It is said that AC is preferred over DC because of the negligible voltage drop over long distances. How does that work?
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The voltage drop in long-distance transmission lines is mostly caused by 1) resistance losses in the wires and 2) capacitive coupling between the wires and the ground underneath them. AC versus DC does not matter to resistive losses in the wires (same in either case) but the capacitive coupling to the ground happens with the AC transmission and gets progressively worse as the transmission voltage is raised.
Since higher transmission voltages mean lower resistive losses in the wires, the tendency is to go for higher voltages and that means the AC-specific losses become dominant. For this reason, very high voltage power transmission experiments are being done on lines carrying DC. Note however that AC transmission lends itself to easy conversion of high to lower voltages with transformers, which cannot be used with DC lines.