Basic Electrical and Electronics Engineering – Complete IOE Notes

Fundamentals of Electrical and Electronics Circuits

12 hours | 18 marks

Basic Electrical and Electronics Engineering

This chapter provides a comprehensive foundation in Basic Electrical and Electronics Engineering, covering essential concepts from circuit fundamentals to three-phase systems. Understanding these principles is crucial for any engineering discipline and forms the basis for advanced electrical studies.

Chapter Information

Chapter 1: Fundamentals of Electrical and Electronics Circuits (12 hours) – 18 marks

Course: Basic Electrical and Electronics Engineering, I Year I Part

Description: This guide provides complete coverage of electrical circuit fundamentals, Ohm’s Law, Kirchhoff’s Laws, AC circuit analysis, and three-phase systems as per the IOE syllabus.

Credit: Asst. Prof. Shahabuddin Khan

Chapter 1: Fundamentals of Electrical and Electronics Circuits

12 hours

18 marks

Detailed Chapter Notes

1.1 Current and Potential

Electric Charge and Current ⚡️

Electric Charge (Q): A fundamental property of matter that causes it to experience a force when placed in an electromagnetic field. The SI unit of charge is the coulomb (C). An electron possesses a negative charge of -1.602×10⁻¹⁹ C, while a proton has a positive charge of +1.602×10⁻¹⁹ C.

Electric Current (I): The rate of flow of electric charge. It is the directed movement of free electrons in a conductor. The SI unit is the ampere (A).

I = dQ/dt

For a constant flow, this simplifies to:

I = Q/t

One ampere is defined as the flow of one coulomb of charge per second.

Electron Flow vs. Conventional Current:

Electron Flow: The actual movement of electrons is from a point of lower potential (negative terminal) to a point of higher potential (positive terminal).
Conventional Current: By historical convention, the direction of current is considered the direction that positive charge would flow, i.e., from a higher potential (positive terminal) to a lower potential (negative terminal). This is the standard used in circuit analysis.

Potential Difference and EMF

Potential Difference (V): Also known as voltage, it is the work done per unit charge to move a charge between two points in an electric field. It’s the “push” or “pressure” that causes the current to flow. The SI unit is the volt (V).

V = W/Q

Where W is work done or energy expended in joules (J). One volt is the potential difference between two points when one joule of energy is used to move one coulomb of charge from one point to the other.

Electromotive Force (EMF): The energy supplied by a source (like a battery or generator) to each unit of charge. It is the voltage of a source when no current is being drawn. It is also measured in volts (V). While potential difference refers to the energy lost by a charge moving through a component, EMF refers to the energy gained by a charge moving through a source.

1.2 Circuit Components: Source, Conductor, Resistor, Inductor, Capacitor

Basic Components

Source: Provides the EMF to drive current in a circuit. Sources can be independent (voltage or current is fixed) or dependent (voltage or current depends on another parameter in the circuit). Examples include batteries (DC source) and generators (AC source).
Conductor: A material, typically a metal like copper, with low resistance that allows electric current to flow easily through it.
Resistor (R): A passive component that opposes the flow of current and dissipates energy in the form of heat.
- Resistance: The measure of this opposition, quantified in ohms (Ω).
- Resistance depends on the material’s resistivity (ρ), length (L), and cross-sectional area (A):
R = ρL/A
Inductor (L): A passive component, typically a coil of wire, that stores energy in a magnetic field when current flows through it. It opposes changes in current.
- Inductance: The property of an inductor to oppose a change in current. The SI unit is the henry (H).
- The voltage across an inductor is proportional to the rate of change of current:
v(t) = L di(t)/dt
Capacitor (C): A passive component that stores energy in an electric field. It consists of two conductive plates separated by a dielectric (insulating) material. It opposes changes in voltage.
- Capacitance: The ability of a capacitor to store charge. The SI unit is the farad (F).
- The current through a capacitor is proportional to the rate of change of voltage:
i(t) = C dv(t)/dt

1.3 Ohm’s Law

Ohm’s Law states that the voltage across a conductor is directly proportional to the current flowing through it, provided all physical conditions and temperature remain constant.

V ∝ I

V = IR

Where:

V = Voltage in volts (V)
I = Current in amperes (A)
R = Resistance in ohms (Ω)

This relationship forms the basis of DC circuit analysis. Conductance (G) is the reciprocal of resistance (G = 1/R) and measures how easily current flows. Its unit is the siemens (S).

1.4 Series and Parallel Circuits

Resistors in Series and Parallel

Series Circuit: Components are connected end-to-end, providing only one path for the current.

Current is the same through all components: I_total = I₁ = I₂ = …
Total voltage is the sum of individual voltages: V_total = V₁ + V₂ + …
Equivalent resistance is the sum of individual resistances:

R_eq = R₁ + R₂ + … + R_n

Parallel Circuit: Components are connected across the same two points, providing multiple paths for the current.

Voltage is the same across all components: V_total = V₁ = V₂ = …
Total current is the sum of the currents in each branch: I_total = I₁ + I₂ + …
The reciprocal of the equivalent resistance is the sum of the reciprocals of individual resistances:

1/R_eq = 1/R₁ + 1/R₂ + … + 1/R_n

Inductors and Capacitors

Connection	Inductors (L)	Capacitors (C)
Series	L_eq = L₁ + L₂ + …	1/C_eq = 1/C₁ + 1/C₂ + …
Parallel	1/L_eq = 1/L₁ + 1/L₂ + …	C_eq = C₁ + C₂ + …

1.5 Kirchhoff’s Law and its Application

Kirchhoff’s laws are fundamental for analyzing complex circuits where simple series/parallel rules are insufficient.

