How Long Can a 12V Battery Power a 220W Appliance Using a 300W Inverter?

[Muh1982]

Hello, I have a question, I've googled to find the answer but I didn't find any.

I have 12v 100amp battery, 12v-220v 300watt inverter and 220w 220v appliance.

I want to run the 220w appliance on the 12v battery by using the inverter.

My Question is: How long will it last until the battery is fully discharged?

Please write the equation so it will help me in the future, Thank you.

 

[vk6kro]

That would be a 100 amp-hour battery.

It would be useful to know the eficiency of the inverter, but make a guess and call it 70 %

Power into the inverter from the battery = (100 % / 70 %) * 220 watts or 314 watts.

Current into the inverter from the battery = 314 watts / 12 volts = 26 amps.

The battery is 100 amp - hours so the time it would run is 100 amp-hours / 26 amps or 3.8 hours.

However, I have assumed that the load is not inductive or capacitive which could make the result worse.
What are you actually trying to do?