# 1.1 Basic Concepts

### **1. Ohm’s Law**

Ohm’s Law states that the current flowing through a conductor is directly proportional to the voltage across it and inversely proportional to its resistance.

Mathematically:

* V=I×R

Where:

* V is voltage (in volts)
* I is current (in amperes)
* R is resistance (in ohms)

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### **2. Electric Voltage**

Voltage is the potential difference between two points in an electric field, which causes electric charge to flow in a circuit. It is the force that pushes the current through the circuit and measured in volts (V).

Mathematically:

* V=I×R

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### **3. Current**

Electric current is the flow of electric charge (usually electrons) through a conductor. It is measured in amperes (A). The flow of current is caused by the electric voltage.

Mathematically:

* I=V/R

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### **4. Power**

Power in electrical systems is the rate at which electrical energy is consumed or transferred. It is measured in watts (W).

Mathematically:

* P=V×I

Where:

* P is power (in watts)
* V is voltage
* I is current

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### **5. Energy**

Electrical energy is the capacity to do work using electric power. It is typically measured in joules (J) or kilowatt-hours (kWh).

Mathematically:

* E=P×t

Where:

* E is energy (in joules or kilowatt-hours)
* P is power
* t is time in seconds (or hours for kWh)

***

### **6. Conducting and Insulating Materials**

Electrical materials are broadly classified into **conductors** and **insulators** based on their ability to allow or resist the flow of electric current. These materials play a crucial role in designing electrical circuits, devices, and safety systems.

1. **Conducting materials** (e.g., copper, aluminum) allow the flow of electric current due to the presence of free electrons.
2. **Insulating materials** (e.g., rubber, wood, glass) prevent the flow of electric current by restricting the movement of electrons.

**Semiconductors (e.g., silicon, germanium)** have properties **between conductors and insulators**. They are used in transistors, diodes, and computer chips, where their conductivity can be controlled using doping or external voltage.

***

### **7. Series and Parallel Electric Circuits**

Suppose the resistances in the circuit are denoted as: $$R\_1, R\_2, R\_3, \dots, R\_n$$. The currents flowing through the circuit are represented as: $$I\_1, I\_2, I\_3, \dots, I\_n$$. The voltages across the components are represented as: $$V\_1, V\_2, V\_3, \dots, V\_n$$

<figure><img src="https://content.gitbook.com/content/A9j5jkcDSyh4kRyuGhhN/blobs/w4utYrfYrmH4OC7mRTVH/1.1_series_parallel.png" alt=""><figcaption></figcaption></figure>

**Key Point:**

* If one component fails in a series circuit, the entire circuit is interrupted, and current flow stops.
* If one component fails in a series circuit, the entire circuit is interrupted, and current flow stops.

***

### **8. Star-Delta and Delta-Star Conversion**

Star-Delta (Y-Δ) and Delta-Star (Δ-Y) conversions are used to simplify complex electrical circuits. They allow for transformation between **star (Y)** and **delta (Δ)** configurations without changing the overall resistance of the circuit.

1. **Star (Y) Configuration**

Three resistances $$R\_1, R\_2, R\_3$$ are connected at a common point. Each resistance connects from this common point to one terminal.

2. **Delta (Δ) Configuration**

Three resistances $$R\_{A}, R\_{B}, R\_{C}$$ form a closed loop.

<figure><img src="https://content.gitbook.com/content/A9j5jkcDSyh4kRyuGhhN/blobs/K1MCNNCHJmJmsJbnOkUU/1.1_star_delta.png" alt=""><figcaption></figcaption></figure>

***

**Applications**

* Simplifying circuit analysis.
* Solving balanced and unbalanced bridge circuits.
* Used in power distribution networks, motor connections, and impedance matching in electrical systems.

***

### **9. Kirchhoff’s Laws**

Kirchhoff’s Laws are two fundamental principles that apply to electrical circuits. They are essential for analyzing and solving complex electrical networks.

1. **Kirchhoff’s Current Law (KCL)**

Kirchhoff’s Current Law (KCL) states that the sum of currents entering a junction (or node) is equal to the sum of currents leaving the junction. In other words, the algebraic sum of currents at any node in a circuit is zero. This is based on the principle of conservation of electric charge.

Mathematically:

* $$\sum I\_{\text{in}} = \sum I\_{\text{out}}$$

Where:

* $$I\_{in}$$ represents the current flowing into the node.
* $$I\_{out}$$ represents the current flowing out of the node.

This law helps us ensure that the total current flowing into a node is balanced by the total current flowing out, thereby conserving charge.

***

2. **Kirchhoff’s Voltage Law (KVL)**

Kirchhoff’s Voltage Law (KVL) states that the sum of all the voltages around a closed loop or mesh is equal to zero. This law is based on the principle of conservation of energy, which means that energy supplied by the sources is exactly equal to the energy lost in the resistive elements of the circuit.

