Formula & Calculator
Thevenin's Theorem Equivalent Resistance
The equivalent resistance seen from a pair of terminals with all independent sources deactivated.
Interpretation
Thévenin's theorem: any linear circuit can be reduced to a single voltage source (V_TH) in series with a single resistance (R_TH).
R_TH is the ratio of the open‑circuit voltage to the short‑circuit current.
Example: V_oc=10V, I_sc=2A → R_TH = 10/2 = 5Ω.
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
Frequently Asked Questions
Thevenin's theorem states that any linear two-terminal network can be replaced by a voltage source V_TH in series with a resistance R_TH. R_TH is the resistance seen from the terminals with all independent sources deactivated.
Deactivate all independent sources (short voltage sources, open current sources) and compute the equivalent resistance between the terminals.
R_TH = V_OC / I_SC, where V_OC is the open-circuit voltage and I_SC is the short-circuit current at the terminals.
Keep dependent sources active and apply a test voltage (or current) at the terminals; compute R_TH = V_test / I_test.
It simplifies the circuit to a single voltage source and series resistance, making analysis of load variations easy.
Yes, using impedances instead of resistances and phasors for voltages and currents.
Maximum power is transferred when the load resistance equals R_TH.
It applies only to linear circuits. Non-linear circuits require piecewise linearization.
I_N = V_TH / R_TH and R_N = R_TH. The Norton current source is in parallel with R_N.
Common errors include: 1) incorrectly deactivating sources, 2) mixing up V_TH and I_SC, 3) using the wrong equivalent resistance, 4) applying to non-linear circuits, and 5) forgetting to include dependent sources correctly.