**Ideal and Non-Ideal Current Sources:**

## Ideal Current Source:

### 1. **Characteristics:**

**Constant Current:**An ideal current source maintains a constant current regardless of the connected circuit elements or voltage changes across its terminals. It provides an unchanging current in the specified direction.

### 2. **Internal Resistance:**

**Infinite Internal Resistance:**An ideal current source is assumed to have an infinite internal resistance, meaning that it is not affected by the external resistance connected in the circuit. It delivers the specified current without any voltage drop.

### 3. **Perfect Control:**

**No Voltage Dependency:**The current provided by an ideal current source is not influenced by the voltage across its terminals. It is immune to changes in the connected circuit.

### 4. **Mathematical Representation:**

**Symbolic Representation:**In circuit diagrams, an ideal current source is symbolized by a circle with an arrow indicating the direction of the constant current.

### 5. **Real-world Limitations:**

**Impracticality:**In reality, achieving an ideal current source is impractical as it would require an infinite amount of energy. However, it serves as a theoretical concept for analysis and understanding.

## Non-Ideal Current Source:

### 1. **Characteristics:**

**Variable Current:**A non-ideal current source may exhibit variations in current due to changes in connected resistances or external conditions. It is influenced by the voltage across its terminals.

### 2. **Internal Resistance:**

**Finite Internal Resistance:**Unlike the ideal counterpart, a non-ideal current source has a finite internal resistance. This internal resistance causes voltage drops across the source as the current flows through it.

### 3. **Voltage Dependency:**

**Voltage Sensitivity:**A non-ideal current source is sensitive to the voltage across its terminals. Changes in voltage can affect the current it supplies to the circuit.

### 4. **Mathematical Representation:**

**Representation with Internal Resistance:**In circuit diagrams, a non-ideal current source is often represented with a current source symbol in series with an internal resistor.

### 5. **Real-world Representation:**

**Practical Components:**Non-ideal current sources can be realized using practical components like transistors, operational amplifiers, or controlled current sources with finite internal resistances.

**Ideal and Non-Ideal Voltage Sources:**

## Ideal Voltage Source:

### 1. **Characteristics:**

**Constant Voltage:**An ideal voltage source maintains a constant voltage across its terminals, independent of the current flowing through the circuit or the connected external resistance.

### 2. **Zero Internal Resistance:**

**Zero Internal Resistance:**An ideal voltage source is assumed to have zero internal resistance. It can deliver the specified voltage without any voltage drop even when connected to various loads.

### 3. **Perfect Control:**

**No Current Dependency:**The voltage provided by an ideal voltage source is not influenced by the current flowing through it. It remains constant regardless of the load.

### 4. **Mathematical Representation:**

**Symbolic Representation:**In circuit diagrams, an ideal voltage source is symbolized by a circle with a plus and minus sign, indicating the specified voltage.

### 5. **Real-world Limitations:**

**Impracticality:**Achieving a true ideal voltage source is impractical in the real world as it would require an infinite amount of power. However, it serves as a theoretical concept for analysis and understanding.

## Non-Ideal Voltage Source:

### 1. **Characteristics:**

**Voltage Variation:**A non-ideal voltage source may exhibit variations in voltage due to changes in the connected load, internal resistance, or external conditions.

### 2. **Finite Internal Resistance:**

**Internal Resistance:**Unlike the ideal counterpart, a non-ideal voltage source has a finite internal resistance. This internal resistance can cause voltage drops when current flows through the source.

### 3. **Current Dependency:**

**Sensitivity to Current:**A non-ideal voltage source is influenced by the current flowing through it. Changes in current can affect the voltage it supplies to the circuit.

### 4. **Mathematical Representation:**

**Representation with Internal Resistance:**In circuit diagrams, a non-ideal voltage source is often represented with a voltage source symbol in series with an internal resistor.

### 5. **Real-world Representation:**

**Practical Components:**Non-ideal voltage sources can be realized using practical components like batteries, generators, or electronic voltage sources with finite internal resistances.

In summary, while ideal current and voltage sources serve as theoretical concepts for analysis, real-world sources exhibit non-ideal characteristics due to factors such as internal resistance, practical limitations, and external conditions. Understanding both ideal and non-ideal sources is crucial for accurate analysis and design of electronic circuits.