Thevenin's Theorem

Thevenin's Theorem

-States that"Any linear circuit containing several voltages and resistance can be replaced by just a single voltage in series with a single resistor".In other words, it is possible to simplify and Linear circuit, no matter how complex, to an equivalent circuit with just a single voltage source in series with a resistance connected to a load

Example:

as far as the load resistor RL is connected, any network consisting of resistive circuit elements and energy source can be replaced by one single Equivalent resistence Rs and equivalent voltage Vs, where Rs is the source resistance value looking back into the circuit and Vs is the open circuit at the terminals.

For example:

 Consider the circuit from the previous section

First, we have to remove the center 40Ω resistor and short out all the emf's connected to the circuit, or open circuit any current sources. the value of Rs is found by calculating the total resistance at the terminal A and B with the emf's removed, and the value of the voltage required Vs is the total voltage across terminals A and B with an open circuit and no load resistor Rs connected.then we get the following circuit.

We now need to reconnect the two voltages back into the circuit, and as Vs=Vab the current flowing around the loop is calculated as:

so the voltage drop across the 20Ω resistor can be calculated as:

Vab=20 - (20Ω x 0.33A)= 13.33V 

then the thevenins Equivalent circuit is shown below with the 40Ω resistor connected.

and from this current flowing in the circuit is given as:

I=(13.33V/6.67 + 40)=0.286A