Mathematically:

* $$\sum V = 0$$

Where:

* $$\sum V$$ represents the sum of voltages around a closed loop in the circuit.

This law helps in determining unknown voltages in a circuit, which is essential for analyzing complex circuits.

***

**Applications of Kirchhoff's Laws**

* **Current distribution analysis** in parallel circuits (using KCL).
* **Voltage distribution analysis** in series circuits (using KVL).
* Solving **complex electrical networks** with multiple loops and junctions.
* Used in the design and analysis of **circuits with resistors, capacitors, and inductors**.

Kirchhoff's Laws are fundamental tools in electrical engineering, enabling engineers to model, analyze, and solve both simple and complex electrical circuits.

***

### **10. Linear and Non-Linear Circuits**

Electrical circuits can be classified as **linear** or **non-linear** based on how their voltage and current behave with respect to each other. This classification is important in circuit analysis and design, as it determines how the circuit responds to different inputs and signals.

1. **Linear Circuits**: The relationship between voltage and current is linear, as in the case of resistors.
2. **Non-Linear Circuits**: The relationship between voltage and current is non-linear, as in the case of diodes and transistors.

<figure><img src="https://content.gitbook.com/content/A9j5jkcDSyh4kRyuGhhN/blobs/1jqlndLcbthsTBO9DTFN/1.1_linear_non_linear.png" alt=""><figcaption></figcaption></figure>

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### **11. Bilateral and Unilateral Circuits**

**Bilateral Circuits**: These circuits behave the same way in both directions of current flow. They have symmetric properties involving resistors, capacitors and inductors.

**Key Characteristics of Bilateral Circuits:**

* **Symmetry**: The circuit components maintain the same properties in both directions. For example, a resistor will have the same resistance whether the current flows from left to right or from right to left.
* **Linear Behavior**: Bilateral circuits are typically linear, meaning their response to an input is directly proportional to the input. If the input voltage is doubled, the output current will also double.
* **Applications**: Bilateral circuits are widely used in analog systems where the direction of current flow doesn’t affect the system behavior, such as power supplies, filters, and simple DC circuits.

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**Unilateral Circuits**: These circuits have different properties depending on the direction of current flow, such as those involving diodes or transistors.

**Key Characteristics of Unilateral Circuits:**

* **Direction-Dependent Behavior**: The circuit will behave differently depending on the current's direction. For instance, in an **AC circuit**, components like diodes or transistors allow current to flow only in one direction, making them directional elements.
* **Nonlinear Behavior**: Unilateral circuits tend to exhibit nonlinear behavior, meaning the relationship between input and output is not proportional. For example, in a diode, the current flow is only allowed when the voltage exceeds a certain threshold, and the relationship between voltage and current is not linear.
* **Applications**: Unilateral circuits are often used in switching, rectification, signal modulation, and amplification. Examples include:
  * **Rectifiers**: In power supplies, diodes are used in circuits that convert AC to DC (rectifiers).
  * **Amplifiers**: Transistors in amplifiers can behave differently depending on the current flow, allowing amplification of AC signals.

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### **12. Active and Passive Circuits**

Electrical circuits are classified into **active** and **passive** circuits based on the types of components they contain and their ability to supply or process energy. Understanding this classification helps in designing and analyzing different electronic and electrical systems.

1. **Active Circuits**:

An **active circuit** contains at least one **active component** that can **amplify signals, control current flow, or introduce energy into the circuit**. These circuits typically require an external power source to function.

**Examples of Active Components:**

* **Transistors** (BJT, MOSFET) – Used in amplifiers and switching circuits
* **Operational Amplifiers (Op-Amps)** – Used in signal processing and control circuits
* **Diodes** (in some configurations, like LEDs and Zener diodes)
* **Integrated Circuits (ICs)** – Used in microprocessors, logic gates, etc.

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2. **Passive Circuits**:

A **passive circuit** contains **only passive components** (resistors, capacitors, and inductors) that can **store, dissipate, or transfer energy** but **cannot amplify or inject power** into the circuit.

**Examples of Passive Components:**

* **Resistors** – Dissipate energy as heat
* **Capacitors** – Store energy in an electric field
* **Inductors** – Store energy in a magnetic field

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### Conclusion

* **Ohm’s Law, Voltage, Current & Power:** Ohm’s Law defines the relationship between voltage, current, and resistance (V=IR), while power (P=VI) measures energy transfer in a circuit, with energy calculated as E=Pt.
* **Kirchhoff's Laws & Circuit Types:** Kirchhoff’s Current and Voltage Laws (KCL and KVL) help analyze current and voltage distribution in circuits, while linear and non-linear circuits differ based on voltage-current relationships, and bilateral vs unilateral circuits react differently to current flow direction.
* **Active vs Passive Circuits & Material Types:** Active circuits use components like transistors that supply energy, while passive circuits (resistors, capacitors) only store or dissipate energy; conductors (e.g., copper) allow current flow, while insulators (e.g., rubber) prevent it.
