Picture a circuit consisting of a galvanic cell whose terminals are connected to a resistor. Within the galvanic cell, a chemical reaction occurs moving charges to increase their electric potential energy. The voltage of the battery tells us how many joules of potential energy are imparted to each coulomb of charge elevated. As the charge moves through the resistor, on its way back down the potential energy slope, it loses this potential energy, undergoing collisions with atoms in the resistor that lead to the production of heat. The rate at which the charge loses potential energy in the resistor is the power of the circuit.
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