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It’s quicker
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It's only faster because your half ass electrical system is only 120V Also the microwave makes the mug to hot to touch
Wait how does the microwave go faster when it's also on half the supply voltage?
Because resistive heating is inefficient. You need to pump a lot of power through to get a lot of heat. A microwave does not use resistive heating and works on a completely different principle and therefore the amount of power available is much less importance.
Resistive heating is almost perfectly efficient. Where else would the energy go? Using a hot piece of metal to heat water might be slower than using microwave radiation, but that's a different kettle of fish.