To find the Thevenin voltage in a circuit, we can follow simple steps. The Thevenin theorem helps us simplify complicated electrical circuits into a much easier version. This version has just one voltage source (called Thevenin voltage, $V_{TH}$) and one resistor (called Thevenin resistance, $R_{TH}$). Let’s break down how to find the Thevenin voltage in a straightforward way.

Steps to Find Thevenin Voltage

1. Identify the Part of the Circuit You Need

First, pick the two points in the circuit where you want to find the Thevenin equivalent. Let's label these points A and B.

2. Remove the Load

If there’s something connected between A and B (called a load), take it out. This helps us look at the rest of the circuit without it, making our calculations easier.

3. Find the Thevenin Voltage ($V_{TH}$)

Now, we need to discover the Thevenin voltage. There are two main methods to do this, but we will focus on the easier one called the open-circuit voltage method.

Open-Circuit Voltage Method

1. Open the Circuit: Make sure that points A and B are left open, meaning no current can flow through them. This way, we can check the voltage at A and B without anything connected.

2. Calculate Open-Circuit Voltage ($V_{OC}$): Next, we find the voltage across the open terminals A and B, which is our Thevenin voltage ($V_{TH}$). There are a few ways to do this:

   • Voltage Division: If it’s a simple circuit with resistors in a row, you can use the voltage division rule. This rule says:
   $$V_{out} = V_{in} \cdot \frac{R_{2}}{R_{1} + R_{2}}$$

   Here, $R_1$ is the resistor connected to the source, and $R_2$ is the resistor connected across A and B.

   • Nodal Analysis: For more complex circuits, you can use something called node voltage analysis. This involves creating equations from Kirchhoff’s current law to find the voltages near the open terminals.

   • Mesh Analysis: If the circuit has loops, you can make equations using Kirchhoff’s voltage law to solve for the voltage between the points.

3. Check for Dependent Sources: If there are special sources in your circuit that depend on other values, make sure you keep the load in place while finding $V_{TH}$. This is important because these sources depend on how the circuit behaves when the load is connected.

Example Calculation

Let’s look at a simple circuit with a 10V voltage source ($V_S$) connected to two resistors, $R_1 = 5 \Omega$ and $R_2 = 10 \Omega$. We want the Thevenin equivalent for points A and B across $R_2$.

1. Open Circuit A and B: Remove the load between A and B.

2. Use Voltage Division: Now let’s find the voltage across $R_2$, which is also our Thevenin voltage:

   $$V_{TH} = V_S \cdot \frac{R_2}{R_1 + R_2} = 10V \cdot \frac{10\Omega}{5\Omega + 10\Omega} = 10V \cdot \frac{10}{15} = \frac{100}{15} = 6.67V.$$

Final Thoughts

After you find the open-circuit voltage between A and B, you have the Thevenin voltage ($V_{TH}$). This voltage shows the maximum voltage that can be sent to a load connected to these points.

Once you know the Thevenin voltage, the next step is to find the Thevenin resistance ($R_{TH}$). This helps make analyzing circuits simpler, letting you add loads without dealing with the original circuit's complexity.

Summary of Steps

• Identify the terminals and take out the load.
• Open the circuit at those terminals.
• Calculate the open-circuit voltage using methods like voltage division or nodal analysis.
• If there are dependent sources, remember to include their effect.
• The voltage you find is your Thevenin voltage, $V_{TH}$.

Conclusion

Learning how to find the Thevenin voltage is an important skill in electrical engineering. It allows you to simplify complex circuit analysis and understand how circuits act with different loads. Whether it’s a simple circuit with resistors or a more complicated one with dependent sources, following these clear steps will help you analyze and design better circuits.