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You are here: Home / Basic Electronics / The Thevenin Theorem – A Simple Explanation

The Thevenin Theorem – A Simple Explanation

August 21, 2013 By Øyvind Nydal Dahl 8 Comments

The Thevenin Theorem explains how to simplify a complex circuit. It states that any linear circuit with only voltage sources, current sources and resistors can be simplified to a voltage source with a series resistor.

But what does this really mean?

Sometimes a picture says more than thousand words, so here are two pictures to explain what Thevenin’s Theorem is about.

This circuit…

Thevenin theorem step 1
By SteveZodiac [GFDL or CC-BY-SA-3.0], via Wikimedia Commons

…can be represented by this simple circuit

Thevenin equivalent circuit
By SteveZodiac [GFDL or CC-BY-SA-3.0], via Wikimedia Commons

How to use Thevenin’s Theorem

To get from the complex circuit to the simple Thevenin equivalent we:

  1. Calculate the Thevenin equivalent voltage between terminals A-B open circuited
  2. Calculate the Thevenin equivalent resistance between terminals A-B with all current sources open circuited and all voltage sources short circuited

Finding the Thevenin Equivalent Voltage

First we’ll find the equivalent voltage.

Finding Thevenin voltage
By SteveZodiac [GFDL or CC-BY-SA-3.0], via Wikimedia Commons

We see that R4 makes a voltage divider together with R3 and R2. Since R4 = R2 + R3 the voltage will be divided in half on the right side of R4.

Since A is not connected to anything, no current will pass through R1 and therefore no voltage drop will occur over R1. So terminal A is 7.5 V.

Finding the Thevenin Equivalent Resistance

Then, let’s find the equivalent resistance.

Finding thevenin resistance
By SteveZodiac [GFDL or CC-BY-SA-3.0], via Wikimedia Commons

First, we short-circuit the voltage source. This puts R4 in parallel with R2+R3. We calculate this and get 1k Ohm. This is in series with R1 (also 1k Ohm), so we get an equivalent resistance of 2k Ohms.

Then we put these two together and get the following Thevenin equivalent circuit:

Resulting Thevenin equivalent circuit
By SteveZodiac [GFDL or CC-BY-SA-3.0], via Wikimedia Commons

What do you use the Thevenin equivalent circuit for?

The Thevenin theorem is really useful for doing calculations with circuits. If you have a complex circuit, you can simplify it and make calculations much easier.

But, I have to admit that I can’t remember ever having applied this outside of a classroom though ;)

Return from Thevenin’s Theorem to Electronic Schematics

Filed Under: Basic Electronics

Reader Interactions

Comments


  1. Anurag says

    July 1, 2015

    Dint unstand this….can u plz elaborate it….

    Reply

  2. David Deelstra says

    July 19, 2015

    This is in (should read “in series”) with R1 (also 1k Ohm), so we get an equivalent resistance of 2k Ohms.

    Reply

    • admin says

      July 21, 2015

      Thanks!

      Oyvind

      Reply

  3. king says

    October 8, 2018

    any example for dependent sources will be appreciated.

    Reply

  4. Madhu says

    January 10, 2019

    Hi,olyvind
    What is short circuit?

    Reply

  5. admin says

    January 14, 2019

    Hi Madhu,

    Check out this article:
    https://www.build-electronic-circuits.com/short-circuit/

    Best,
    Oyvind

    Reply

  6. lttruc682 says

    January 17, 2019

    When short-circuit the voltage source, why didn’t we get R2 in parallel with R4+R3?
    Sorry about my English!

    Thank you!

    Reply

  7. Thomas C. Anselm says

    December 13, 2020

    This doesn’t make sense. Since there is no voltage potential at A, you have a complete circuit through R2 then R3 and then R4 back to the power source. All of these are in series. So why is it not the sum of all three resisters or 4K ohms?

    Reply

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