Norton Equivalent

Rn = Voc / Isc

Quick answer

This calculator solves Rn = Voc / Isc for Norton Resistance. With Open-Circuit Voltage 12 V, Short-Circuit Current 2 A, the result is 6 Ω. It solves in 3 directions, so you can enter the values you have and get the one you need.

Calculator

Norton Resistance (Ω)
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Formula

Rn = Voc / Isc

Description

Norton's theorem is the dual of Thévenin's theorem: any linear two-terminal circuit can be replaced by a current source (Isc) in parallel with a resistance (Rn). The Norton current equals the short-circuit current, and the Norton resistance equals the Thévenin resistance. Converting between Thévenin and Norton equivalents is straightforward: Vth = In × Rn, and the resistance is the same in both representations. Norton equivalents are often more convenient when analyzing parallel circuits or current-mode systems.

Variables

  • Rn — Norton equivalent resistance (Ω)
  • Voc — Open-circuit voltage (V), equal to In × Rn
  • Isc — Short-circuit (Norton) current (A)

Practical Notes

Current sources are less intuitive than voltage sources for many engineers, but Norton equivalents are natural for transistor modeling (the output of a BJT in active mode is well modeled as a current source). Current mirrors in analog ICs are described using Norton equivalent circuits. Source transformation between Thévenin and Norton is reversible and lossless.

Symbols and units

Symbol Meaning Default unit Accepted units
Rn Norton Resistance Ω mΩ, Ω, kΩ, MΩ
Voc Open-Circuit Voltage V pV, nV, µV, mV, V, kV
Isc Short-Circuit Current A pA, nA, µA, mA, A, kA

Step by step

  1. 1. What you know: Open-Circuit Voltage 12 V, Short-Circuit Current 2 A
  2. 2. The relation: Rn = Voc / Isc
  3. 3. Substitute: Voc = 12 V, Isc = 2 A
  4. 4. Result: Norton Resistance = 6 Ω

Related quantities from the same inputs

  • P = V × I = 24 W

Nearest standard component values

Series Nearest value Error
E12 5.6 Ω 6.7%
E24 6.2 Ω 3.3%

Worked examples

Minimum range

Given: Open-Circuit Voltage 0.33 V, Short-Circuit Current 2 mA

Result: Norton Resistance = 0.165 kΩ

Low range

Given: Open-Circuit Voltage 3.3 V, Short-Circuit Current 20 mA

Result: Norton Resistance = 0.165 kΩ

Typical

Given: Open-Circuit Voltage 12 V, Short-Circuit Current 2 A

Result: Norton Resistance = 6 Ω

High range

Given: Open-Circuit Voltage 0.23 kV, Short-Circuit Current 100 A

Result: Norton Resistance = 2.3 Ω

Maximum range

Given: Open-Circuit Voltage 2.3 kV, Short-Circuit Current 1 kA

Result: Norton Resistance = 2.3 Ω

Solving for each variable

Solve for Norton Resistance

Open-Circuit Voltage 0.33 V, Short-Circuit Current 2 mA → 0.165 kΩ

Solve for Open-Circuit Voltage

Norton Resistance 1 Ω, Short-Circuit Current 2 mA → 2 mV

Solve for Short-Circuit Current

Norton Resistance 1 Ω, Open-Circuit Voltage 0.33 V → 0.33 A

How Norton Resistance changes with Open-Circuit Voltage

Open-Circuit Voltage (input) Norton Resistance (result)
1.2 V 0.6 Ω
3 V 1.5 Ω
6 V 3 Ω
9 V 4.5 Ω
12 V 6 Ω
18 V 9 Ω
24 V 12 Ω
48 V 24 Ω
84 V 42 Ω
120 V 60 Ω

The same result in other units

Unit Value
mΩ 6000
Ω 6
kΩ 0.006

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Frequently asked questions

How do you calculate Norton Equivalent?

Use Rn = Voc / Isc. With Open-Circuit Voltage 12 V, Short-Circuit Current 2 A, Norton Resistance works out to 6 Ω.

What is the formula for Norton Equivalent?

The formula is Rn = Voc / Isc. Norton's theorem is the dual of Thévenin's theorem: any linear two-terminal circuit can be replaced by a current source (Isc) in parallel with a resistance (Rn).

How do you find Open-Circuit Voltage when you know the other values?

Rearrange for Open-Circuit Voltage: with Norton Resistance 1 Ω, Short-Circuit Current 2 mA, Open-Circuit Voltage is 2 mV.

How do you find Short-Circuit Current when you know the other values?

Rearrange for Short-Circuit Current: with Norton Resistance 1 Ω, Open-Circuit Voltage 0.33 V, Short-Circuit Current is 0.33 A.

What units does Norton Equivalent use?

Norton Resistance is shown in mΩ, Ω, kΩ. Values are held in SI base units internally, so you can mix prefixes without converting by hand.

Related Concepts

All Basic Electronics formulas →
Ohm's Law Electrical Power Voltage Divider Current Divider Thévenin Equivalent Norton Equivalent Temperature Coefficient of Resistance Kirchhoff's Voltage Law (KVL)

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