Thevenin's theorem is a fundamental principle in electrical circuit analysis. It states that any linear electrical network containing voltage sources, current sources, and resistances can be replaced with an equivalent circuit comprising a single voltage source and a single series resistor. This equivalent circuit has the same voltage-current relationship at the load terminals as the original network.
In other words, a complex circuit can be simplified to a Thevenin equivalent circuit, which consists of a voltage source in series with a single equivalent resistance. The Thevenin voltage (V_th) is the open-circuit voltage across the load terminals of the original network, and the Thevenin resistance (R_th) is the equivalent resistance seen from the load terminals when all voltage and current sources within the network are turned off (replaced by their internal resistances).
The Thevenin equivalent circuit makes it easier to analyze and solve complex circuits, particularly in cases where only the behavior at the load terminals is of interest, and the internal details of the network are not necessary for the analysis.