# Equivalent voltage source

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### Thévenin's (voltage-source) equivalent circuit

Contents

Here we show how to convert any circuit with a voltage source and several resistors into an equivalent voltage source with only one internal resistor.

Thevenin’s theorem states that any linear circuit, no matter how complex, can be simplified to an equivalent circuit consisting of a single voltage source with only one internal series resistance.

Learning by doing. Here is a simple example:

#### Thévenin's (voltage-source) equivalent circuit – how to use it - example

What we want: To simplify the circuit in pic a and get an equivalent voltage source with only one internal resistor Req as shown in pic b:

Thévenin's (voltage-source) equivalent circuit – how to use it - example

Step 1: Determining the new source voltage Veq

The open-circuit voltage is the voltage that is tapped at terminals A and B when no load current is flowing. In this case, the open-circuit voltage corresponds to the voltage VR2, as no current flows via R3. The open-circuit voltage can therefore be easily determined using the voltage divider formula:

Step 2: Determine the equivalent resistance Req

To determine the equivalent internal resistance, we eliminate the voltage source by short-circuiting it.

Thevenin’s theorem - Determine the equivalent resistance

The equivalent internal resistance is the resistance to be measured between terminals A and B. You can see that R1 and R2 are in parallel and also in series with R3:

We have now determined all the parameters of the equivalent voltage source. If desired, the short-circuit current can be easily determined using Ohm's law:

Imax Veq
Req

#### Exercises

Simplify the following real voltage source according to Thevenin's theorem.
Values: V0 = 30 V; R1 = 10 Ω; R1 = R2 = 20 Ω

Thévenin's (voltage-source) equivalent circuit – exercise