1. Concept of Basic Electrical and Electronics Engineering (AExE01)

1.1 Basic Concepts

Ohm’s Law

• Statement: The current flowing through a conductor is directly proportional to the voltage applied across it and inversely proportional to the resistance.
• Formula: $$V = I \times R$$ where:
  • $V$ = Voltage (Volts)
  • $I$ = Current (Amperes)
  • $R$ = Resistance (Ohms, $\Omega$)

Electric Voltage, Current, Power, and Energy

• Voltage (V): The potential difference between two points.
• Current (I): Flow of electric charge.
• Power (P): The rate of doing work. $$P = V \times I$$
• Energy (E): The total power consumed over time. $$E = P \times t$$

Conducting and Insulating Materials

• Conductors: Materials that allow easy current flow (e.g., Copper, Aluminum).
• Insulators: Materials that resist current flow (e.g., Rubber, Glass).

Series and Parallel Circuits

• Series Circuit: Current is the same; Resistance adds up. $$R_{\text{total}} = R_1 + R_2 + R_3$$
• Parallel Circuit: Voltage is the same; Reciprocal of resistance adds up. $$\frac{1}{R_{\text{total}}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}$$

Star-Delta and Delta-Star Conversion

• Star (Y) to Delta (Δ): $$R_{ab} = \frac{R_A R_B + R_B R_C + R_C R_A}{R_C}$$
• Delta (Δ) to Star (Y): $$R_A = \frac{R_{ab} R_{ca}}{R_{ab} + R_{bc} + R_{ca}}$$

Kirchhoff’s Laws

• Kirchhoff’s Current Law (KCL): $$\sum I_{\text{in}} = \sum I_{\text{out}}$$
• Kirchhoff’s Voltage Law (KVL): $$\sum V = 0$$

Linear and Non-Linear Circuits

• Linear Circuits: Follow Ohm’s Law (e.g., Resistors).
• Non-Linear Circuits: Do not follow Ohm’s Law (e.g., Diodes).

Bilateral and Unilateral Circuits

• Bilateral Circuits: Allow current flow in both directions (e.g., Resistors).
• Unilateral Circuits: Allow current flow in one direction (e.g., Diodes).

Active and Passive Circuits

• Active Circuits: Contain active components (e.g., Transistors).
• Passive Circuits: Contain only passive components (e.g., Resistors, Capacitors).

1.2 Network Theorems

Superposition Theorem

• Used for circuits with multiple independent sources.
• Each source is considered separately, and the total response is the sum of individual responses.

Thevenin’s Theorem

• Any linear circuit with multiple sources can be reduced to an equivalent circuit with a single voltage source ($V_{th}$) and a series resistance ($R_{th}$). $$V_{\text{th}} = V_{\text{open-circuit}}$$

Norton’s Theorem

• Any circuit can be reduced to a current source ($I_N$) in parallel with a resistance ($R_N$). $$I_N = \frac{V_{\text{open-circuit}}}{R_{\text{th}}}$$

Maximum Power Transfer Theorem

• Maximum power is transferred when: $$R_{\text{load}} = R_{\text{source}}$$

Resonance in AC Circuits

• Series Resonance: $$f_r = \frac{1}{2\pi \sqrt{LC}}$$
• Parallel Resonance: Occurs when reactive components cancel each other out.

1.3 Alternating Current Fundamentals

AC Generation

• Alternating voltage is generated when a conductor moves through a magnetic field.
• Voltage equation: $$V = V_{\text{max}} \sin(\omega t)$$

Average, Peak, and RMS Values

• RMS Value: $$V_{\text{rms}} = \frac{V_{\text{max}}}{\sqrt{2}}$$
• Average Value: $$V_{\text{avg}} = 0.637 V_{\text{max}}$$

Three-Phase System

• Three AC voltages, 120° apart in phase, improve efficiency in power transmission.

1.4 Semiconductor Devices

Diodes

• Characteristics: Conduct in one direction only.
• Applications: Rectifiers, Voltage Regulators.

BJT (Bipolar Junction Transistor)

• Types: NPN, PNP
• Biasing:
  • Forward bias: Conducts current.
  • Reverse bias: Blocks current.

MOSFET (Metal-Oxide-Semiconductor Field-Effect Transistor)

• Working Principle: Voltage-controlled transistor with high input impedance.
• Applications: Switching, Amplification.

CMOS (Complementary Metal-Oxide-Semiconductor)

• Low power consumption and used in digital circuits.

1.5 Signal Generators

Oscillator Types

• RC Oscillator: Uses resistors and capacitors for frequency control.
• LC Oscillator: Uses an inductor and capacitor.
• Crystal Oscillator: Uses a quartz crystal for high stability.

Waveform Generators

• Types:
  • Sine Wave Generator
  • Square Wave Generator
  • Triangular Wave Generator

1.6 Amplifiers

Classification of Amplifiers

• Class A: High fidelity, low efficiency (~30%).
• Class B: Higher efficiency (~78%) but with distortion.
• Class AB: Compromise between A and B.

Biasing the Class AB Stage

• A small forward bias is applied to reduce crossover distortion.

Power BJTs (Bipolar Junction Transistors)

• Applications: Used in high-power amplification.

Transformer-Coupled Push-Pull Stages

• Reduces distortion and improves efficiency.

Tuned Amplifiers

• Used in radio and TV receivers.

Operational Amplifiers (Op-Amps)

• Features: High gain, differential input.
• Applications: Filters, signal processing.