Thevenin Theorem

    Thevenin Theorem

It provides a mathematical technique for replacement a given network, as viewed from 2 output terminals, by one voltage supply with a series resistance.  It makes the answer of sophisticated networks (particularly, electronic networks) quite fast and straightforward. the appliance of this extraordinarily helpful theorem are going to be explained with the assistance of the subsequent easy example.

Suppose, it's needed to seek out current flowing through load resistance RL, as shown in Fig. 2.127 (a). we'll proceed as underneath :

           1. take away RL from the circuit terminals A and B and redraw the circuit as shown in Fig. 2.127 (b).  Obviously, the terminals became open-circuited. 

           2. Calculate the open-circuit voltage Voc that seems across terminals A and B after they square measure open i.e. once RL is removed. As seen, Voc = drop across R2 = IR2 wherever I is that the circuit current once A and B square measure open.

         3. Now, imagine the battery to be far from the circuit, effort its internal resistance r behind and redraw the circuit, as shown in Fig. 2.127 (c). once viewed inwards from terminals A and B, the circuit consists of 2 parallel methods :  one containing R2 and also the different containing (R1 + r).   The equivalent resistance of the network, as viewed from these terminals is given as

 This resistance is additionally known as,* Thevenin resistance Rsh (though, it's conjointly generally written as RI or R0).
    Consequently, as viewed from terminals A and B, the entire network (excluding R1) will be reduced to one supply (called Thevenin’s source) whose e.m.f. equals V? (or Vsh) and whose internal resistance equals Rsh (or Ri) as shown in Fig. 2.128.

        4. RL is currently connected back across terminals A and B from wherever it had been briefly removed earlier. Current flowing through RL is given by

 it's clear from on top of that any network of resistors and voltage sources (and current sources as well) once viewed from any points A and B within the network, will be replaced by one voltage supply and one resistance** nonparallel with the voltage supply.

After this replacement of the network by one voltage supply with a series resistance has been accomplished, it's simple to seek out current in any load resistance joined across terminals A and B.  This theorem is valid even for those linear networks that have a nonlinear load.

Hence, Thevenin’s theorem, as applied to d.c. circuits, is also expressed as underneath :

The current flowing through a load resistance RL connected across any 2 terminals A and B of a linear, active bilateral network is given by Voc || (Ri + RL) wherever Voc is that the open-circuit voltage (i.e. voltage across the 2 terminals once RL is removed) and RI is that the internal resistance of the network as viewed back to the open-circuited network from terminals A and B with all voltage sources replaced by their internal resistance (if any) and current sources by infinite resistance.

* when the French engineer M.L. Thevenin (1857-1926) United Nations agency whereas operating in Telegraphic Department printed an announcement of the concept in 1893.
** Or resistivity within the case of a.c. circuits.