eee-1109
EEE-1109 Basic Electrical Engineering

Active Element

An active element is one that can deliver energy or power to a circuit.
Examples: Voltage source, current source, transistor, op-amp.

Passive Element / Passive Network

A passive element absorbs or stores energy but cannot generate it.
Examples: Resistor, inductor, capacitor.
A passive network contains only passive elements.

Unilateral Element / Circuit

A unilateral circuit allows current to flow only in one direction, and its characteristics change with direction of current or voltage.
Example: Diode.

Bilateral Element / Circuit

A bilateral circuit allows current to flow equally in both directions, with same V–I relationship for each.
Examples: Resistor, inductor, capacitor.

Mesh (with example)

A mesh is a loop that contains no other loop within it — the smallest closed path in a network.
Example: In a rectangular network with 2 loops sharing a resistor, each individual loop is a mesh.

Loop (with example)

A loop is any closed path in a circuit formed by branches and nodes.
Example: The outer perimeter of a circuit or a mesh are both loops; every mesh is a loop, but not every loop is a mesh.

Node

A node is a point where two or more circuit elements meet, having a common potential.
Example: The junction connecting a resistor and a capacitor.

Linear Circuit

A linear circuit obeys the principles of superposition and homogeneity — current changes linearly with applied voltage.
Example: Circuits with resistors, inductors, and capacitors only.

Nonlinear Circuit

A nonlinear circuit has elements where the current–voltage relationship is not linear.
Examples: Diode, transistor.

Electric Circuit

An electric circuit is a closed conducting path through which current flows, including sources, loads, and connecting conductors.

Branch (with diagram note)

A branch is a part of a circuit that contains one element and its associated connections between two nodes.
(In diagram: each resistor or source between two nodes represents one branch.)

Active Components

Active components are devices that can control current flow and amplify signals by using an external power source.
Examples: Transistors, ICs, operational amplifiers.

Superposition Theorem

In a linear network with multiple independent sources, the response (current or voltage) due to all sources acting together is equal to the algebraic sum of responses produced by each source acting alone, with all other sources replaced by their internal resistances.

Norton’s Theorem

Any linear network can be replaced by an equivalent current source INI_NIN in parallel with a resistance RNR_NRN**, where
INI_NIN = short-circuit current, and RNR_NRN = equivalent resistance seen at the terminals.

Millman’s Theorem

When several voltage sources (with internal resistances) are connected in parallel, the equivalent voltage is the weighted average of individual voltages divided by total conductance:

$V e q = \sum (Vi / R i) \sum (1/ R i) V_{e q} = \frac{\sum ( V _{i} / R _{i} )}{\sum ( 1/ R _{i} )} V e q = \sum (1/ R i ) \sum (Vi / R i ) $

Reciprocity Theorem

In a linear, bilateral network, if a voltage source in branch A causes a current in branch B, then the same current will flow in branch A if the same voltage source is placed in branch B.

Supernode

A supernode is formed when two or more nodes are connected by a voltage source, making them act as one extended node in nodal analysis.
It is used to apply KCL to the combined node while considering the voltage source constraint between them.

1. Source (Voltage and Current Source)

A source is an element that supplies electrical energy to a circuit.

Voltage Source: Provides a constant voltage regardless of current drawn.
Current Source: Provides a constant current regardless of load.
Examples: Battery, ideal current generator.

2. Independent and Dependent Sources

Independent Source: Output is fixed or preset, not affected by other circuit quantities.
Dependent Source: Output depends on voltage or current elsewhere in the circuit (voltage- or current-controlled).
Used in transistor and op-amp modeling.

4. Planar and Non-Planar Networks

Planar Network: Can be drawn on a plane without crossing branches.
Non-Planar Network: Requires at least one crossing branch when drawn on a plane.
Example: Cube network is non-planar.

5. Ohm’s Law

Current through a conductor is directly proportional to the applied voltage and inversely proportional to resistance, provided temperature remains constant.

V=IRV = IRV=IR

6. Kirchhoff’s Laws

KCL (Kirchhoff’s Current Law): The algebraic sum of currents at a node is zero. (Charge conservation.)

$\sum I in = \sum I o u t \sum I_{in} = \sum I_{o u t} \sum I in = \sum I o u t $

KVL (Kirchhoff’s Voltage Law): The algebraic sum of voltages around a closed loop is zero. (Energy conservation.)

$\sum V = 0 \sum V = 0 \sum V = 0$

7. Open Circuit

A circuit condition where the current path is broken (infinite resistance, zero current).

8. Short Circuit

A path of zero resistance across a component or branch — causes maximum current flow.

9. Network Theorem

Any mathematical rule that simplifies circuit analysis (e.g., Thevenin’s, Norton’s, Superposition, Millman’s, Reciprocity, Maximum Power Transfer).

