Fundamentals of Electrical Engineering unit-I: DC Circuits Notes & Analysis

Complete Unit-1 DC Circuits notes for 2nd semester Electrical Engineering. Covers R, L, C elements, Kirchhoff’s Laws, Mesh & Nodal Analysis with PDF download.

Feb 12, 2026 - 23:56 Updated: Feb 13, 2026 - 01:27

0 44

DC circuit setup with resistor, capacitor, inductor and multimeter on breadboard

Fundamentals of Electrical Engineering

Unit – 1: DC Circuits (Second Semester)

Introduction

Electrical Engineering is one of the core branches of engineering that deals with the study, design, and application of electrical systems and components. In the second semester of most diploma and B.Tech programs, Fundamentals of Electrical Engineering (FEE) forms the foundation for advanced subjects like Electrical Machines, Power Systems, Control Systems, and Power Electronics.

Unit–1 of this subject mainly focuses on DC Circuits, which are the building blocks of electrical network analysis. Understanding DC circuits helps students develop analytical skills required for solving real-life electrical problems.

This detailed post covers the following topics:

Electrical Circuit Elements (R, L and C)
Concept of Active and Passive Elements
Voltage and Current Sources
Concept of Linearity
Unilateral and Bilateral Elements
Kirchhoff’s Laws
Mesh Method of Analysis
Nodal Method of Analysis
Adding PDF Notes

1. DC Circuits – Basic Concept

A DC circuit (Direct Current Circuit) is an electrical network powered by a DC source where the current flows in one direction only.

In DC circuits:

Voltage polarity remains constant.
Current direction does not change with time.
Examples: Battery-operated circuits, DC motors, LED circuits, mobile chargers (after rectification stage).

A simple DC circuit consists of:

Source (battery or DC supply)
Conductors (wires)
Load (resistor, lamp, motor, etc.)

The fundamental relation governing DC circuits is Ohm’s Law:

R

V = IR = 28.8

Where:
V = Voltage (Volts)
I = Current (Amperes)
R = Resistance (Ohms)

2. Electrical Circuit Elements (R, L and C)

Electrical circuits are made of three fundamental passive elements:

Resistor (R)
Inductor (L)
Capacitor (C)

These are called basic circuit elements.

2.1 Resistor (R)

A resistor is a device that opposes the flow of electric current.

Formula:

V = IR

V = IR = 12

Unit:

Ohm (Ω)

Function:

Limits current
Divides voltage
Dissipates power as heat

Power Dissipation:

$P = I^2R = VI = \frac{V^2}{R}$

Types of Resistors:

Carbon resistor
Wire-wound resistor
Variable resistor (Potentiometer)

Properties:

Does not store energy
Purely dissipative element
Linear device (if temperature constant)

2.2 Inductor (L)

An inductor is a device that stores energy in the form of a magnetic field.

Formula:

$V = L \frac{dI}{dt}$

Where:
L = Inductance (Henry)

Unit:

Henry (H)

Characteristics:

Opposes change in current
Stores energy in magnetic field
In steady DC state → behaves like short circuit

Energy Stored:

$W = \frac{1}{2}LI^2$

Applications:

Transformers
Chokes
Filters

2.3 Capacitor (C)

A capacitor stores energy in the form of an electric field.

Formula:

$I = C \frac{dV}{dt}$

Where:
C = Capacitance (Farad)

Unit:

Farad (F)

Characteristics:

Opposes change in voltage
Stores energy in electric field
In steady DC → behaves like open circuit

Energy Stored:

$W = \frac{1}{2}CV^2$

Applications:

Filtering
Energy storage
Timing circuits

3. Active and Passive Elements

Electrical elements are classified as:

Active elements
Passive elements

3.1 Active Elements

An active element is one that can supply energy to a circuit.

Examples:

Battery
Generator
Current source
Voltage source

Characteristics:

Provides power
Maintains voltage or current

3.2 Passive Elements

A passive element cannot generate energy. It can only absorb or store energy.

Examples:

Resistor
Inductor
Capacitor

Key Difference:

Active Element	Passive Element
Supplies energy	Absorbs/stores energy
Example: Battery	Example: Resistor

4. Voltage and Current Sources

Sources are devices that provide energy to the circuit.

4.1 Voltage Source

A voltage source maintains a constant voltage across its terminals.

Types:

Ideal Voltage Source
Practical Voltage Source

Ideal Voltage Source:

Internal resistance = 0
Voltage remains constant regardless of current

Practical Voltage Source:

Has small internal resistance
Voltage drops under load

4.2 Current Source

A current source maintains constant current.

Types:

Ideal Current Source
Practical Current Source

Ideal Current Source:

Infinite internal resistance
Current remains constant

Practical Current Source:

Has high internal resistance
Current slightly varies

5. Concept of Linearity

A system is linear if it satisfies:

Superposition Principle
Homogeneity Principle

Superposition:

Response due to multiple sources = Sum of responses due to each source.

Example:

If input doubled → output doubles.

Linear Elements:

Resistor (constant R)
Ideal inductor
Ideal capacitor

Non-Linear Elements:

Diode
Transistor
SCR

6. Unilateral and Bilateral Elements

6.1 Bilateral Element

A bilateral element behaves the same in both directions of current.

Example:

Resistor
Inductor
Capacitor

6.2 Unilateral Element

A unilateral element behaves differently in opposite directions.

Example:

Diode
Transistor

7. Kirchhoff’s Laws

Kirchhoff’s laws are fundamental laws used to analyze complex circuits.

They are:

Kirchhoff’s Current Law (KCL)
Kirchhoff’s Voltage Law (KVL)

7.1 Kirchhoff’s Current Law (KCL)

Statement:

The algebraic sum of currents at a node is zero.

$\sum I = 0$

Incoming currents = Outgoing currents

Example:

If:
I₁ + I₂ = I₃

Then:
I₁ + I₂ - I₃ = 0

7.2 Kirchhoff’s Voltage Law (KVL)

Statement:

The algebraic sum of voltages around any closed loop is zero.

$\sum V = 0$

Voltage rise = Voltage drop

8. Mesh Method of Analysis

Mesh analysis is based on KVL.

Steps:

Identify meshes
Assign mesh currents
Apply KVL in each loop
Solve equations

Advantage:

Useful for planar circuits
Reduces equations

Example:

For two-loop circuit:

Loop 1:

$R₁I₁ + R₃(I₁ - I₂) = V₁$

Loop 2:

$R₂I₂ + R₃(I₂ - I₁) = V₂$

Solve simultaneous equations.

9. Nodal Method of Analysis

Nodal analysis is based on KCL.

Steps:

Select reference node (ground)
Assign node voltages
Apply KCL at nodes
Solve equations

Example:

At node:

$\frac{V - V₁}{R₁} + \frac{V - V₂}{R₂} = 0$

Solve for unknown voltage.

Advantage:

Best for circuits with many current sources
Easier than mesh for large networks

10. Comparison: Mesh vs Nodal Analysis

Mesh Analysis	Nodal Analysis
Based on KVL	Based on KCL
Uses loop currents	Uses node voltages
Suitable for planar circuits	Suitable for any circuit
Fewer equations if fewer loops	Fewer equations if fewer nodes