I do not understand the situation you encountered, nor your repair, nor the test you did after your repair. But I will try to answer your first question.
I am sure that you know that if you put two resistors in series, the total resistance gets higher, and is equal to the sum of the two resistances. If you put five identical resistors in series, then the total resistance is equal to five times the value of any one of them. If you make a series connection of resistors that are of different values, then you simply add up the individual values to get the total resistance.
A long conductor can be regarded as a series connection of small resistors. Consider a 1 foot long section of #4 bare copper wire. It has some value of resistance. Now consider a 100 foot long section of the same wire. It is essentially a series connection of 100 resistors, each having the value of resistance as your initial 1 foot section, and the total resistance is 100 times the value of the 1 foot section. If you tie together (good luck on getting good connections here, but stay with me, and let’s pretend you can do this with zero extra resistance at the connection points) 100 sections of 1 foot long bare wires of varying AWG sizes, then the total resistance will be the sum of the resistances of the one hundred individual pieces.
In your example, you have 399 feet plus 11 inches of #4 wire in series with a 1/2 inch section of #4 wire that has been trimmed down and placed into a lug on one end, plus another 1/2 inch section of #4 wire that has been trimmed down and placed into a lug on the other end. This is a total of three resistors in series, and the total resistance is the sum of the three individual resistances. The resistance per unit length of the trimmed down sections at either end is higher than the resistance per unit length of the long section. But the total resistance of the 399+ foot long piece in the middle has not been altered by what was done at either end.
Does this answer your question?
By the way, welcome to the forum.
Last edited by charlie b; 07-08-09 at 10:50 AM.
Charles E. Beck, P.E., Seattle
Comments based on 2014 NEC unless otherwise noted.