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Cell produces electric current as a result of the chemical reaction taking place between the positive and negative terminals and electrolyte
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More specifically: during a discharge of electricity, the chemical on the anode releases electrons to the negative terminal and ions in the electrolyte through what's called an oxidation reaction. Meanwhile, at the positive terminal, the cathode accepts electrons, completing the circuit for the flow of electrons.

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Batteries convert chemical energy directly to electrical energy. A battery consists of some number of voltaic cells. Each cell consists of two half-cells connected in series by a conductive electrolyte containing anions and cations. One half-cell includes electrolyte and the negative electrode, the electrode to which anions (negatively charged ions) migrate; the other half-cell includes electrolyte and the positive electrode to which cations (positively charged ions) migrate. Redox reactions power the battery. Cations are reduced (electrons are added) at the cathode during charging, while anions are oxidized (electrons are removed) at the anode during charging.[14] During discharge, the process is reversed. The electrodes do not touch each other, but are electrically connected by the electrolyte. Some cells use different electrolytes for each half-cell. A separator allows ions to flow between half-cells, but prevents mixing of the electrolytes.
Answer

The electrolyte is a chemical medium that allows the flow of electrical charge between the cathode and anode. When a device is connected to a battery — a light bulb or an electric circuit — chemical reactions occur on the electrodes that create a flow of electrical energy to the device.

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