The ideal voltage and current sources is fundamental to mastering electrical circuit analysis. These theoretical constructs, while not existing in their perfect form in the real world, provide essential building blocks for analyzing complex electrical circuits and form the foundation for advanced concepts like Thévenin and Norton equivalent circuits. This blog post explores the definitions, characteristics, applications, and practical implications of both ideal voltage and current sources.
What is a Source in Electrical Engineering?
A Source in Electrical Engineering is a device or a system that converts any form of energy such as mechanical energy, chemical energy, thermal energy, etc into Electrical Energy. In other words, a source is a device or system that generates energy that powers the electric circuit. The sources are the starting point of an electrical system that supplies the necessary energy to power the electrical components.
Type of Sources
There are generally two types of sources: voltage sources and current sources.
What is a Voltage Source?
A voltage source in an electric circuit is a two-terminal device or component that provides electrical energy by maintaining a specific potential difference across its terminals.
What is the Ideal Voltage Source?
An ideal voltage source is a two-terminal electrical device that maintains a constant voltage across its terminals regardless of the current flowing through it. This theoretical component represents the perfect voltage-generating device, capable of supplying any amount of current while maintaining its specified voltage output.
The symbolic representation of an Ideal Voltage source is given below:
The key characteristics of an ideal voltage source include:
- Zero internal resistance: Unlike real-world voltage sources, an ideal voltage source has absolutely no internal resistance, ensuring no voltage drop occurs within the source itself
- Constant voltage output: The terminal voltage remains fixed at the source’s rated value, independent of load conditions
- Unlimited current capability: The source can theoretically supply infinite current when required
- 100% efficiency: No power is lost within the source due to its zero internal resistance
Mathematical Representation of Ideal Voltage Source
For an ideal voltage source, the relationship between voltage and current is straightforward. If we consider an ideal voltage source with EMF \(V_s\) connected to a load resistance \(R_L\), the equations governing the circuit are:
\(V_{terminal}=V_s\)
\(I=\frac{V_s}{R_L}\)
Where \(V_{terminal}\) is the voltage across the load, which equals the source voltage since there’s no internal resistance to cause voltage drop.
Voltage-Current Characteristics of Ideal Voltage Source
The V-I characteristic of an ideal voltage source appears as a horizontal line on a voltage-current graph. This horizontal line indicates that regardless of how much current flows through the source, the voltage remains constant at the source’s rated value.
From the above figure, the X-axis shows current and Y-axis shows voltage. As you can see, the voltage is always constant even if the current is increasing. Which depicts that the source is supplying constant voltage.
Differences Between Ideal and Practical Voltage Sources
| Aspect | Ideal Voltage Source | Practical Voltage Source |
| Definition | Maintains a constant voltage regardless of current drawn. | Provides nearly constant voltage but is affected by internal resistance. |
| Internal Resistance | Zero. | Small, non-zero resistance in series with the source. |
| Behaviour with Load | Voltage remains fixed regardless of load changes. | Voltage decreases as load current increases. |
| Current Supply | Can provide infinite current. | Limited by the internal resistance and source capacity. |
| Voltage Limit | Voltage does not vary under any condition. | Voltage output reduces under heavy load due to internal resistance. |
| Example | A 12V ideal source always provides exactly 12V, irrespective of load. | A 12V car battery may drop to 11.8V when powering high loads. |
What is a Current Source?
A current source in an electric circuit is a two-terminal device or component that provides a specific current regardless of load or voltage across its terminals.
What is the Ideal Current Source?
An ideal current source is a two-terminal device that maintains a constant current flow through its terminals regardless of the voltage across them. This theoretical component represents the perfect current-generating device, capable of adjusting its terminal voltage to maintain the specified current output
The symbolic representation of an Ideal Current source is given below:
The fundamental characteristics of an ideal current source include:
- Infinite internal resistance: An ideal current source has infinite parallel internal resistance, ensuring that all generated current flows through the external load
- Constant current output: The current through the source remains fixed regardless of load resistance or terminal voltage
- Unlimited voltage capability: The source can theoretically develop infinite voltage across its terminals if required
- Independent operation: The current output is completely independent of the connected load
Mathematical Representation of Ideal Current Source
For an ideal current source with current \(I_s\)connected to a load resistance \(R_L\), the governing equations are:
\(I_{output}=I_s\)
\(V_{terminal}=I_s\times R_L\)
The current remains constant while the terminal voltage adjusts according to Ohm’s law based on the load resistance.
