# 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

*R*, for five values of

_{L}*R*, assuming that

_{L}*R*R

_{1}._{2}. R

_{3}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 E*

_{0}, in series with a resistance R_{0}where,*E*= open circuited voltage between the two terminals.

_{0}*R*= 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.

_{0}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

*E*in series with resistance

_{0},*R*as shown in Fig. 1.24. The behavior at the terminals

_{0}*AB*and

*A'B'*is the same for the two circuits, independent of the values of

*R*, connected across the terminals.

_{L}#### ACTIVE CIRCUIT (Fig. 1.23), THEVENIN'S EQUIVALENT CKT. Fig. 1.24

### (i)**Finding E**_{0:}

_{0:}

**This is the voltage between terminals**

*A*and

*B*of the circuit when load

*R*is removed. Fig. 125 shows the circuit with load removed. The voltage drop across

_{L},*R*

_{2}, is the desired

*voltage E*

_{0}Current through

*R*=

_{2}[caption id="attachment_5361" align="alignnone" width="180"] Thevenin's Theorem[/caption]

### (ii)**Finding ***R*_{0:}

*R*

_{0:}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*

*R*=parallel combination of R

_{0}_{1}, and R

_{2}, in series with R

_{3},

=

Thus, the value of

*R*is determined. Once the values of

_{0}*E*and

_{0}*R*, are determined, then current through the load resistance

_{0}*R*, can be found out easily (Refer to Fig. 1.24).

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