Household electricity is all AC. Early on Thomas Edison pushed for houses to use DC. Why did AC win out in the end? What do you suppose was Edison's motivation for preferring DC?

Well, now that we have modern ways to turn high voltage DC into low voltage DC, the technology might change. There is discussion of long distance transmission of DC from for example wind farms to cities.

However back to your question:
The power losses in transmission are proportional to the square of the current, i^2 R but the power transmitted is i V. Therefore to minimize power losses along the transmission lines for a given power i V at the end, you want to make i small and V big. That is why those fancy transmission lines you see in the country between cities and power plants are so high and have such big insulators, they are very high voltage. However you do not want that high voltage at the plug in your house. Therefore the voltage is stepped down by transformers for local distribution. Transformers do not work on DC, only AC. That is the long and short of the argument historically.

By the way DC is really handy if you have a battery involved :) I do not think Edison visualized the network of electrical transmission that evolved and therefore the need for transformers. Note that your car works on DC as do virtually all electronic devices (it is rectified from the AC that arrives at the meter outside your house). Even your modern car generator is an alternator these days and the AC is rectified to DC before distribution to the radio and battery and lights etc.

AC (alternating current) won out over DC (direct current) in the battle for household electricity primarily due to two reasons: the ability to transmit AC over long distances more efficiently and the development of reliable AC power systems by Nikola Tesla and George Westinghouse.

One of the key advantages of AC is its ability to be easily transformed to different voltages, allowing for efficient long-distance transmission. As electricity needs grew, it became evident that transmitting DC power over long distances would require extremely thick and expensive copper wires to overcome power loss due to resistance. In contrast, AC could be transmitted with significantly less power loss, thanks to the ability to increase voltage using transformers, and then stepped down to lower voltage for household use. This made AC transmission more practical and cost-effective for distributing electricity to larger areas.

As for Edison's motivation for promoting DC, there were several factors at play. Edison had developed early DC power systems and owned patents related to DC technology, which he stood to profit from. Additionally, DC systems allowed for easier adoption of his incandescent light bulbs, as they operated on DC power. Edison believed that DC was a safer and more stable option for residential lighting and power, as it lacked the potential risks associated with AC, such as higher voltages and rapidly alternating currents.

Furthermore, Edison was involved in the infamous "War of the Currents" with the AC advocates, notably George Westinghouse and Nikola Tesla. This rivalry escalated into a battle to convince the public, with Edison even publicly demonstrating the dangers of AC by electrocuting animals. Despite his efforts, the benefits of AC in transmission efficiency and the successful implementation of AC systems by Westinghouse led to its widespread adoption and eventual victory over DC for household electricity.

In summary, AC won out over DC due to its superior transmission capabilities and the successful development of AC power systems. Edison's preference for DC could be attributed to his financial interests in DC technology, his belief in its safety, and his rivalry with AC proponents.