This is the most extensively utilized theorem in circuit theory. Any of the circuit we have been working with may be viewed as a two terminal network thevenin's theorem provides us with simple way to develop an equivalent circuit of a two terminal network.
Sometimes it is needed to study the variation of current or voltage in a specific branch by varying the resistance of that branch whereas remaining network remains the same, for example designing of electronic circuit. At such places thevenin's theorem is quite suitable.
This theorem states that any two terminal network having energy sources and resistors may be replaced by on equivalent network consisting of a single source of emf and a series resistor, Rth. This emf Eth, is equal to potential difference among the terminals of the network, when the resistor, R, is eliminated. The resistance of the series resistor, Rth, is equal to the equivalent resistance of the network measured among the terminals, with the resistor, R, eliminated and all energy sources eliminated (but not their internal resistances) here, ideal independent voltage sources is replaced by short circuit and ideal independent current sources by open circuit.