Thevenin Equivalent

A section of circuit involving current sources, voltage sources and resistors can always be replaced with a single battery in series with a single resistor with absolutely no affect on the rest of the circuit. We call this single battery and resistor combination the "Thevenin Equivalent" of the circuit section.

The thevenin equivalent voltage, written \(V_{th}\), is given by the voltage between the terminals a and b

The thevenin equivalent resistance, written \(R_{th}\), is found by pretending that terminal a is the positive side of a battery and terminal b is the negative side and replacing all other voltage sources with wires and all current sources with open circuits then finding the equivalent resistance from a to b.

A second method to find \(R_{th}\) is to connect a and b with a wire and find the current running through that wire and calling it \(I_{th}\) then \(R_{th} = \frac{V_{th}}{I_{th}}\)