Thevenin’s Theorem Thevenin’s Voltage and Resistance

Thevenin’s Theorem is a process of circuit analysis. It converts a comparatively complicated active circuit to a simplified form. According to Thevenin’s Theorem, we can consider an entire two-port circuit network as an ideal voltage source in series with a resistance.  Usually, we refer to the open circuit voltage between the ports of the circuit as Thevenin’s voltage.  This is the open circuit voltage of the imaginary source. On the other hand, the equivalent resistance of the circuit between the ports is Thevenin’s resistance. We take this resistance in series with the voltage source.

Leon Charles Thevenin
Léon Charles Thévenin

Explanation of Thevenin’s Theorem

The explanation of Thevenin’s Theorem is quite simple. If we think in a little bit deeper we can easily understand it. Suppose we have an active network or circuit as shown below as a block only.

linear active network

Thevenin’s Voltage

As it is an active network, it causes a certain voltage and current in each branch of the network. Now let us consider a certain branch of the network. Obviously, the rest of the network imposes a certain voltage across the branch. First, we remove that branch from the network. Then, we measure the voltage across the terminals of the network from where we have removed the branch. Therefore, we get the open circuit voltage. This is the Thevenin’s Voltage of the network with respect to those two terminals. For example, as shown in the figure below, we have measured the Thevenin’s voltage of 3.00 volts.

Thevenin's Voltage
Thevenin’s Voltage

Thevenin’s Resistance

Secondly, we measure the resistance of the network across those opened terminals. We need to measure the terminal resistance after replacing all the sources of the network with their internal resistance. This measurement, here in the example, is of 9.80 Ω as shown below. Thus, we get the equivalent resistance of the network with respect to those two terminals. This is the Thevenin’s Resistance of the network with respect to these two terminals.

Thevenin's Resistance
Thevenin’s Resistance

Thirdly, we connect one battery of emf equal to that Thevenin’s Voltage (3.00 volts) across the already separated branch of the network. The internal resistance of the source is as same as the Thevenin’s Resistance (9.80 Ω). This gives the same effect on the branch as the active network did. Therefore, we can replace the entire circuit or network with a single voltage source.

Thevenin's Circuit

Example of Thevenin’s Theorem

Let’s understand Thevenin’s Theorem with a general circuit given below. Here we will have to calculate the current through the resistance RL.

For that, we first remove the resistance RL from the rest of the circuit.

Now by applying some circuit analysis method, we have to calculate the open circuit voltage between A and B. This open circuit voltage is Thevenin’s Voltage.

Now we replace all the sources of the circuit by their internal resistance. If the sources drawn on the circuit are ideal, then we can replace each of the voltage sources with a short circuit and each of the current sources with an open circuit. Since the internal resistance of an ideal voltage source is zero and that of a current source is infinity. Although in this circuit, we do not have any current source. After replacing all the sources by their internal resistance we have to calculate the equivalent resistance of the circuit across the terminals. That would be Thevenin’s Resistance.

After that, we shall draw a voltage source of Thevenin’s Voltage and the Thevenin’s Resistance in series with it. Then we connect the load resistance RL across the source with series resistance.

Finally, from this simplified single loop circuit we can easily find out the current through RL and that would be 10 V/(2 + 8) Ω = 1 A.

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