Thevenin's Theorem states that any two-terminal network of resistors and voltage sources is equivalent to a single resistor in series with an ideal voltage source.

That is, any network of voltages and resistances with two terminals A and B connected to it, no matter how complicated, may be simplified to an equivalent circuit consisting of precisely one voltage source of VTh Volts in series with a resistance of RTh Ohms.

This circuit is the Thevenin Equivalent Circuit.
VTh is the Thevenin Equivalent Voltage.
RTh is the Thevenin Equivalent Resistance.

The Thevenin Voltage is the open circuit voltage accross terminals A and B.

The Thevenin Resistance is the quotient of the open circuit voltage and short circuit current at AB. Incidentially this is also the resistance seen at AB with all voltage sources replaced by short circuits. (The latter method is often more straightforward for finding RTh.)

Thevenin's Equivalent Circuit is often used to simplify more complex circuits in order to aid further analysis.

There is another theorem that allows you to do the same with an ideal current source in series with a resistance, this is Norton's Theorem.

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