Why is mains supply ac not DC?

Answer 1

From Wikipedia's listing under the "war of currents" (http://en.wikipedia.org/wiki/War_of_Currents): In the alternating current system, a transformer was used between the (relatively) high voltage distribution system and the customer loads. Lamps and small motors could still be operated at some convenient low voltage. However, the transformer would allow power to be transmitted at much higher voltages, say, ten times that of the loads. For a given quantity of power transmitted, the wire size would be inversely proportional to the voltage used; or to put it another way, the allowable length of a circuit, given a wire size and allowable voltage drop, would increase approximately as the square of the distribution voltage. This had the practical significance that fewer, larger, generating plants could serve the load in a given area. Large loads, such as industrial motors or converters for electric railway power, could be served by the same distribution network that fed lighting, by using a transformer with a suitable secondary voltage. Bottom line: Less voltage drop across long distances of wire, and easily stepped up or down in voltage as needed. "One voltage fits all" approach.

Answer 2

Losses in AC power transmission are significantly lower than in DC. The power lost in transmission can be calculated from the resistance of the transmission line using the equation P=V^2/R where V is the voltage, R is the resistance of the transmission line, and P is the power lost. Also, changing DC voltage from one level to another requires complex power electronics, while changing AV voltage from one level to another simply requires a transformer (which is a relatively inexpensive and simple device).