In general you can connect almost any appliance to an inverter, with a few practical exceptions. Although the inverter can easily supply a heavy load like an electric heater, the battery capacity is often too low to maintain the supply for any longer duration of time. The same applies to air conditioning units. As long as the battery capacity is high enough, you can use a high rating inverter to run a washing machine, a large single cooking element or a small two-ring electric cooker.