10. Thevenin’s Theorem (often paired with Norton’s)

Any linear network can be replaced by a single voltage source (Vth) in series with a resistance (Rth).
Used to simplify complex circuits into two-terminal equivalents.

11. Duality Principle

States that electrical equations have dual relationships (e.g., voltage ↔ current, series ↔ parallel, resistance ↔ conductance).

12. Equivalent Resistance / Impedance

The single resistance (or impedance) that can replace a combination of resistors (or impedances) and produce the same current–voltage relation.

13. Linearity

A property where output changes proportionally with input. Fundamental requirement for using superposition or reciprocity theorems.

14. Time Invariant Circuit

A circuit whose parameters do not change with time — the response depends only on the input, not on when it’s applied.

15. Ideal vs Practical Source

Ideal Voltage Source: Zero internal resistance.
Practical Voltage Source: Small internal resistance.
Ideal Current Source: Infinite internal resistance.
Practical Current Source: High but finite internal resistance.

16. Network Elements Classification Summary

Category	Examples
Active	Battery, transistor, op-amp
Passive	R, L, C
Unilateral	Diode
Bilateral	Resistor, inductor, capacitor
Linear	RLC circuits
Nonlinear	Diode, transistor
Time-Invariant	Fixed resistor, coil
Time-Variant	Varistor, thermistor

Maximum Power Transfer

Why it matters in communication engineering (and when it doesn’t)

Matters (RF/antennas/lines): Matching (e.g., 50 Ω systems) maximizes delivered signal power and minimizes reflections/VSWR → predictable gain, bandwidth, and SNR at tiny signal levels.
Doesn’t (power delivery, audio line-level, sensors): You don’t want to burn 50% in the source. There you use voltage bridging (RL≫RsR_L\gg R_sRL≫Rs) for efficiency and low distortion/noise.

Application Area	Purpose / Importance
Antenna & Transmission Lines	Ensures maximum RF power transfer and minimizes reflections (impedance matching).
Amplifiers & Receivers	Provides optimum inter-stage power transfer and stable gain.
Communication Systems	Maximizes signal strength and maintains better SNR at low power levels.
Measurement Instruments	Matches device impedances for accurate readings and minimal signal loss.
Wireless Power / Resonant Circuits	Improves coupling efficiency between coils or resonators.
Audio Circuits	Ensures effective signal transfer between source and load without distortion.

Basic Laws of Electrical Engineering (2016)

The two fundamental laws of electrical engineering are Ohm’s Law and Kirchhoff’s Laws.

Ohm’s Law: It states that the current flowing through a conductor is directly proportional to the voltage across it, provided temperature remains constant.
$V = I R$
Where, ( V ) = Voltage, ( I ) = Current, ( R ) = Resistance.
Kirchhoff’s Laws:
1. Kirchhoff’s Current Law (KCL): The algebraic sum of currents at any node is zero (charge is conserved).
  $\sum I_{in} = \sum I_{o u t}$
2. Kirchhoff’s Voltage Law (KVL): The algebraic sum of all voltages around any closed loop is zero (energy is conserved).
  $\sum V = 0$

Ohm’s Law (2017)

Statement: The current (I) flowing through a conductor between two points is directly proportional to the voltage (V) across the two points, if temperature and other physical conditions remain constant.

Mathematical form: ( V = IR )

Limitations:

Not applicable to non-linear elements such as diodes, transistors, etc.
Temperature must remain constant.
Material must remain homogeneous and isotropic.
Not valid for electrolytic or gaseous conductors.

Kirchhoff’s Laws (2023, 2024)

Kirchhoff’s Current Law (KCL):
The sum of currents entering a junction equals the sum of currents leaving it.
Example: In a node where three currents meet, ( I_1 + I_2 = I_3 ).
Kirchhoff’s Voltage Law (KVL):
The algebraic sum of voltages in any closed loop is zero.
Example: For a loop with a source and two resistors, ( V - IR_1 - IR_2 = 0 ).

Application: Used for network analysis using mesh and nodal methods.

Classification of Energy Sources

(a) Primary Classification:

Active Sources: Provide energy (e.g., voltage and current sources).
Passive Sources: Consume or store energy (e.g., R, L, C).

(b) Based on Nature:

DC Sources: Supply constant voltage/current.
AC Sources: Supply alternating voltage/current.

(c) Characteristics Curves:

Ideal Voltage Source: Horizontal line on V–I curve (voltage constant regardless of current).
Practical Voltage Source: Slightly sloped line due to internal resistance.
Ideal Current Source: Vertical line (current constant regardless of voltage).
Practical Current Source: Slightly tilted line due to finite internal resistance.

