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I have a 10,000 watt Fermen, and it is a sign wave, simply because the motor spins the generator.What wattage is the generator? Also is it a pure sine wave or modified sine wave? To put it simply most generators labelled pure sine wave are inverter generators, while most non inverter generators are modified sine wave. The sine wave makes a difference on what is used, for example an lcd tv or a desktop computer might work but act unpredictably, while a laptop might run fine on a modified sinewave as the battery and power inverter acts as a filter.
The more delicate the circuitry, the more the wave matters. If you have old incandescent bulbs in a light fixture, try it with a modified sine wave, the bulb flickers like crazy, on some electronics this can cause hell. The good news it however if you have something like computers modern tv sets and other modern gizmos you want to protect and run with a modified sine wave, an uninteruptable power supply or upc convertes the wave for you and they are fairly cheap so you can keep those if you do not have an inverter generator or are unsure. Things like light bulbs, refridgerators, microwaves electric space heaters etc do not care how pure the wave is, they do not need a pure wave.
Depending on the size of the house and how many are using electronics, 5-10k generator will run the entire house minus ac, electric heaters(house heaters not space heaters) dryers and electric stoves. For the rest it depends on how much juice you need to kickstart, and the running wattage. Some houses may run 5-6k watts continuous but need upwards of 20k watts to kick start multiple devices like ac and other not so soft start devices. This also depends on the size of the ac unit, or wattage of heaters and electric stove, as well as the wattage needed to start the fan for said heater/ac.
Many devices have capacitors to handle surge voltage, infact most do, however the capacitors reduce starting voltage requirement, but can not eliminate it short of a monster sized one as startup draws a lot of juice, it also depends on the charge and discharge rate of the capacitor, as a capacitor is basically a quick charge/discharge battery.
My AC controller seems to be the most sensitive, but came up just fine.
I ended up running on generator for about 12 hours Yesterday, but power down when we went to bed.
I also test ran a small AC for a few hours to dehumidify my bedroom.
Fridge, Freezer, microwave, electric stove top all worked fine. Next time I run it, I will drag out the Oscilloscope and look at the quality of the sign wave.