Thevenin's Theorem

Thevenin's Theorem

 

Thevenin's Theorem

 


Thevenin's Theorem-Sometimes it is desirable to find a particular branch current in a circuit as the rest branch is varied while all other resistances and voltage sources remain constant. For instance, in the circuit shown in Fig. 1.23, it may be desire to find the current through RL, for five values of RL, assuming that R1. R2. R3 and E remain constant. In such situations, the *solution can be obtain readily by applying

Thevenin's theorem stated below:


Any two-terminal network containing a number of e.m.f. sources and resistances can be replace by an equivalent series circuit having a voltage source E0, in series with a resistance R0 where,

E0 = open circuited voltage between the two terminals.

R0 = the resistance between two terminals of the circuit obtained by looking "in" at the terminals with load removed and voltage sources replaced by their internal resistances, if any.

To understand the use of this theorem, consider the two terminal circuit shown in Fig. 1.23. The circuit enclosed in the dotted box can be replace by one voltage E0, in series with resistance R0 as shown in Fig. 1.24. The behavior at the terminals AB and A'B' is the same for the two circuits, independent of the values of RL, connected across the terminals.

ACTIVE CIRCUIT (Fig. 1.23), THEVENIN'S EQUIVALENT CKT. Fig. 1.24


 

(i)Finding E0:


 This is the voltage between terminals A and B of the circuit when load RL, is removed. Fig. 125 shows the circuit with load removed. The voltage drop across R2, is the desired voltage E0

Current through R2 =

[caption id="attachment_5361" align="alignnone" width="180"]Thevenin's Theorem Thevenin's Theorem[/caption]

 

(ii)Finding R0:


This is the resistance between terminals A and B with load removed and e.m.f. reduced to zero (See Fig. 1.26).

 

Resistance between terminals A and B is

R0=parallel combination of R1, and R2, in series with R3,

 

=

Thus, the value of R0 is determined. Once the values of E0 and R0, are determined, then current through the load resistance RL, can be found out easily (Refer to Fig. 1.24).

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