Short answer: Yes, your phone does weigh a tiny bit more when fully charged.
Long answer: It’s a common misconception that a battery contains a reservoir of electrons, like a bucket full of water. Rather, batteries are a reservoir of energy, stored in chemical bonds between ions, which can be used to produce an electric current in a circuit. The number of particles in the phone doesn’t change from use.
So if there is the same amount of matter present in the battery, whether or not it is charged or dead, why does the battery weigh more when it’s charged?
The reason comes from general relativity. We know that E=mc2 – energy and mass are connected in some fundamental way – and we know a charged battery contains more energy than a dead one. Again, this doesn’t mean there is more mass or matter in your phone when it is charged, it just means that there is more stuff present for gravity to pull on, which makes the battery weigh more.
Gravity pulls on both mass and energy, so the weight is determined by the total mass and energy contained in the object. Since a charged battery contains a greater total amount of energy than a dead battery, the earth’s gravity will pull more strongly on it. However, the difference in weight is tiny. A 2000 mAh, 5 V battery contains about 36000 Joules of energy. If this energy were an equivalent mass (by E=mc2), then it’s not much more than a lone bacteria.
For comparison, if you could annihilate your phone (perhaps with an antimatter phone) to turn the matter into energy, you’d die because the resulting explosion would be as powerful as an atomic bomb. As far as batteries go, nothing stores energy quite as good as matter itself.
Watch the video below to find out more: