Let's avoid the working principle and directly jump to the calculations part.
Calculations for the rating of an inverter.
We need to first know what all things we need to turn on when no grid power is available.
Let's say that we want these things:
4 fans of 75 W each
2 tube lights of 50 W each
2 CFLs 20 W each
Total Watts: 4*75+2*50+2*20 = 440 W
Now the power factor of these home inverters will range from 0.7-0.9
Let's take average power factor, 0.8
Final VA rating of your inverter should be 440/0.8 = 550 VA
Calculations for the rating of a battery.
We will do reverse calculations
Let's say that we need this power for 4 hrs
The battery output voltage is 12V
So the rating in Ah should be (440*4)/12 = 146Ah
You will not get these exact ratings so always go for more i.e.
Inverter: 550VA is needed so you can take 600VA
Battery: 146Ah is needed so you can take 150Ah
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