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# Ideal Voltage Source

An ideal voltage source is a fundamental concept in electrical engineering and in network theory. It provides a perfect, unchanging voltage to any connected circuit, unaffected by any external factors or load variations.

## Characteristics of an Ideal Voltage Source

• Constant Voltage: An ideal voltage source maintains a constant voltage across its terminals regardless of the current drawn by the load. This means that the voltage remains the same even if the load changes.
• Zero Internal Resistance: An ideal voltage source has zero internal resistance, meaning there are no voltage drops within the source itself. All the supplied voltage appears across the external load.
• Infinite Current Supply: In theory, an ideal voltage source can supply infinite current to the load without any loss in voltage. However, this is not practical in real-world scenarios.

## Representation

In circuit diagrams, an ideal voltage source is represented by a circle with a plus (+) and minus (-) sign indicating the polarity of the voltage.

## Mathematical Representation

For an ideal voltage source with voltage $$V_s$$:

$V_{\text{out}} = V_s$

Where:

• $$V_{\text{out}}$$ is the voltage across the load.
• $$V_s$$ is the source voltage.

## Practical Implications

• Non-ideal Sources: In reality, all voltage sources have some internal resistance and cannot supply infinite current. These are known as non-ideal or practical voltage sources.
• Load Variation: The ability to maintain a constant voltage under varying load conditions is a key feature, making ideal voltage sources a useful theoretical model for understanding and designing electrical circuits.

## Example

Consider a simple circuit with an ideal voltage source and a resistor as the load:

Ideal Voltage Source → $$R_{\text{load}}$$

If the voltage source is 10V and the resistor is 5 ohms, the current $$I$$ through the resistor can be calculated using Ohm’s Law:

$I = \frac{V}{R} = \frac{10V}{5\Omega} = 2A$

The voltage across the resistor remains 10V regardless of the current, illustrating the concept of an ideal voltage source.

## Real-World Application

In practice, ideal voltage sources are approximated using regulated power supplies, batteries, and other devices designed to minimize internal resistance and maintain a steady voltage under various conditions.

Understanding the ideal voltage source is crucial for analyzing and designing electrical circuits, as it provides a simplified model to predict circuit behavior under ideal conditions.