A closeup of the Eva's power outlet is inserted here.
Ritsuko (OFF - radio):“Normally, the Eva runs off electric power supplied by a cable.”
Reichu: The full name of this doodad (the cord part, anyhow) is "umbilical cable", which is a fairly obvious reference to the umbilical cord of in utero mammal youngsters -- with the difference that those of most mammals don't come out of their backs. ;;p Says the D&R Deluxe Program Book:
Incidentally, "UMBILICAL CABLE (cord)" means the blood vessels which extend from baby's navel to the placenta of its mother's womb. Thus, like a baby receives nutrients through this umbilical cord, Evangelion receives electric power through the umbilical cable.
Mr. Tines: The use of "umbilical" as a fancier name for what in everyday use we'd refer to as an extension cord is quite common in military and space contexts — see e.g. here.
Hexon.Arq: I've always been curious as to what is ultimately on the other end of that thing. Granted they do feed out of the sides of buildings, but I'm a bit disappointed that more was not made of this thematic name-calling. Should there have been a depiction of a Mother Generator? Maybe I'm the only one who thinks so. Shukkins.