# ELECTRICAL STUDY MATERIAL | THEVENIN’S THEOREM

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THEVENIN’S THEOREM

This theorem is extensively used in networks when it is desired to determine the current through any element, or voltage across any element, without rigorous calculations required for solving a set of network equations.

Thevenin’s theorem states that any linear active bilateral network can be replaced by an equivalent circuit consisting of a voltage source in series with a resistance.

The voltage source is the open-circuit voltage across the open-circuited load terminals and the resistance being the internal resistance of the source network looking from the open-circuited load terminals.

Let us consider a simple circuit shown in Figure. (a) for the explanation of the Thevenin’s theorem to find the current through rL.

• Let us first remove the element rL from the circuit shown in Figure. (a). The circuit configuration then becomes as shown in Figure. (b). Now let us apply the following procedure: Figures: Application of thevenin’s theorem

• Here Voc is the voltage across resistance r2 since there is no current through r3. The current through r2 is given by   [from figure (b)] VTh is the Thevenin’s voltage.

• Next we will find the Thevenin’s resistance RTh . To find it , the voltage source is de-activated by a short circuit as the source does not have any internal resistance. The circuit shown in figure (c). Figure (c): The thevenin’s resistance RTh

Thus, • Next we will reconnect the load resistance rL across the terminals A-B. The circuit is shown in figure (d). Figure (d): The thevenin equivalent circuit

Therefore the current I through rL is given by

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