# Thevenin's Theorem

## Thevenin’s Theorem Explanation

Thevenin's theorem is a powerful concept in electrical engineering that simplifies the analysis of complex linear circuits. It states that any complex network of resistors, voltage sources, and current sources can be reduced to a single equivalent circuit. This equivalent circuit consists of a single voltage source *V _{s}* and a series resistor

*R*.

_{s}In the Thevenin equivalent circuit, the original circuit's resistive elements are consolidated into a single equivalent resistance *R _{s}*. Similarly, multiple independent voltage sources are replaced by a single equivalent voltage source

*V*.

_{s}### Thevenin’s Theorem Example

Thevenin’s Theorem can be understood with the help of the following example

**Example:**

**Step 1:**Begin by removing the load resistor*R*, such as 40 ohms in this example, to simplify the circuit._{load}**Step 2:**To eliminate the effect of internal resistance in voltage sources within a circuit, short-circuiting all voltage sources is essential (setting v=0). If there are any current sources present, they should be open-circuited to similarly remove their internal resistance. This procedure is crucial for establishing ideal voltage or current sources, optimizing the circuit for accurate analysis and solution.**Step 3:**To find the equivalent resistance of a circuit, you start by removing the load resistance and identifying the voltage sources.

- In a given example, resistors like 10 Ω and 20 Ω are connected in parallel with a 20 Ω resistor.

- By applying the parallel resistor formula, the equivalent resistance of the circuit is calculated to be 6.67 ohms."
**Step 4:**Find the equivalent voltage.

- To find the equivalent voltage, reconnect the voltage sources within the circuit. Calculate the current circulating through the loop using the equation: "as the voltage between Vs = VAB."

Since both resistors carry identical currents, we can calculate the voltage drop across them using either of these formulas:

- For the 20-ohm resistor: \( V_{AB} = 20V - (20 \Omega \times 0.33A) = 13.33V \)
- For the 10-ohm resistor: \( V_{AB} = 10V + (10 \Omega \times 0.33A) = 13.33V \)

This means both resistors experience the same voltage drop across them.

**Step 5:**Construct the Thevenin equivalent circuit, which comprises a single voltage source*V*(e.g., 13.33 V) and a series resistor_{s}*R*(e.g., 6.67 ohms)._{s}

We can calculate the current in the circuit as:

## Application of Thevenin’s Theorem

Thevenin’s theorem is widely applicable in both AC and DC circuits, particularly those containing linear components such as resistors, inductors, and capacitors. By replacing a complex circuit with a simpler equivalent, it facilitates easier analysis and design, making it a fundamental tool in electrical engineering.

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## Frequently Asked Questions on Thevenin's Theorem

Thevenin's theorem states that any complex electrical circuit can be simplified into an equivalent circuit with a single voltage source and a single resistor connected in series.

The formula for Thevenin's equivalent voltage (VTH) is the open-circuit voltage across the terminals of the circuit. The formula for Thevenin's equivalent resistance (RTH) is the resistance seen looking into the terminals of the circuit with all voltage sources replaced by short circuits and current sources replaced by open circuits.

Norton's theorem states that any complex electrical circuit can be simplified into an equivalent circuit with a single current source and a single resistor connected in parallel.

VTH is the Thevenin equivalent voltage, which is the open-circuit voltage across the terminals of the circuit. RTH is the Thevenin equivalent resistance, which is the resistance seen looking into the terminals of the circuit with all voltage sources replaced by short circuits and current sources replaced by open circuits.

The main benefit of Thevenin's theorem is that it allows complex electrical circuits to be simplified into an equivalent circuit with a single voltage source and a single resistor connected in series. This simplification makes it easier to analyze the behavior of the circuit, especially when the load resistance changes.