Thevenin Equivalent Calculator
Compute Vth and Rth for standard voltage divider circuits
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Vs
R1
R2
A
B
Topology: Voltage Source (Vs) in series with R1, connected to load resistor R2 (parallel).
Output is across terminals A and B (across R2).
Output is across terminals A and B (across R2).
V
Ω
Ω
Please enter valid numeric values for all fields. Resistors must be non-negative.
Thevenin Equivalent Results
Thevenin Voltage (Vth):
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Thevenin Resistance (Rth):
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Norton Current (IN):
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(Short Circuit Current Isc)
What is Thevenin's Theorem?
Thevenin's Theorem is a fundamental principle in electrical engineering theory. It states that any linear electrical network containing only voltage sources, current sources, and resistances can be replaced at terminals A-B by an equivalent combination of a single voltage source (Vth) in a series connection with a single resistance (Rth).
This simplification is incredibly powerful for circuit analysis, allowing engineers to focus on how a load (connected between terminals A and B) interacts with the rest of the circuit without recalculating the entire network every time the load changes.
Formulas Used in This Calculator
This calculator assumes a standard voltage divider circuit topology where a voltage source ($V_s$) is in series with a resistor ($R_1$), and we are looking at the output across a parallel resistor ($R_2$).
Thevenin Voltage (Vth):
Vth = Vs × [ R2 / (R1 + R2) ]
Vth = Vs × [ R2 / (R1 + R2) ]
Thevenin Resistance (Rth):
Rth = (R1 × R2) / (R1 + R2)
Rth = (R1 × R2) / (R1 + R2)
Norton Current (IN):
IN = Vth / Rth
IN = Vth / Rth
How to Calculate Manually
To find the Thevenin equivalent of a circuit manually, follow these two main steps:
- Find Vth (Open Circuit Voltage): Remove the load resistor (if any) and calculate the voltage across the open terminals A and B. In our voltage divider configuration, this is simply the voltage drop across R2.
- Find Rth (Equivalent Resistance): Turn off all independent sources. Replace voltage sources with a short circuit (wire) and current sources with an open circuit. Then, calculate the total resistance looking back into terminals A and B. For the circuit above, shorting Vs places R1 and R2 in parallel.
Why is this important?
- Simplification: Reduces complex networks to a simple 2-component model.
- Load Analysis: Makes it easy to calculate voltage regulation and power transfer for varying loads.
- Maximum Power Transfer: The theorem is essential for determining the load resistance required to achieve maximum power transfer (which occurs when RLoad = Rth).
Example Calculation
Suppose you have the following circuit parameters:
- Source Voltage (Vs) = 24V
- Series Resistor (R1) = 100Ω
- Parallel Resistor (R2) = 300Ω
Step 1: Calculate Vth
Vth = 24 × (300 / (100 + 300)) = 24 × 0.75 = 18 V
Step 2: Calculate Rth
Rth = (100 × 300) / (100 + 300) = 30000 / 400 = 75 Ω