Thevenin's Equivalent Circuit Calculator
Enter the values for a simple circuit (voltage source Vs, resistors R1 and R2 forming a voltage divider) to find its Thevenin's equivalent looking into the node between R1 and R2 and ground.
Thevenin Voltage (Vth)
0.00 V
Intermediate Values:
Thevenin Resistance (Rth): 0.00 Ohms
Open Circuit Voltage (Voc): 0.00 Volts
Equivalent Resistance (Req): 0.00 Ohms
For this circuit (Vs in series with R1, then R2 to ground, looking into node between R1&R2 and ground):
Vth = Vs * (R2 / (R1 + R2))
Rth = (R1 * R2) / (R1 + R2)
Load Analysis with Thevenin's Equivalent
The table below shows the calculated load current and power for different load resistor (RL) values connected to the Thevenin equivalent circuit.
| Load Resistor (RL) (Ohms) | Load Current (IL) (mA) | Load Power (PL) (mW) |
|---|---|---|
| – | – | – |
Chart: Load Current (mA) vs. Load Resistance (Ohms)
What is Thevenin's Equivalent Circuit Calculator?
A Thevenin's Equivalent Circuit Calculator is a tool used to simplify a complex linear electrical circuit into a much simpler equivalent form. This equivalent circuit consists of a single ideal voltage source (Vth) in series with a single equivalent resistance (Rth). The calculator helps determine these two values, Vth and Rth, for a given circuit configuration viewed from two terminals.
Thevenin's theorem is incredibly useful in circuit analysis, especially when you want to analyze the behavior of a load connected to a complex network without re-analyzing the entire network every time the load changes. By using a Thevenin's Equivalent Circuit Calculator, you can quickly find the equivalent source and resistance, making it easier to calculate load current, voltage, and power.
This calculator is beneficial for electrical engineering students, technicians, and engineers who need to simplify circuits for analysis or design. It reduces a portion of a circuit to its simplest form, allowing for easier calculations and better understanding of the circuit's behavior at the terminals of interest.
A common misconception is that Thevenin's theorem can be applied to any circuit. However, it is only applicable to linear circuits, meaning circuits composed of resistors, capacitors, inductors, and linear dependent and independent sources.
Thevenin's Equivalent Circuit Formula and Mathematical Explanation
Thevenin's theorem states that any linear two-terminal circuit can be replaced by an equivalent circuit consisting of a voltage source (Vth) in series with a resistor (Rth).
- Finding Vth (Thevenin Voltage): Vth is the open-circuit voltage (Voc) at the two terminals (say A and B) where you want to find the Thevenin equivalent. To find it, you disconnect any load from terminals A and B and calculate the voltage across them. For our calculator's circuit (Vs in series with R1, then R2 to ground, looking into node and ground), Vth = Vs * (R2 / (R1 + R2)).
- Finding Rth (Thevenin Resistance): Rth is the equivalent resistance of the circuit looking back into terminals A and B, with all independent voltage sources short-circuited (replaced by a wire) and all independent current sources open-circuited (removed). For our calculator's circuit, shorting Vs means R1 and R2 are in parallel when viewed from the output node and ground: Rth = (R1 * R2) / (R1 + R2).
The simplified circuit is then Vth in series with Rth, connected to the terminals A and B where the load would be connected.
| Variable | Meaning | Unit | Typical Range |
|---|---|---|---|
| Vs | Source Voltage | Volts (V) | 0.1 V – 400 kV |
| R1, R2 | Resistance | Ohms (Ω) | 1 Ω – 10 MΩ |
| Vth (Voc) | Thevenin Voltage (Open-circuit Voltage) | Volts (V) | Depends on circuit |
| Rth (Req) | Thevenin Resistance (Equivalent Resistance) | Ohms (Ω) | Depends on circuit |
| RL | Load Resistance | Ohms (Ω) | 1 Ω – 1 MΩ |
| IL | Load Current | Amperes (A) or milliamperes (mA) | μA – kA |
Practical Examples (Real-World Use Cases)
Example 1: Simple Voltage Divider
Consider a circuit with Vs = 10V, R1 = 5 kΩ, and R2 = 15 kΩ. We want to find the Thevenin equivalent looking into the node between R1 and R2, and ground.
- Vth = 10V * (15000 / (5000 + 15000)) = 10 * (15/20) = 7.5 V
- Rth = (5000 * 15000) / (5000 + 15000) = 75000000 / 20000 = 3750 Ω (or 3.75 kΩ)
The equivalent circuit is a 7.5V source in series with a 3.75 kΩ resistor. If we connect a 10 kΩ load, the load current IL = 7.5 / (3750 + 10000) ≈ 0.545 mA.
Example 2: Analyzing a Sensor Interface
A sensor provides an output through a circuit that can be modeled with Vs = 5V, R1 = 2 kΩ, and R2 = 8 kΩ before being connected to a measurement device (the load). Using the Thevenin's Equivalent Circuit Calculator or formulas:
- Vth = 5V * (8000 / (2000 + 8000)) = 5 * (8/10) = 4 V
- Rth = (2000 * 8000) / (2000 + 8000) = 16000000 / 10000 = 1600 Ω (or 1.6 kΩ)
The sensor's output can be modeled as a 4V source with 1.6 kΩ internal resistance. This helps in understanding the loading effect when connecting the measurement device.
