My first question is what RV do you own?
It is my understanding that in our 2017 Seneca the inverter is in standby mode when the coach is powered by shore power. It will become active if shore power fails. So, that said if you have a Seneca you were not using power from the inverter.
While on the inverter in the Seneca only the microwave outlet and the TV outlet are powered. As an example.. One a recent trip my wife/First Officer wanted to use a heating pad while traveling. I ran a power cord from the microwave outlet to her seat. Heating pad worked perfectly.
To calculate watts available multiply amps x volts. 50 Amps X 240 Volts = 12000 Watts total available. On the Seneca the legs are split into 2 120 Volt legs. So that gives 6000 Watts per leg. You can calculate watt demand by adding up all appliances running on each leg. Remember the air conditioner and perhaps the refrigerator have a higher demand at start than when operating.
With a high demand hair dryer you could overload a leg if at the same time a high demand appliance started.
I hope this helps. It's MAGIC!!