11 for 12.56 or R3.
From here, I'm lost...
I call the second half of my current circuit Loop 2 and using KVL, I *think* R3I3 - R2I2 = 0. Going through this formula gives me a current of .858 for I2. Now, with KCL... I2+I3 = I1 = 2.264.
Now when applying KVL to loop 1, R1I1 - R3I3 should = 0, but that's not what I get.
I'm almost positive I'm messing something up when it comes to KVL but I can't tell what and all the examples I've found online haven't helped...