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In a simple DC circuit, a battery creates a potential difference by a chemical process. This potential difference exerts a force on the free electrons present in the conductor inducing a current. When the current meets a resistor like a light bulb the energy of the current is converted into heat and light. When a battery runs out does this "chemical process" no longer have enough reactants to continue?

Also, when the current is converted into heat and light do the electrons in the current leave the system as heat and light? If so is it possible for a light in a circuit to go out before the battery's chemical process ends because the conductor simply ran out of electrons to convert into heat and light?

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yes, the electrochemical reaction stops when the reactants are spent. the electrons themselves do not leave the circuit when heat and light are emitted; it is the energy they carried that performs the work.

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