Everything in the computer will require some power, so adding more memory will shorten the battery life as Naples has pointed out. Something else to consider though is that if you have more RAM, the computer can load more data into memory and will use the hard drive less. As the hard drive is mechanical, it can easily use more power than RAM. More RAM also means that the OS wil not need to use virtual memory as much, which again means less use of the hard drive.
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