Classification of Dependent Sources

Dependent (controlled) sources provide output controlled by another circuit variable.

Voltage Controlled Voltage Source (VCVS)
Current Controlled Voltage Source (CCVS)
Voltage Controlled Current Source (VCCS)
Current Controlled Current Source (CCCS)

Primary and Secondary Cells

Primary Cell: Chemical reaction is not reversible; once discharged, cannot be recharged.
Examples: Dry cell, Leclanché cell.
Secondary Cell: Chemical reaction is reversible; can be recharged and reused.
Examples: Lead-acid battery, Li-ion battery.

Type	Reversible	Rechargeable	Example
Primary	No	No	Dry cell
Secondary	Yes	Yes	Lead-acid cell

Properties of Open and Short Circuits (2017)

Type	Resistance	Current	Voltage	Example
Open Circuit	Infinite	Zero	Maximum	Switch open
Short Circuit	Zero	Maximum	Zero	Wire connection

Classification of Networks (2017)

Type	Definition	Example
Linear Network	Obeys Ohm’s law and superposition	RLC circuits
Nonlinear Network	V–I relation not linear	Diode circuit
Bilateral Network	Same behavior in both current directions	RLC circuits
Unilateral Network	Behavior changes with direction	Diode circuit
Active Network	Contains energy source	Source + resistor
Passive Network	Contains no source	RLC only
Planar Network	Can be drawn without crossing branches	Simple series-parallel
Non-planar Network	Has crossing branches	Cube network

Distinguish Between Types of Elements (2018)

Comparison	Active vs Passive	Bilateral vs Unilateral	Linear vs Nonlinear
Definition	Supply/Control energy	Same or different behavior in both directions	Linear obeys Ohm’s law; nonlinear doesn’t
Examples	Battery, transistor	Resistor (bilateral), diode (unilateral)	RLC (linear), diode (nonlinear)

Difference Between DC and AC

Aspect	DC (Direct Current)	AC (Alternating Current)
Direction of Flow	Constant	Alternates periodically
Magnitude	Fixed	Varies with time
Source Example	Battery	Generator
Waveform	Straight line	Sine wave
Transmission Loss	High	Low (easy voltage transformation)
Use	Electronics, electroplating	Power distribution

🔺 Δ ↔ Y Conversion Formulas

1️⃣ Δ (Delta) → Y (Star) Conversion

Let the Δ resistors be $R_{A B}, R_{BC}, R_{C A}$ .

Then the equivalent Y resistors are:

$R_{A} = \frac{R _{A B} \times R _{C A}}{R _{A B} + R _{BC} + R _{C A}}$

$R_{B} = \frac{R _{A B} \times R _{BC}}{R _{A B} + R _{BC} + R _{C A}}$

$R_{C} = \frac{R _{BC} \times R _{C A}}{R _{A B} + R _{BC} + R _{C A}}$

Mnemonic:
Each Y arm = (Product of two adjacent Δ sides) ÷ (Sum of all three Δ sides)

2️⃣ Y (Star) → Δ (Delta) Conversion

Let the Y resistors be $R_{A}, R_{B}, R_{C}$ .

Then the equivalent Δ resistors are:

$R_{A B} = \frac{R _{A} R _{B} + R _{B} R _{C} + R _{C} R _{A}}{R _{C}}$

$R_{BC} = \frac{R _{A} R _{B} + R _{B} R _{C} + R _{C} R _{A}}{R _{A}}$

$R_{C A} = \frac{R _{A} R _{B} + R _{B} R _{C} + R _{C} R _{A}}{R _{B}}$

Mnemonic:
Each Δ side = (Sum of products of all Y arms taken two at a time) ÷ (Opposite Y arm)

3️⃣ Balanced Case (Shortcut)

Type	Given	Equivalent
Balanced Δ	$R_{A B} = R_{BC} = R_{C A} = R$	$R_{A} = R_{B} = R_{C} = \frac{R}{3}$
Balanced Y	$R_{A} = R_{B} = R_{C} = r$	$R_{A B} = R_{BC} = R_{C A} = 3 r$

🧠 When to Use It

Situation	Conversion to Apply	Why
You see a Δ (triangle) connection of resistors that prevents series/parallel simplification.	Convert Δ → Y	The Y form usually connects more cleanly with the rest of the circuit, making it easier to reduce.
You see a Y (star) network that blocks direct simplification.	Convert Y → Δ	The Δ form may connect in series/parallel with nearby resistors.
A network looks like a bridge (Wheatstone type) that is not balanced (so no branch can be removed).	Try converting the inner Y or Δ	It helps reduce it into simpler series-parallel form.

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EEE DC Class Test 1 Definitions & Theory