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Funny enough the microwave is the best for a single cup. The kettle has a lot of metal in the element ( along with a lot of insulation in the form of powdered silica to insulate the element electrically) and has to heat this up as well as the water and the kettle. You also have to place enough water in to cover the element, and this is typically nearly a second cup of water. You lose energy to heat the cold cup you pour the water into, and you probably have used the amount of energy to heat theoretically 4 cups to do one. The stove is the same, just you have a lot bigger element, a lot of glass or ceramic to heat up as well, and then the pot that holds the water. This makes a good room heater for the 5 minutes or so it takes to heat up.The microwave is around 50% efficient in converting electricity to heat, but almost all of the energy it places in the cavity is absorbed by the single cup of water inside, nothing else gets hot inside.If you are doing 15l of water the stove will be best, as you can place a 15l pot on it, whilst the kettle is best for doing 6 cups of hot water.
The best method would be to use one of those small electric immersion heaters and use it to heat the required amount of water in the cup (well insulated, of course).