---
title: "Steps to find Norton resistance"
subject: "Basic Electrical Engineering"
chapter: 3
key: "semester_1/basic_electrical_engineering:norton-equivalent-resistance-steps"
source: https://www.bctengineer.com/q/semester_1/basic_electrical_engineering/norton-equivalent-resistance-steps
site: BCT Engineering
---

# Steps to find Norton resistance

Basic Electrical Engineering · Chapter 3: Network Theorems

- Asked in: 2070 Asar, 4 marks
- Video: [Norton's Theorem Example Problem](https://www.youtube.com/watch?v=hyNtfEuH2ug) — ElectronX Lab
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_1/basic_electrical_engineering/norton-equivalent-resistance-steps
- Whole chapter: https://www.bctengineer.com/md/semester_1/basic_electrical_engineering/chapter-3

## Question

Write down the steps to calculate Norton's equivalent resistance in the circuit with a suitable example.

## Short answer

Remove the load, short-circuit independent voltage sources, open-circuit independent current sources, then find the equivalent resistance between the terminals. Example: for a 20 V source with 4 Ω and 6 Ω, RN = 4 Ω ∥ 6 Ω = 2.4 Ω.

## Answer

**Norton's equivalent resistance (R_N)** is the resistance seen from the two terminals of the network with all independent sources deactivated. It is found as follows.

#### Steps
1. Identify the two terminals (a, b) across which the Norton equivalent is required, and remove the load.
2. Replace every independent **voltage source by a short circuit**.
3. Replace every independent **current source by an open circuit**. (Dependent sources stay.)
4. Reduce the remaining resistors between a and b by series, parallel (or star-delta) rules. This single resistance is R_N (equal to R_th).
5. Connect R_N in parallel with the Norton current source I_N (the short-circuit current between a and b).

```text
 Step 2-3 (sources off)          Result
 o--+----[R1]----+--o a          o---+-------o a
    |            |                  [R_N]
   [R2]         [R3]                  |
    |            |                o---+-------o b
 o--+------------+--o b
```

#### Example
A 20 V source with R₁ = 4 Ω in series, R₂ = 6 Ω across the output terminals a-b.

- Turn the 20 V source off (short): R₁ = 4 Ω is now in parallel with R₂ = 6 Ω between a and b.
- R_N = 4 ∥ 6 = 4 × 6/10 = **2.4 Ω**

For the full Norton equivalent: short a-b, I_N = 20/4 = 5 A. So the equivalent is a 5 A source in parallel with 2.4 Ω. Open-circuit voltage = 5 × 2.4 = 12 V (check: 20 × 6/10 = 12 V).

## Check yourself

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

1. How is a voltage source treated for R_N?
   A. Replaced by a short circuit
   B. Open circuit
   C. Left in
   D. Doubled
   Answer: A. Independent voltage sources are shorted. (Key point: Voltage sources)

2. How is a current source treated?
   A. Short circuit
   B. Replaced by an open circuit
   C. Left in
   D. Replaced by 1 ohm
   Answer: B. Independent current sources are opened. (Key point: Current sources)

3. What happens to dependent sources?
   A. Shorted
   B. Opened
   C. They stay in the circuit
   D. Doubled
   Answer: C. Only independent sources are deactivated. (Key point: Dependent sources)

4. In the 20 V, 4 ohm, 6 ohm example, what is R_N?
   A. 10 ohm
   B. 24 ohm
   C. 5 ohm
   D. 4 || 6 = 2.4 ohm
   Answer: D. With 20 V shorted, 4 and 6 ohm are in parallel. (Key point: Example)

## 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
- [Star-delta equivalent resistance A to B](https://www.bctengineer.com/question.md?key=semester_1%2Fbasic_electrical_engineering%3Astar-delta-resistance-ab-6-4-3-5) — Basic Electrical Engineering, chapter 2
- [Equivalent resistance between A and B](https://www.bctengineer.com/question.md?key=semester_1%2Fbasic_electrical_engineering%3Aequivalent-resistance-24-8-8) — Basic Electrical Engineering, chapter 2
- [Equivalent resistance RAB, ladder network](https://www.bctengineer.com/question.md?key=semester_1%2Fbasic_electrical_engineering%3Aequivalent-resistance-rab-3-6-4-5-ohm) — Basic Electrical Engineering, chapter 2
- [Equivalent resistance and power in 5Ω](https://www.bctengineer.com/question.md?key=semester_1%2Fbasic_electrical_engineering%3Aequivalent-resistance-power-5-ohm) — Basic Electrical Engineering, chapter 2
- [Equivalent resistance between A and B](https://www.bctengineer.com/question.md?key=semester_1%2Fbasic_electrical_engineering%3Aequivalent-resistance-ab-3-4-4-4-1-3) — Basic Electrical Engineering, chapter 2

## Related in other subjects

- [IC manufacturing steps; top-down F = xz + y](https://www.bctengineer.com/question.md?key=semester_6%2Fembedded_system%3Aic-manufacturing-steps-topdown-xz-y) — Embedded System, chapter 8
- [Induction motor equivalent circuit from no-load and blocked rotor tests](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3Aim-noload-blocked-400v-equivalent) — Electrical Machines I, chapter 5
- [Equivalent circuit of 5 kVA 200/400 V transformer](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3Aoc-sc-5kva-200-400-primary) — Electrical Machines I, chapter 2, asked 2×
- [Equivalent circuit of 10 kVA 250/1000 V transformer](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3Aoc-sc-10kva-250-1000-primary) — Electrical Machines I, chapter 2, asked 2×