This instructable displays how to find a Thévenin equivalent circuit by eliminating all other current and voltage sources. Thévenin equivalence circuits contain one independent voltage source in series with a resistance and are equivalent to the original circuit from which they were formed. This instructable presents an example from the Electrical Engineering: Principles and Applications textbook and explains all of the steps a person must take to complete this task. After calculating all of the necessary components and designing the circuit, you will now have blueprints that can be used to construct the same circuit but with fewer parts. Calculating and designing the circuit should take no longer than 10 to 20 minutes to complete.
- A pencil
- Some paper
- A calculator
Teachers! Did you use this instructable in your classroom?
Add a Teacher Note to share how you incorporated it into your lesson.
Step 1: Step 1: Thévenin Equivalent Circuit Diagrams and Their Components
Circuit diagrams for Thévenin equivalent circuits will consist of one voltage source (Vt) and one resistance (Rt) with one current (Isc) flowing through the circuit, as shown above. The relationship between all of these components is also depicted by the above equation which will be used throughout this instructable to find the values of each individual component.
Step 2: Step 2: Identifying Parts of a Circuit Diagram
Circuit diagrams consist of multiple components and each one has its own value. The image above lists each of the components along with a depiction, to the left of each term, of how they appear on a circuit diagram. Use this list to help remember what components you will need to draw when completing this example.
Step 3: Step 3: Eliminating the Other Sources
When solving for this particular circuit, there is often a current source (represented by Is in the image above) which needs to be zeroed out by calculating the current flow throughout the entire circuit. Different parts of a circuit may have different current values depending on the resistance through which it flows.
Step 4: Step 4: Solving for the Thévenin Equivalent Current
In order to find the current for the Thévenin equivalent circuit (Isc), you should use all of the various currents to solve for it. The currents I1 and Is flow through one section of the circuit while I2 and Isc flow through another section; however, both combinations of currents are equal in value. I2 has a value of 0 A as the current flow through this resistor is negated once the current source is zeroed out. Use the relationship between these currents to determine the value of Isc. You can find the value of I1 by taking the source voltage (Vs) and dividing it by R1.
Step 5: Step 5: Parallel and Series Resistors in Thévenin Circuits
You can determine the Thévenin Resistance using the knowledge about the relationship between parallel and series resistors, as displayed in the above image. For the circuit used in the example, the two resistors are considered to be in parallel since the multiple currents flow through different series of the circuit.
Step 6: Step 6: Calculating the Thévenin Resistance
Since these resistors are in parallel, use the formula for solving total resistance to calculate the Thévenin equivalent resistance for the circuit.
Step 7: Step 7: Determinig the Thévenin Voltage
Now that you have determined the resistance and current of the Thévenin Equivalent Circuit, the last component you need to solve for is the Thévenin voltage. Use the same equation that you used to find I1 and replace those components with Rt and Isc to find the Thévenin voltage, Vt.
Step 8: Step 8: Drawing a Complete Thévenin Equivalent Circuit
You have now found all of your components for the Thévenin Equivalent Circuit, it is now time to draw the diagram for this circuit. Be sure to refer back to the image in step 1 so that you match each of components to the correct depiction. All Thévenin Equivalent Circuits consist of one voltage source and one resistor that is in series with the source. Although this circuit diagram looks significantly different from its original schematic, both circuits are still equivalent to each other. You should try and model your drawing after the ideal depiction of this circuit, which is shown in the diagram above.
Step 9: Step 9: Using This Diagram in the Real World
Now that you can calculate and design the Thévenin equivalent of a circuit that has more than one source, you can use these diagrams to construct a similar circuit to that of the original circuit, but with fewer components to construct the circuit with.