Anytime you plug in any additional electrical appliance into your home electrical system it will increase electrical usage. Will you see a dramatic increase in your electric bill by just running an RV Fridge, no you should not.
What you need to understand is that when you plug your RV in to your home electric is that other electrical items in your RV such as the RV's Power Converter/Battery Charger also start running as well. The converter/charger will use more electric then your fridge.
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