# Thevenin’s Theorem

**Thevenin’s Theorem** states that any complicated network across its load terminals can be substituted by a voltage source with one resistance in series. This theorem helps in the study of the variation of current in a particular branch when the resistance of the branch is varied while the remaining network remains the same.

For example in designing electrical and electronics circuits.

A more general statement of Thevenin’s Theorem is that any linear active network consisting of independent or dependent voltage and current source and the network elements can be replaced by an equivalent circuit having a voltage source in series with a resistance.

Where the voltage source being the open-circuited voltage across the open-circuited load terminals and the resistance being the internal resistance of the source.

In other words, the current flowing through a resistor connected across any two terminals of a network by an equivalent circuit having a voltage source E_{th} in series with a resistor R_{th}. Where E_{th} is the open-circuit voltage between the required two terminals called the Thevenin voltage and the R_{th} is the equivalent resistance of the network as seen from the two-terminal with all other sources replaced by their internal resistances called Thevenin resistance.

**Contents:**

## Explanation of Thevenin’s Theorem

The Thevenin’s statement is explained with the help of a circuit shown below:

Let us consider a simple DC circuit as shown in the figure above, where we have to find the load current **I _{L}** by the Thevenin’s theorem.

In order to find the equivalent voltage source,** r _{L}** is removed from the circuit as shown in the figure below and

**V**or

_{oc}**V**is calculated.

_{TH}So,

Now, to find the internal resistance of the network (Thevenin’s resistance or equivalent resistance) in series with the open-circuit voltage **V _{OC }**, also known as Thevenin’s voltage

**V**, the voltage source is removed or we can say it is deactivated by a short circuit (as the source does not have any internal resistance) as shown in the figure below:

_{TH}So,

As per Thevenin’s Statement, the load current is determined by the circuit shown above and the equivalent Thevenin’s circuit is obtained.

The load current **I _{L}** is given as:

Where,

**V _{TH}** is the Thevenin’s equivalent voltage. It is an open circuit voltage across the terminal AB known as

**load terminal**

**R**is the Thevenin’s equivalent resistance, as seen from the load terminals where all the sources are replaced by their internal impedance

_{TH}**r**is the

_{L}**load resistance**

## Steps for Solving Thevenin’s Theorem

**Step 1 –** First of all remove the load resistance **r _{L}** of the given circuit.

**Step 2 – **Replace all the sources by their internal resistance.

**Step 3 –** If sources are ideal then short circuit the voltage source and open circuit the current source.

**Step 4 –** Now find the equivalent resistance at the load terminals, known as Thevenin’s Resistance (R_{TH}).

**Step 5 –** Draw the Thevenin’s equivalent circuit by connecting the load resistance and after that determine the desired response.

This theorem is possibly the most extensively used networks theorem. It is applicable where it is desired to determine the current through or voltage across any one element in a network. Thevenin’s Theorem is an easy way to solve a complicated network.

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