Thevenin's Theorem
Thevenin's Theorem states that any linear electrical network with voltage sources, current sources, and resistances can be replaced by an equivalent circuit consisting of a single voltage source (V_th) in series with a single resistance (R_th). This simplification makes it much easier to analyse the behaviour of a load connected to a complex network, as only the terminal behaviour matters. It is widely used in circuit design, power systems, and electronics to simplify analysis without solving the full network repeatedly.
Key Formula
V_th = open-circuit voltage; R_th = V_oc / I_sc (open-circuit voltage divided by short-circuit current)
LaTeX: V_{th} = V_{oc}, \quad R_{th} = \frac{V_{oc}}{I_{sc}}
| Symbol | Meaning | Unit |
|---|---|---|
| V_{th} | Thevenin equivalent voltage (open-circuit voltage at terminals) | Volt (V) |
| R_{th} | Thevenin equivalent resistance (seen from terminals with sources deactivated) | Ohm (Ω) |
| V_{oc} | Open-circuit voltage across the terminals | Volt (V) |
| I_{sc} | Short-circuit current through the terminals | Ampere (A) |
Worked Example
Problem
A circuit has a 10 V source in series with a 4 Ω resistor, and a parallel 6 Ω resistor across the output terminals. Find the Thevenin equivalent.
Solution
Step 1: Find V_th (open-circuit voltage across terminals). The 6 Ω is the load; with it removed, V_oc = voltage across the 6 Ω in the original network. Using voltage divider with 4 Ω and 6 Ω: V_oc = 10 × 6/(4+6) = 6 V. Step 2: Find R_th (deactivate the 10 V source → replace with short). R_th = 4 Ω ∥ 6 Ω = (4×6)/(4+6) = 24/10 = 2.4 Ω. Step 3: Thevenin equivalent: 6 V source in series with 2.4 Ω.
Answer
V_th = 6 V, R_th = 2.4 Ω
Steps to Find the Thevenin Equivalent Circuit
| Step | Action | Method | Result |
|---|---|---|---|
| 1 | Identify terminals | Remove the load (open circuit) | Terminals A and B exposed |
| 2 | Find V_th | Calculate open-circuit voltage at A–B | V_th in Volts |
| 3 | Deactivate sources | Replace voltage sources with short, current sources with open | Passive network remains |
| 4 | Find R_th | Calculate resistance seen from A–B | R_th in Ohms |
| 5 | Build equivalent | V_th in series with R_th | Thevenin equivalent circuit |
| 6 | Reconnect load | Attach load to equivalent circuit | Analyse load behaviour easily |
Interactive Tools
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Related Terms
Norton's Theorem
Norton's Theorem states that any linear electrical network can be replaced by an equivalent circuit consisting of a single current source (I_N) in parallel with a single resistance (R_N). It is the dual of Thevenin's Theorem and is particularly convenient when analysing circuits where current distribution is of primary interest. Norton and Thevenin equivalents are interconvertible, and choosing between them depends on whether the circuit is better suited to series or parallel analysis.
Superposition Theorem
The Superposition Theorem states that in any linear circuit with multiple independent sources, the response (voltage or current) at any element equals the algebraic sum of the responses caused by each independent source acting alone, with all other independent sources deactivated. Voltage sources are deactivated by replacing them with short circuits, while current sources are deactivated by replacing them with open circuits. This theorem greatly simplifies the analysis of circuits with multiple sources and applies only to linear systems.
Kirchhoff's Voltage Law
Kirchhoff's Voltage Law (KVL) states that the algebraic sum of all voltages around any closed loop in a circuit equals zero. This principle is a direct consequence of the conservation of energy — as a charge traverses a complete loop, the energy gained from sources equals the energy lost across resistances. KVL is fundamental for analysing series circuits, mesh analysis, and determining unknown voltages in complex networks.
Named after Léon Charles Thévenin (1857–1926), a French telegraph engineer who published the theorem in 1883. The theorem was independently discovered by Hermann von Helmholtz in 1853. "Theorem" comes from Greek "theorema" meaning a proposition proved by reasoning.