Current-Voltage Characteristics of Ideal Current Source
The V-I characteristic of an ideal current source appears as a vertical line on a voltage-current graph. This vertical line demonstrates that regardless of the terminal voltage, the current remains constant at the source’s rated value.
From the above figure, the X-axis shows the voltage across the terminals of a current source and Y-axis shows the current supplied by the source. As you can see, the current is always constant even if the voltage is increasing. Which depicts that the current source is supplying constant current.
Differences Between Ideal and Practical Current Sources
| Aspect | Ideal Current Source | Practical Current Source |
| Definition | Maintains a constant current regardless of voltage across terminals. | Provides nearly constant current but is affected by internal resistance. |
| Internal Resistance | Infinite. | Large but finite resistance in parallel with the source. |
| Behaviour with Load | Current remains fixed regardless of load or terminal voltage changes. | Current may decrease slightly with changes in load resistance or voltage. |
| Voltage Supply | Can supply infinite voltage to maintain constant current. | Limited by the source’s maximum voltage capability. |
| Current Limit | Current does not vary under any condition. | Current may vary due to practical limitations like internal resistance. |
| Example | A 5A ideal source delivers 5A regardless of load resistance. | A constant current driver may deliver approximately 5A but varies slightly. |
V-I Characteristics of Current and Voltage Sources
Comparison Between Ideal Voltage and Ideal Current Sources
Behavior of Ideal Sources in Short Circuit Conditions
- Ideal voltage source: Maintains rated voltage, current approaches infinity
- Ideal current source: Maintains rated current, voltage drops to zero
Behavior of Ideal Sources in Open Circuit Conditions:
- Ideal voltage source: Maintains rated voltage, current equals zero
- Ideal current source: Maintains rated current, voltage approaches infinity
Practical Applications of Voltage Source
While ideal voltage sources don’t exist, many practical devices closely approximate their behavior under normal operating conditions:
Batteries and Power Supplies: Lead-acid batteries, lithium-ion cells, and regulated DC power supplies maintain relatively constant voltage output across their normal operating range. Their low internal resistance makes them effective voltage sources for most applications.
Electrical Generators: AC and DC generators in power plants function as voltage sources, maintaining consistent voltage levels across the electrical grid.
Automotive Alternators: These devices maintain the vehicle’s electrical system voltage while providing current as needed.
Practical Applications of Current Source
Current sources are less common as standalone devices but play crucial roles in various applications:
Solar Photovoltaic Cells: Solar panels behave more like current sources than voltage sources, maintaining relatively constant current output under varying illumination conditions while voltage changes with load. The photovoltaic effect generates electron-hole pairs that create a consistent current flow.
Current Transformers: Used in power systems for measurement, these devices provide a constant current output proportional to the primary current, regardless of the secondary load impedance.
Transistor Circuits: In many electronic applications, transistors are configured to act as current sources or current sinks, providing constant current to drive LEDs or bias other circuit elements.
Van de Graaff Generators: These high-voltage generators act as relatively pure current sources, providing constant charge flow.
Why Ideal Sources Cannot Exist
The theoretical perfection of ideal sources fundamentally contradicts the laws of physics and the limitations of real materials, making their physical realization impossible.
The primary reasons for their impossibility are:
- Infinite Power Requirement: Ideal sources would need to generate limitless power to function under extreme conditions. An ideal voltage source connected to a short circuit, or an ideal current source connected to an open circuit, would theoretically demand infinite power to maintain its specified voltage or current.
- Material Impossibility: Real-world materials do not have the perfect properties required. It is physically impossible to create a material with absolutely zero internal resistance for an ideal voltage source or infinite internal resistance for an ideal current source.
- Violation of Physical Laws: In certain configurations, such as connecting two different ideal voltage sources in parallel, these models create logical paradoxes that contradict the laws of energy conservation.
Behavior of Practical Sources
Real-world sources deviate from ideal behavior due to their internal resistance:
Practical Voltage Sources: Include series internal resistance that causes terminal voltage to decrease as load current increases. The relationship follows:
\(V_{terminal}=V_{source}-I\times R_{internal}\)
Practical Current Sources: Include parallel internal resistance that causes output current to decrease as terminal voltage increases.
Conclusion
Ideal voltage and current sources represent fundamental concepts that bridge theoretical circuit analysis with practical electrical engineering applications. While these perfect sources cannot exist in reality due to their infinite power requirements, they provide essential tools for understanding circuit behavior, performing network analysis, and designing electrical systems.