I have 3G mobile data plan on my smartphone. I also have a WiFi router in my home. I want to know which of these 2 can provide internet to my smartphone in the most battery efficient manner? Consider same amount of data transfer with same speed for comparison.
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Short answer: WiFi requires less energy than 3G.
Both WiFi and 3G waste energy right after completing a transfer. As the phone uses much more power than normally when transfering data, there is a short time after each transfer where the phone is still using a lot of power, even though there is no longer a need. This is unavoidable, but WiFi is significantly more efficient than 3G, so if you spend the same amount of time connected, using the network in the same way, your battery will drain faster with 3G.
Note that if you are using the phone where the 3G coverage is limited, your device will waste more energy constantly trying to connect. Same goes for WiFi.
Also, there is something I read about, that by keeping WiFi on all the time, you are actually keeping 3G off, so it increases battery life. From AndroidCentral:
This tip is one that seems counter-intuitive, but you can save a lot of wear and tear on your Android phone's battery if you tell it to keep the Wifi radio turned on and connected while the phone is sleeping. Your phone needs a lot of juice to keep pinging those cell towers, and even more to transmit data to and from them. Wifi radios use much less power because of their design, and they don't have to keep searching for a better access point. It's the way cellular data communication was designed, and it's a necessary evil.
But what if you're spending all day (or all evening) in one place, connected to Wifi? If you tell your phone to shut off Wifi when idle, it bounces back to cellular data (be it 2G, 3G, or 4G) and starts sucking down the electrons again when the screen shuts off. That's no good, and easy to fix:
Open the advanced Wifi settings by pressing the menu button, then Settings, Wireless & networks, Wi-Fi settings, and tapping the menu button again. You'll have a choice to either Scan, or go Advanced -- go Advanced. Tap the Wi-Fi sleep policy entry, and you'll get a pop up dialog with the choices you see in the picture above. Choose Never.
Now even when your phone goes into standby mode, you'll stay connected to Wifi and be able to get mail and messages without turning the cell radio back on and trouncing your battery life. And for the times when you're not in an area with a Wifi connection, just shut Wifi off, either through the menu or with a handy toggle widget. Your battery will thank you for it.