Thévenin Equivalent

Rth = Voc / Isc

Quick answer

This calculator solves Rth = Voc / Isc for Thévenin 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

Thévenin Resistance (Ω)
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Formula

Rth = Voc / Isc

Description

Thévenin's theorem states that any linear two-terminal circuit can be replaced by an equivalent voltage source (Voc) in series with a resistance (Rth). The Thévenin voltage equals the open-circuit voltage measured at the terminals, and the Thévenin resistance equals the open-circuit voltage divided by the short-circuit current. This simplification is invaluable for analyzing complex circuits when you only care about the behavior at a specific pair of terminals, such as determining maximum power transfer or load regulation.

Variables

  • Rth — Thévenin equivalent resistance (Ω)
  • Voc — Open-circuit voltage at the terminals (V)
  • Isc — Short-circuit current at the terminals (A)

Practical Notes

Maximum power transfer occurs when the load resistance equals Rth, delivering Voc²/(4×Rth) watts to the load. In practice, power supplies are designed with very low Rth for good voltage regulation, while signal sources may intentionally have 50Ω or 75Ω Thévenin impedance for impedance matching.

Symbols and units

Symbol Meaning Default unit Accepted units
Rth Thévenin 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: Rth = Voc / Isc
  3. 3. Substitute: Voc = 12 V, Isc = 2 A
  4. 4. Result: Thévenin 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: Thévenin Resistance = 0.165 kΩ

Low range

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

Result: Thévenin Resistance = 0.165 kΩ

Typical

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

Result: Thévenin Resistance = 6 Ω

High range

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

Result: Thévenin Resistance = 2.3 Ω

Maximum range

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

Result: Thévenin Resistance = 2.3 Ω

Solving for each variable

Solve for Thévenin Resistance

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

Solve for Open-Circuit Voltage

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

Solve for Short-Circuit Current

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

How Thévenin Resistance changes with Open-Circuit Voltage

Open-Circuit Voltage (input) Thévenin 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 Thévenin Equivalent?

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

What is the formula for Thévenin Equivalent?

The formula is Rth = Voc / Isc. Thévenin's theorem states that any linear two-terminal circuit can be replaced by an equivalent voltage source (Voc) in series with a resistance (Rth).

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

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

What units does Thévenin Equivalent use?

Thévenin 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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