I'm trying to find out if I can run an appliance of mine can off the grid, completely on solar power and a battery. The appliance uses 4.91 amps and uses 110 volts on the power cord. The solar panel produces 45 watts of power. The battery is a 12 Volt, 35 Ah Sealed Lead Acid Battery. Now, I live in sunny FL, so sunlight shouldn't be an issue as it is sunny most of the time. Will a single solar panel and battery be able to run it 24/7, without fail? Meaning it must be able to run even when it dark out, cloudy, etc. If my setup won't work, how many solar panels and batteries will I need? Thank you in advance for your answers and advice.
4.91 amps at 110VAC is a power of 540 watts so no-matter how long a day it shines this won't work because average power in should exceed average power out by a few percent to account for conversion losses.
Your solar panel produces only 45 watts of power.
Now maybe you mean your appliance takes 4.91 amps from a 12V dc supply - this equates to a power of 59 watts and still you have a sizable deficit. Maybe your appiance uses a 5V supply at 4.91 amps? This is a power of 24.6 watts and I can see that with a little bit of clever design (sun tracking solar panel maybe) and a decent battery to power it thru the night) that this might work.