Apologies if this is incredibly clueless, but I've read various threads on Empower and am still not 100% confident about what I need.

From what I've read so far, it looks like I need an "inverter", that will turn the aircraft's low-voltage DC supply into US mains-style 110V AC. Then presumably I plug in my laptop's power supply which will transform it straight back to low-voltage DC! Is this right? If so, why is it necessary? Is it because different laptops work at different voltages and the only foolproof way round this is to go back to a common starting point of a mains-type supply?

Also, if I buy an inverter device such as the Teleadapt Inflight Power, will it connect directly to my laptop's power supply brick, as opposed to via my existing UK mains-style lead? Do I need to buy a special lead, or is one normally supplied with the inverter? How do I know that a third-party lead will fit my Dell power supply? Has a common standard been adopted at this end? (I've seen various references to "clover leaf")

Again, sorry for so many basic questions and thanks in advance for any assistance. I don't want to waste money on the wrong things and/or find myself "high and dry"!