---
title: "Thevenin theorem with example"
subject: "Basic Electrical Engineering"
chapter: 3
key: "semester_1/basic_electrical_engineering:state-explain-thevenin-theorem"
source: https://www.bctengineer.com/q/semester_1/basic_electrical_engineering/state-explain-thevenin-theorem
site: BCT Engineering
---

# Thevenin theorem with example

Basic Electrical Engineering · Chapter 3: Network Theorems

- Asked in: 2073 Chaitra, 4 marks
- Video: [Thevenin's Theorem - Circuit Analysis](https://www.youtube.com/watch?v=zTDgziJC-q8) — The Organic Chemistry Tutor
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_1/basic_electrical_engineering/state-explain-thevenin-theorem
- Whole chapter: https://www.bctengineer.com/md/semester_1/basic_electrical_engineering/chapter-3

## Question

State and explain thevenin's theorem with suitable example.

## Short answer

Thevenin's theorem states any linear two-terminal network can be replaced by a voltage source V_th in series with a resistance R_th, where V_th is open-circuit voltage and R_th is equivalent resistance with sources zeroed. It simplifies analysis when load varies, e.g., a network of 24V, 6Ω, 3Ω yields V_th=8V, R_th=2Ω, and load current is V_th/(R_th+RL).

## Answer

#### Statement
**Thevenin's theorem:** any linear two-terminal network containing sources and resistors can be replaced, as seen from its two terminals, by a **single voltage source V_th in series with a resistance R_th**.
- V_th = open-circuit voltage between the terminals (load removed).
- R_th = resistance between the terminals with all independent sources set to zero (voltage sources shorted, current sources opened).

```text
 Linear network           Thevenin equivalent
 o-------+------o a        o--[R_th]--+------o a
         |                    (V_th)  |  load
 (sources|                            |
  and R) |                            |
 o-------+------o b        o----------+------o b
```

#### Steps
1. Remove the load resistor and mark the two terminals.
2. Find V_th (open-circuit voltage) by any method.
3. Set all independent sources to zero and find R_th.
4. Connect the load to the equivalent: I_L = V_th/(R_th + R_L).

#### Example
A 24 V source feeds R₁ = 6 Ω in series, with R₂ = 3 Ω across the output terminals, and a load R_L = 4 Ω.

- V_th = 24 × 3/(6 + 3) = 8 V
- R_th = 6 ∥ 3 = 2 Ω
- I_L = 8/(2 + 4) = 1.333 A, V_L = 5.33 V

Check on the original circuit: R_total = 6 + (3 ∥ 4) = 7.714 Ω, I = 3.111 A, and the load receives 3.111 × 3/7 = 1.333 A. The results are the same.

It is useful when one branch (the load) changes while the rest of the network stays the same.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. What does Thevenin's theorem replace the network with?
   A. A voltage source V_th in series with R_th
   B. A current source in parallel with R
   C. A voltage source in parallel with R
   D. A single resistor
   Answer: A. V_th in series with R_th. (Key point: Statement)

2. How is V_th obtained?
   A. Short-circuit current
   B. Open-circuit voltage between terminals with load removed
   C. Source voltage
   D. Voltage across the load with load connected
   Answer: B. V_th is the open-circuit voltage. (Key point: V_th)

3. How is R_th found?
   A. Open voltage sources
   B. Divide V_th by load current
   C. Sources set to zero (voltage shorted, current opened), resistance across terminals
   D. Add all resistors
   Answer: C. Deactivate independent sources and look in. (Key point: R_th)

4. In the example (24 V, 6 ohm, 3 ohm, 4 ohm load), what is I_L?
   A. 4 A
   B. 2 A
   C. 8/4 = 2 A
   D. 8/(2 + 4) = 1.333 A
   Answer: D. V_th = 8 V and R_th = 2 ohm. (Key point: Example)

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