The liquid’s undergoing a chemical reaction. The chemical reaction picks up electrons from one end of the battery and drops them at the other end.
When the battery’s disconnected, the chemical reaction builds up electrons to a certain level, then stops. It stops because the “back-pressure” of the built-up electrons doesn’t allow new ones to be deposited (like charges repel, which means as negatively charged electrons build up in a localized area, it gets harder and harder to force more electrons into that area).
When you connect the terminals (by putting the battery in a circuit), the built-up electrons can flow (through any devices in the circuit). This eases off the “back-pressure” which lets the chemical reaction continue (until the ingredients are used up, which is when the battery “dies”).
Some kinds of batteries use a chemical reaction that can be run backwards. If you use an external power source to force electrons to flow in the opposite direction, it causes the reverse chemical reaction to happen and re-generate the original ingredients. This is how rechargeable batteries work.
The composition of a battery can hold electrical energy charge. Therefore, if you insert two pieces of metal on a lemon, you will get some electricity.
The same works for a lithium ion battery. It is a dry cell battery, meaning that it has no liquids inside. There is a long strip of lithium (it is rolled up inside the battery. That is where electricity is stored, and it gets the electricity by attaching metal conductors on each end.
Imaging having a long tube filled with water placed horizontally, if you were asked to make current, a smart way to do it is by raising one side of the tube so that it flows to the other direction. And that’s how batteries work they raise the voltage on one side so that electrons can flow to the other side.
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