Thevenin Equivalent Resistance Calculator
Any linear circuit seen from two terminals behaves like a voltage source VOC in series with a resistance RTH. Divide the open-circuit voltage by the short-circuit current to get RTH. Enter any two of RTH, VOC and ISC and the third is solved. Then see the Norton equivalent and the power delivered to a load.
RTH = VOC / ISCPmax = VOC² / (4RTH)Step-by-step solution
Norton equivalent and load results
Find VOC, ISC and RTH from a circuit
A: VOC = VsR2/(R1+R2), RTH = R1 ∥ R2. B: RTH = (Vb − Va) / (Va/Ra − Vb/Rb), then VOC = Va(1 + RTH/Ra).
Thevenin and Norton equivalents
The two circuits give identical voltage and current at the terminals for any load.
Load power and efficiency versus RL
Reference data
| RL | VL | IL | PL | Efficiency |
|---|
| Source | Typical RTH | Note |
|---|---|---|
| Car battery (12 V lead-acid) | 5 to 20 mΩ | Very stiff, delivers hundreds of amps |
| Fresh AA alkaline cell | 0.1 to 0.3 Ω | Rises as the cell discharges |
| 9 V alkaline battery | 1 to 3 Ω | Poor at high current |
| Function generator output | 50 Ω | Matched to 50 Ω cable |
| Bench power supply (regulated) | under 10 mΩ | Within the current limit |
| Piezo or high-impedance sensor | kΩ to MΩ | Needs a high-impedance input |
Values vary with temperature, state of charge and model. Your row is highlighted when the load equals RTH (maximum power point).
FAQ
What is Thevenin's theorem?
Any linear circuit with two output terminals can be replaced by a single voltage source VTH in series with a resistor RTH. VTH is the open-circuit terminal voltage and RTH is the resistance seen at the terminals with independent sources turned off.
Why is RTH = VOC / ISC?
Shorting the terminals makes the whole open-circuit voltage drop across RTH, so ISC = VOC/RTH. Rearranged, RTH = VOC/ISC. This is a convenient measurement or calculation shortcut.
What is maximum power transfer?
A load takes the most power when RL = RTH. Then Pmax = VOC²/(4RTH), but the efficiency is only 50% because half the power is lost in the source resistance.
Is it safe to short-circuit a real source to measure ISC?
Often not. Batteries and supplies can overheat or fail. It is safer to measure the voltage across two known loads (method B above) and compute RTH from them.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| R_TH | Thevenin equivalent resistance | Ω |
| V_OC | Open-circuit voltage | V |
| I_SC | Short-circuit current | A |
What it means
Thévenin’s theorem simplifies any linear circuit to a single voltage source (V_TH) in series with a single resistance (R_TH). The Thévenin voltage V_TH is the open‑circuit voltage at the terminals. The Thévenin resistance R_TH is the equivalent resistance seen from the terminals with all independent sources turned off (voltage sources shorted, current sources opened). R_TH can also be found as the ratio V_TH / I_SC, where I_SC is the short‑circuit current. This theorem is invaluable for analyzing circuits with multiple sources and varying loads. It reduces a complex network to a simple series circuit, making it easy to determine the load current and voltage. The theorem is widely used in power systems, amplifier design, and signal processing. Example: If the open‑circuit voltage across the terminals is 10V and the short‑circuit current is 2A, then R_TH = 10V / 2A = 5Ω. The Thévenin equivalent is a 10V source in series with 5Ω.
Worked example
Thevenin's Theorem – Practical Example
Real‑World| Parameter | Value |
|---|---|
| VOC | 10 V |
| ISC | 2 A |
| Formula | RTH = VOC / ISC |
Common mistakes
- V_OC: Open‑circuit voltage across the terminals – not the voltage across a load.
- I_SC: Short‑circuit current – the current that flows when the terminals are shorted.
- R_TH: The ratio V_OC / I_SC – also the equivalent resistance with sources deactivated.
- Dependent sources: For R_TH, you cannot simply deactivate dependent sources – use a test source or compute V_OC/I_SC.
- Maximum power: R_TH is the load resistance that maximises power transfer (when R_L = R_TH).
Applications
Thévenin's theorem reduces any linear circuit to a single voltage source (V_TH) in series with a single resistance (R_TH). V_TH is the open‑circuit voltage, and R_TH is the resistance seen from the terminals. This theorem is a cornerstone of circuit analysis, enabling engineers to simplify networks for design and troubleshooting. It is used to analyse power supplies, to determine load voltage and current, and to design matching networks. By applying Thévenin's theorem, professionals can quickly assess the effect of changing loads without re‑analysing the entire circuit. It is also used in the calculation of maximum power transfer and in the design of operational amplifier circuits. Mastering Thévenin's theorem is essential for any electrical engineer.
- Network simplification for load analysis
- Design of voltage sources and regulators
- Maximum power transfer and impedance matching
- Fault analysis and circuit protection design
- Educational cornerstone of circuit theory
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