This page is all about this simple lines " If two connections lead away from an arbitrary connection of batteries and resistors, then the electrical effects of the circuit in the box on whatever is connected to the box is just the same as if in the box were merely a single battery connected in series to a single resistance".

To illustrate it, you might have seen the combination of linear bilateral circuit elements and active sources, regardless of the connection or complexity, connected to a given load R

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Thevenin's theorem is popularly known for analyzing the power systems and other complicated circuits where we could determine the value of load resistance which helps to calculate voltage and current across it. It states that

**"Any combination of linear network that is bilateral having circuit elements connected with active sources, regardless of the complexity, applied across a given load R**_{L}, may be replaced by a simple two terminal network that consists of a single voltage source V_{TH} in series with a single impedance R_{TH}, connected across the two terminals having load resistance R_{L}. The V_{TH} is the open circuit voltage measured at the two terminals of interest, with load impedance Z_{L} removed. Here voltage V_{TH} is Thevenin's equivalent voltage and R_{TH} is the equivalent impedance".

The Thevenin's equivalent circuit is the electrical equivalent circuit of resistances connected across the load resistance. To get the Thevenin equivalent circuit we need to first remove the power supply connected across the original circuit, voltage sources should be short circuited, while current sources should be open circuited and total resistance should be determined between the open connection points R_{TH}. This equivalent circuit simplifies the entire circuit into a circuit of a single voltage source, series resistance and series load.

We often see the circuit when open circuited i.e terminals when not connected to anything, there would be no flow of current in the circuit but there would the voltage across the terminals what we call open circuit voltage. The Thevenin voltage is an ideal voltage source that would be equal to voltage when open circuited at the terminals.

**Thevenin Voltage**

In the circuits, Thevenin voltage and Norton current can be expressed as

or

Where V_{TH }is Thevenin equivalent voltage, I_{N} is Norton current and R_{TH} = R_{N} (R_{N} is Norton resistance)

From the Thevenin and Norton's equivalent circuit we could determine

- Thevenin resistance is equal to and Norton resistance (R
_{TH}= R_{N})

- Thevenin voltage V
_{TH}is equal to Norton current I_{N}times Norton resistance R_{N}(V_{TH}= I_{N}R_{N})

- Norton current is equal to Thevenin voltage divided by Thevenin resistance.

Step 2:

Step 3:

Step 4:

Calculate the equivalent voltage for the given Thevenin circuit:

Solution:

Open the terminals AB and then calculate the voltage across AB,

- V

V

Determine the V

Short the terminal AB,

Applying mesh analysis,

- 20 + 2I + 2 (I - I

4I - 2 I

2I -I

Now short the terminal AB. Applying mesh analysis,

-20 + 2I + 2 (I-I

4I - 2I

2I - I

2 (I

2I

By equations (1) and (2), we get I

Now

The thevenin equivalent circuit is given by

= $\frac{20}{3 + 1}$

=

The Norton equivalent circuit is determined using current division formula

= $\frac{3}{3 + 1}$ $\times$ $\frac{20}{3}$

=

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