---
title: "Thevenin and Norton duality"
subject: "Basic Electrical Engineering"
chapter: 3
key: "semester_1/basic_electrical_engineering:thevenin-norton-dual"
source: https://www.bctengineer.com/q/semester_1/basic_electrical_engineering/thevenin-norton-dual
site: BCT Engineering
---

# Thevenin and Norton duality

Basic Electrical Engineering · Chapter 3: Network Theorems

- Asked in: 2070 Asar, 6 marks
- Video: [Norton's Theorem and Thevenin's Theorem - Electrical Circuit Analysis](https://www.youtube.com/watch?v=-kkvqr1wSwA) — 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/thevenin-norton-dual
- Whole chapter: https://www.bctengineer.com/md/semester_1/basic_electrical_engineering/chapter-3

## Question

"Thevenin's theorem and Norton's theorem are dual of each other". Justify the statement with suitable example.

## Short answer

Thevenin’s series voltage source with Rth is dual to Norton’s parallel current source with RN, where Vth = IN × RN and Rth = RN. For a 12 V, 4 Ω network, the Norton equivalent is 3 A in parallel with 4 Ω.

## Answer

#### The statement
Thevenin's theorem replaces a network by a voltage source V_th in series with R_th. Norton's theorem replaces the same network by a current source I_N in parallel with R_N. The two are **duals**: voltage and current, series and parallel are interchanged, and one can be converted into the other by source transformation.

```text
 Thevenin                      Norton
 o--[R_th]--o a                o---+------+---o a
   (V_th)                         (I_N)  [R_N]
 o---------o b                 o---+------+---o b
```

#### Justification
| Quantity | Thevenin | Norton |
|---|---|---|
| Source | voltage source V_th | current source I_N |
| Resistance connection | R_th in series | R_N in parallel |
| Source value | open-circuit voltage | short-circuit current |
| Resistance | R_th | R_N = R_th |

Relations from the two equivalents (same terminal behaviour):
- I_N = V_th/R_th
- V_th = I_N R_N
- R_N = R_th

Because the two circuits give the same load current for every load, each can replace the other (source transformation).

#### Example
Network: 12 V source with 4 Ω in series, load R_L = 6 Ω across a-b.

- Thevenin: V_th = 12 V, R_th = 4 Ω. I_L = 12/(4 + 6) = 1.2 A.
- Norton: I_N = 12/4 = 3 A, R_N = 4 Ω. I_L = 3 × 4/(4 + 6) = 1.2 A.

The load current is the same, and V_th = I_N R_N = 3 × 4 = 12 V confirms the duality.

## Check yourself

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

1. Which pairing correctly shows the duality between Thevenin and Norton equivalents?
   A. Current source with R_th in series <-> voltage source with R_N in parallel
   B. Voltage source with R_th <-> voltage source with R_N
   C. Voltage source in series with R_th <-> current source in parallel with R_N
   D. Voltage source in parallel with R_th <-> current source in series with R_N
   Answer: C. Thevenin uses a voltage source with a series resistance, Norton uses a current source with a parallel resistance; voltage/current and series/parallel are interchanged. (Key point: Duality of the two theorems)

2. In the Thevenin and Norton equivalents, what do V_th and I_N represent?
   A. Both are the load-current values
   B. Both are the open-circuit values
   C. V_th is the short-circuit voltage and I_N the open-circuit current
   D. V_th is the open-circuit voltage and I_N the short-circuit current
   Answer: D. V_th is measured with the terminals open and I_N with the terminals shorted. (Key point: Source values)

3. Which set of relations links the two equivalents?
   A. I_N = V_th/R_th, V_th = I_N R_N and R_N = R_th
   B. I_N = V_th + R_th and R_N = R_th/2
   C. I_N = R_th/V_th and R_N = 2 R_th
   D. I_N = V_th R_th and R_N = 1/R_th
   Answer: A. Same terminal behaviour requires I_N = V_th/R_th, V_th = I_N R_N, and R_N = R_th. (Key point: Conversion relations)

4. A 12 V source with 4 ohm in series feeds a 6 ohm load. What is the Norton equivalent and the load current?
   A. I_N = 3 A, R_N = 6 ohm, I_L = 1.5 A
   B. I_N = 12 A, R_N = 4 ohm, I_L = 3 A
   C. I_N = 3 A, R_N = 4 ohm, I_L = 1.2 A
   D. I_N = 2 A, R_N = 4 ohm, I_L = 0.8 A
   Answer: C. I_N = 12/4 = 3 A, R_N = 4 ohm; the load takes 3 x 4/(4+6) = 1.2 A, equal to the Thevenin result 12/10. (Key point: Example check)

## Related in Basic Electrical Engineering

- [Norton theorem steps and comparison](https://www.bctengineer.com/question.md?key=semester_1%2Fbasic_electrical_engineering%3Anorton-theorem-steps-compare-thevenin) — Basic Electrical Engineering, chapter 3
- [Norton theorem with example](https://www.bctengineer.com/question.md?key=semester_1%2Fbasic_electrical_engineering%3Astate-explain-nortons-theorem) — Basic Electrical Engineering, chapter 3, asked 2×
- [Power in 3Ω using Norton theorem](https://www.bctengineer.com/question.md?key=semester_1%2Fbasic_electrical_engineering%3Anorton-power-3-ohm-20v-10a) — Basic Electrical Engineering, chapter 3
- [Power in 3Ω using Norton theorem (10 V, 10 A)](https://www.bctengineer.com/question.md?key=semester_1%2Fbasic_electrical_engineering%3Anorton-power-3-ohm-10v-10a-1-ohm) — Basic Electrical Engineering, chapter 3
- [Power in 5Ω using Norton theorem (2 A, 10 V)](https://www.bctengineer.com/question.md?key=semester_1%2Fbasic_electrical_engineering%3Anorton-power-5-ohm-2a-10v) — Basic Electrical Engineering, chapter 3
- [Thevenin theorem with example](https://www.bctengineer.com/question.md?key=semester_1%2Fbasic_electrical_engineering%3Astate-explain-thevenin-theorem) — Basic Electrical Engineering, chapter 3

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