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Circuit theory

Thevenin's theorem

  1. What is the Thevenin method? - definition and application
  2. Steps of the Thevenin method - procedure algorithm
  3. Video - explanation of the method
  4. Examples of application of the method
    • Example 1 - calculating current in a branch

What is the Thevenin method?

metoda thevenina
Fig. 1. Diagram illustrating the Thevenin method

Thevenin's theorem, also known as the theorem of the equivalent voltage source, sounds quite complicated at first, but its application will prove to be very simple when we see it in an example.

We will not delve too deeply into the theory behind this theorem; in a significant simplification, it states that:

A stationary, linear, and focused electrical circuit can be replaced by a circuit consisting of an ideal voltage source (Thevenin source) and an impedance (resistor in direct current circuits).

Importantly, this method is used to calculate the current in a single branch of the circuit, so it is great for verifying calculations made by other methods and also simplifies many more advanced issues.

Steps of the Thevenin method

Steps of the method:

  1. We disconnect the branch from the circuit for which we want to calculate the current
  2. For the rest of the circuit, we calculate:
    1. Thevenin voltage
    2. Equivalent impedance (resistance) (compare -> equivalent resistance)
  3. We connect these elements to the examined branch and calculate the current in that branch

Video - explanation of the method

Example 1

Content

Using the Thevenin method, determine the current \(I_x\)

metoda thevenina przykład 1 schemat
Fig. 2. Circuit diagram - example 1

Data: \(R_1=10 \Omega, R_2=20 \Omega, R_3=30 \Omega, R_4=20 \Omega, E_1=130 V, E_2=120 V\)

Solution

Step 1 - We disconnect the branch from the circuit for which we want to calculate the current

metoda thevenina przykład 1 krok 1
Fig. 3. Circuit after disconnecting the examined branch

Step 2 - For the rest of the circuit, we calculate the Thevenin voltage

metoda thevenina przykład 1 krok 2
Fig. 4. Calculating the Thevenin voltage
$$ \begin{aligned} &I=\frac{E_2}{R_1+R_2+R_3}=2A\\ &E_T=-I \cdot R_3=-60V \end{aligned} $$

Step 3 - For the rest of the circuit, we calculate the equivalent impedance (resistance)

metoda thevenina przykład 1 krok 3
Fig. 5. Calculating the equivalent resistance
$$R_T=\frac{\left(R_1+R_2\right) \cdot R_3}{R_1+R_2+R_3}=15\Omega$$

Step 4 - We connect these elements to the examined branch and calculate the current in that branch

metoda thevenina przykład 1 krok 4
Fig. 6. Thevenin equivalent circuit with the examined branch
$$I_x=\frac{E_1+E_T}{R_T+R_4}=2A$$
Thevenin's theorem