How to Use This Thevenin's Equivalent Circuit Calculator
- Enter Source Voltage (Vs): Input the voltage of the independent voltage source in your circuit segment.
- Enter Resistor R1: Input the resistance value of R1, which is in series with Vs.
- Enter Resistor R2: Input the resistance value of R2, which is connected from the node between R1 and the output to ground (for the circuit model used here).
- Calculate: Click the "Calculate" button or just change the input values. The calculator will automatically update Vth and Rth.
- Read Results: The calculator displays Vth and Rth, along with intermediate values.
- Analyze Load: The table and chart show how a load resistor (RL) connected to the Thevenin equivalent would behave, showing current and power for various RL values. This is useful for understanding maximum power transfer (when RL = Rth).
This Thevenin's Equivalent Circuit Calculator simplifies the process, but understanding the underlying circuit configuration it assumes is crucial for correct application.
Key Factors That Affect Thevenin's Equivalent Circuit Results
- Source Voltage (Vs): The magnitude of the independent voltage source(s) directly influences Vth. Higher Vs generally leads to higher Vth.
- Resistor Values (R1, R2, etc.): The values and configuration of resistors in the circuit determine both Vth (through voltage division or other interactions) and Rth (as they form the equivalent resistance).
- Circuit Topology: How the resistors and sources are connected (series, parallel, bridges) fundamentally defines Vth and Rth. This calculator assumes a specific simple topology.
- Presence of Dependent Sources: If the circuit contains dependent sources, the method to find Rth changes (Vth is still Voc, but Rth might require applying a test source). Our calculator assumes only independent sources for simplicity in Rth calculation via source shorting.
- Terminals of Interest: Vth and Rth are always defined with respect to two specific terminals in the circuit. Changing these terminals changes the equivalent circuit.
- Linearity of Components: Thevenin's theorem is valid only for linear circuits. Non-linear components (like diodes operating over a large range) invalidate the direct application.
Understanding these factors is key to correctly applying the Thevenin's Equivalent Circuit Calculator and interpreting its results.
Frequently Asked Questions (FAQ)
- What is Thevenin's theorem used for?
- It's used to simplify a linear circuit into a simple equivalent form (Vth and Rth) to easily analyze its behavior when different loads are connected across its terminals.
- Is Thevenin's theorem applicable to AC circuits?
- Yes, it is. For AC circuits, we use impedances (Z) instead of resistances (R), and Vth and Zth become phasors (complex numbers). The principle remains the same.
- What if there are multiple voltage or current sources?
- If there are multiple independent sources, Vth is found by superposition (sum of open-circuit voltages due to each source acting alone), and Rth is found by deactivating all independent sources (shorting voltage sources, opening current sources) and finding the equivalent resistance.
- How do you find Rth if there are dependent sources?
- If dependent sources are present, Rth cannot be found by simply shorting/opening independent sources. Instead, after finding Voc (Vth), you find the short-circuit current (Isc) between the terminals. Then Rth = Voc / Isc. Alternatively, deactivate independent sources, apply a test voltage (Vtest) at the terminals, find the current (Itest) it supplies, and Rth = Vtest / Itest.
- What is the difference between Thevenin and Norton equivalent circuits?
- Thevenin's equivalent is a voltage source (Vth) in series with a resistor (Rth). Norton's equivalent is a current source (In) in parallel with a resistor (Rn), where Rn = Rth and In = Vth / Rth. They are duals and can be converted from one to the other.
- When is maximum power transferred to the load?
- Maximum power is transferred from the Thevenin equivalent circuit to the load when the load resistance (RL) is equal to the Thevenin resistance (Rth). Our Thevenin's Equivalent Circuit Calculator results can help visualize this by looking at load power for RL near Rth.
- Can I use this calculator for any circuit?
- This specific Thevenin's Equivalent Circuit Calculator is designed for a simple circuit with one voltage source and two resistors in a voltage divider configuration, viewed from specific terminals. For more complex circuits, you need to apply the general principles of Thevenin's theorem manually or use more advanced simulation tools.
- Why is the open-circuit voltage equal to Vth?
- By definition, Vth is the voltage across the terminals when nothing is connected (open circuit). In the Thevenin equivalent (Vth in series with Rth), if the terminals are open, no current flows through Rth, so there's no voltage drop across Rth, and the terminal voltage is just Vth.
Related Tools and Internal Resources
- Norton's Equivalent Circuit Calculator: Find the Norton equivalent (current source and parallel resistance) of a circuit.
- Ohm's Law Calculator: Calculate voltage, current, resistance, or power using Ohm's Law.
- Voltage Divider Calculator: Calculate the output voltage from a simple voltage divider circuit.
- Series and Parallel Resistor Calculator: Calculate the equivalent resistance of resistors in series or parallel.
- Circuit Analysis Basics: An introduction to fundamental circuit analysis techniques.
- Maximum Power Transfer Theorem: Learn about the conditions for maximum power delivery to a load.