## Thevenin Theorem

This theorem is very conceptual. If we think deeply about an electrical circuit, we can visualize the statements made in **Thevenin theorem**. Suppose we have to calculate the electric current through any particular branch in a circuit. This branch is connected with rest of the circuits at its two terminal. Due to active sources in the circuit, there is one electric potential difference between the points where the said branch is connected. The current through the said branch is caused by this electric potential difference that appears across the terminals. So rest of the circuit can be considered as a single voltage source, that's voltage is nothing but the open circuit voltage between the terminals where the said branch is connected and the internal resistance of the source is nothing but the equivalent resistance of the circuit looking back into the terminals where, the branch is connected. So the **Thevenin theorem** can be stated as follows,

- When a particular branch is removed from a circuit, the open circuit voltage appears across the terminals of the circuit, is
**Thevenin equivalent voltage**and, - The equivalent resistance of the circuit network looking back into the terminals, is
**Thevenin equivalent resistance**. - If we replace the rest of the circuit network by a single voltage source , then the voltage of the source would be
**Thevenin equivalent voltage**and internal resistance of the voltage source would be**Thevenin equivalent resistance**which would be connected in series with the source as shown in the figure below.

To make Thevenin theorem easy to understand, we have shown the circuit below,

Here two resistors R_{1} and R_{2} are connected in series and this series combination is connected across one voltage source of emf E with internal resistance R_{i} as shown. One resistive branch of R_{L} is connected across the resistance R_{2} as shown. Now we have to calculate the current through R_{L}.

First, we have to remove the resistor R_{L} from the terminals A and B.

Second, we have to calculate the open circuit voltage or Thevenin equivalent voltage V_{T} across the terminals A and B.

The electric current through resistance R_{2},

Hence voltage appears across the terminals A and B i.e.

Third, for applying Thevenin theorem, we have to determine the Thevenin equivalent electrical resistance of the circuit, and for that; first we have to replace the voltage source from the circuit, leaving behind only its internal resistance R_{i}. Now view the circuit inwards from the open terminals A and B. It is found the circuits now consist of two parallel paths - one consisting of resistance R_{2} only and the other consisting of resistance R_{1} and R_{i} in series.

Thus the Thevenin equivalent resistance R_{T} is viewed from the open terminals A and B is given as. As per Thevenin theorem, when resistance R_{L} is connected across terminals A and B, the network behaves as a source of voltage V_{T} and internal resistance R_{T} and this is called Thevenin equivalent circuit. The electric current through R_{L} is given as,