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A tiny radioactive battery could keep your future phone running for 50 years
(www.techradar.com)
This is a most excellent place for technology news and articles.
A nuclear battery is not actually a battery, it's a generator. Trying to run something purely off a generator is stupidly inefficient because you'd need the output potential for the max load at all times even when on average the load is much lower. You absolutely want to pair a generator with a battery. Even power plants have batteries to store excess power.
If you think a little past the name misnomer it's obvious that this would work by pairing it with a smaller battery to handle spikes in usage. The end result is still the same though, you'd have a phone you'd never have to plug in.
What makes you think I didn't think past the name? If my phone had a generator it would have a 8hr sot/day limit, it'd need a not so small 1000mAh+ battery to balance out night/day usage difference and still wouldn't last an hour while gaming. That's not an upgrade for me