CIRCUIT THEORY-Thevenin theorem

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 circuit at its two terminals. Due to active sources in the circuit there is one potential difference between the points where the said branch is connected. The current through the said branch is caused by this potential difference appears across the terminals. So rest of the circuit can be considered as a single voltage source, whose 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 electrical resistance of the circuit looking back into the terminals where the branch is connected. So the Thevenin theorem can be stated as follows,

1) When a particular branch is remove from a circuit, the open circuit voltage appears across the terminals of the circuit, is Thevenin equivalent voltage and,

2) The equivalent resistance of the circuit network looking back into the terminals, isThevenin equivalent resistance.

3) 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.

For better understanding Thevenin theorem, we have shown the circuit below,

Here two resistors R1 and R2 are connected in series and this series combination is connected across one voltage source of emf E with internal resistance Ri as shown. One resistive branch of RL is connected across the resistance R2 as shown. Now we have to calculate the current through RL.

First we have to remove the resistor RL from the terminals A and B.

Second we have to calculate the open circuit voltage or Thevenin equivalent voltage VT across the terminals A and B.

The current through resistance R2,

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 Ri. Now view the circuit inwards from the open terminals A and B. It is found the circuits now consists of two parallel paths - one consisting of resistance R2 only and the other consisting of resistance R1 and Ri in series.

Thus the Thevenin equivalent resistance RT as viewed from the open terminals A and B is given as. As per Thevenin theorem when resistance RL is connected across terminals A and B the network behaves as a source of voltage VT and internal resistance RT and this is called Thevenin equivalent circuit. The current through RL is given as,

Thevenin Equivalent Circuit