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As Naushad said, OS requires power. Every process in your system consumes corresponding amount of power. The more processes your OS perform, the more it consumes your battery life. I am not particularly knowledgable in handheld devices, but I reckon the same principles in PC's apply here. Graphics, for example, consumes great amount of power. So, if you want your battery to last longer, choose an OS that doesn't have too much graphic effects on buttons, backgrounds, etc. You will have to sacrifice some features and display quality for extra battery life.
the relation between battery life mostly depends on the usage and Software/Hardware compatibility with the OS. battery is sophisticated peripheral attached to laptop/smart phone/tabs.many software are capable of monitoring system resources and how to control those resources so that the battery life gets little bit upper hand.as i mansion it depends on the usage ,like more application/WIFI/start up programs loaded in the ram will drain battery.
Thanks For Reading,
Ahmed.
Yes OS plays important role in saving power and the best example is Android OS whose basic concept was to save power.
i think OS can't affect the battery performance of a device, but number of programs on the OS can effect.
The size of OS won't affect it too.
There is a dependence on power in your device battery for the OS to run and I would think this is not a huge issue. If ever there is a difference in power consumption for different kinds of OS's, it shouldn't be too huge a difference as each of these companies have this under consideration when developing their products.
As it is said that, no any operating system can work without power. So, battery is also one of the useful resource that can give power to OS. thats why, researcher trying to solve the problem "with minimum consumption of power maximum work can be done" . so there is a relation ship between power and OS, and battery is one who provides power and can recharge through sun light.