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Batteries transform chemical energy into electrical energy.
There are many different types of batteries, but all have three basic components: positive electrode (cathode, or "positive terminal"), negative electrode (anode or "negative terminal"), and electrolyte.
When the positive and negative terminals are connected so that electrons (electricity) can flow between them (usually by a wire), chemical reactions occur at the electrodes. These reactions release excess electrons at the anode which flow to the cathode.
The chemical reactions occur between the electrolyte and the cathode and between the electrolyte and the anode. Different types of batteries use different materials for the these three components.
Disposable batteries (batteries that can't be recharged) work until the reactive chemistry of the electrodes and electrolytes is exhausted.
In a battery that is re-chargeable, electricity can be applied to run the process in reverse, restoring the properties of the materials so that electricity-generating reactions will again recur. Car batteries are an example of re-chargeable batteries.
Batteries with a liquid electrolyte are called "wet cell." Lead-acid batteries (typical car battery) are wet cell. Batteries with a solid electrolyte are called "dry cell." Alkaline batteries used around the house are examples of dry cell.
Batteries make energy portable. In effect, they store electricity that can be delivered on demand, when and where it is needed.