It often occurs in practice that a particular element in a circuit is variable
(usually called the load) while other elements are fixed. As a typical
example, a household outlet terminal may be connected to different appliances
constituting a variable load. Each time the variable element is
changed, the entire circuit has to be analyzed all over again. To avoid this
problem, Thevenin's theorem provides a technique by which the fixed
part of the circuit is replaced by an equivalent circuit.
According to Thevenin's theorem, the linear circuit in Fig. 1(a)
can be replaced by that in Fig. 1(b). (The load in Fig. 1 may be a
single resistor or another circuit.) The circuit to the left of the terminals
a-b in Fig. 1(b) is known as the Thevenin equivalent circuit; it was
developed in 1883 by M. Leon Thevenin (1857 — 1926), a French telegraph
engineer.
Fig. 1: Replacing a linear two-terminal
circuit by its Thevenin equivalent: (a) original
circuit, (b) the Thevenin equivalent circuit.
Thevenin's theorem states that a linear two-terminal circuit can be replaced
by an equivalent circuit consisting of a voltage source $V_{Th}$ in series with
a resistor $R_{Th}$, where $V_{Th}$ is the open-circuit voltage at the terminals
and $R_{Th}$ is the input or equivalent resistance at the terminals when
the independent sources are turned off.
Our major concern right now is how to find the Thevenin equivalent voltage
