Thevenin and Norton equivalent circuits are two ways to simplify a complex circuit into a simpler, equivalent circuit. Thevenin equivalent circuit reduces a complex circuit to an equivalent circuit that has a single voltage source in series with a resistor. Norton equivalent circuit, on the other hand, reduces a complex circuit to an equivalent circuit that has a single current source in parallel with a resistor.

In terms of when to use one theorem over the other, it often depends on the specific circuit and the desired analysis. If the circuit has many elements in series, it may be easier to use Thevenin's theorem to find the equivalent circuit. On the other hand, if the circuit has many elements in parallel, it may be easier to use Norton's theorem to find the equivalent circuit. Additionally, if the analysis requires determining the voltage across a load resistor, Thevenin's theorem may be more useful, while if the analysis requires determining the current through a load resistor, Norton's theorem may be more useful.
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