Kirchhoff’s Current Law (KCL)

Statement: The algebraic sum of currents entering a node (or junction) is zero.

∑I_k = 0

Principle: Based on the conservation of charge. It implies that the total current entering a node must equal the total current leaving it.

Application: KCL is the foundation of Nodal Analysis.

Kirchhoff’s Voltage Law (KVL)

Statement: The algebraic sum of all voltages around any closed loop (or mesh) in a circuit is zero.

∑V_k = 0

Principle: Based on the conservation of energy. It means the sum of voltage drops across components equals the sum of voltage rises from sources in a closed loop.

Application: KVL is the foundation of Mesh Analysis.

1.5.1 Nodal Analysis

A method that uses KCL to find the unknown voltages at the different nodes in a circuit.

Steps:

Identify all nodes and select one as the reference node (ground, 0V).
Assign a variable for the voltage at each non-reference node (e.g., V_A, V_B).
Apply KCL at each non-reference node, expressing the branch currents in terms of the node voltages using Ohm’s Law (e.g., I = (V_start – V_end)/R).
Solve the resulting system of linear equations to find the node voltages.

1.5.2 Mesh Analysis

A method that uses KVL to find the currents circulating in the meshes of a planar circuit.

Steps:

Identify all meshes (loops that don’t contain other loops).
Assign a mesh current variable to each mesh (e.g., I₁, I₂), assuming a clockwise direction.
Apply KVL around each mesh. Sum the voltage drops and rises according to the mesh current direction. If a resistor is shared by two meshes, the voltage drop across it is a function of both mesh currents (e.g., R(I₁ – I₂)).
Solve the resulting system of linear equations to find the mesh currents.

1.6 Introduction to AC Circuits and Parameters

1.6.1 Generation of AC Voltage

An alternating voltage can be generated by rotating a coil of wire at a constant angular velocity (ω) in a uniform magnetic field. The induced EMF in the coil varies sinusoidally with time.

The instantaneous EMF (e) is given by:

e(t) = NBAω sin(ωt)

e(t) = E_m sin(ωt)

where E_m = NBAω is the peak or maximum voltage.

1.6.2 Waveforms and Parameters 📈

Waveform: A graph of a quantity (voltage or current) as a function of time. A common AC waveform is the sine wave.
Cycle: One complete set of positive and negative values of an alternating quantity.
Time Period (T): The time taken to complete one cycle. Unit: seconds (s).
Frequency (f): The number of cycles completed per second. Unit: Hertz (Hz). f = 1/T.
Amplitude (V_m or I_m): The maximum or peak value of the waveform.
Angular Frequency (ω): The rate of change of phase angle. Unit: radians per second (rad/s). ω = 2πf.

1.6.3 Average Value

For a symmetrical sine wave, the average value over a full cycle is zero. For a half-cycle, it is:

V_avg = 2V_m/π ≈ 0.637V_m

1.6.4 RMS (Root Mean Square) Value

The effective value of an AC voltage or current. It is the equivalent DC value that would dissipate the same amount of power in a given resistor. For a sinusoidal waveform:

V_rms = V_m/√2 ≈ 0.707V_m

When we talk about an AC voltage (e.g., 230V household supply), we are referring to its RMS value.

1.7 Single Phase AC Circuit Analysis with R, RL, RC and RLC Load

Phasors and Impedance

Phasor: A complex number that represents the magnitude and phase angle of a sinusoidal waveform. Phasors simplify AC circuit analysis by converting differential equations into algebraic ones.

Impedance (Z): The total opposition to current flow in an AC circuit. It is a complex quantity that includes both resistance and reactance. Unit: ohms (Ω).

Z = R + jX

where R is resistance and X is reactance.

AC Circuit with R, L, and C

Purely Resistive Circuit (R):
- Voltage and current are in phase.
- Impedance: Z = R.
Purely Inductive Circuit (L):
- Current lags the voltage by 90°.
- Inductive Reactance (X_L): The opposition offered by the inductor. X_L = ωL = 2πfL.
- Impedance: Z = jX_L.
Purely Capacitive Circuit (C):
- Current leads the voltage by 90°.
- Capacitive Reactance (X_C): The opposition offered by the capacitor. X_C = 1/(ωC) = 1/(2πfC).
- Impedance: Z = -jX_C.

Series RLC Circuit

For a resistor, inductor, and capacitor connected in series:

Total Impedance (Z):

Z = R + j(X_L – X_C)

Magnitude: |Z| = √[R² + (X_L – X_C)²]

Phase Angle (ϕ): ϕ = tan⁻¹[(X_L – X_C)/R]

Current (I): I = V/Z. The phase of the current depends on the phase angle ϕ.

If X_L > X_C, the circuit is inductive, and current lags voltage.
If X_C > X_L, the circuit is capacitive, and current leads voltage.
If X_L = X_C, the circuit is in resonance. The impedance is minimal (Z = R), and the current is maximum.

1.8 Three-Phase AC Circuits

1.8.1 Waveform and Advantages

A three-phase system consists of three AC voltages of the same frequency and magnitude, but with a 120° phase difference between each.

Advantages over single-phase:

Constant Power Delivery: The total instantaneous power is constant, leading to smoother operation of machines.
More Economical: It requires less copper for transmitting the same amount of power.
Self-Starting Motors: Three-phase induction motors are self-starting, unlike many single-phase motors.

1.8.2 Star (Y) and Delta (Δ) Connections

Three-phase sources or loads can be connected in two ways:

Star (Y) Connection: The similar ends (start or finish) of the three windings are joined together to form a neutral point.
Delta (Δ) Connection: The three windings are connected in series to form a closed loop.

Line and Phase Quantities

Phase Voltage (V_P) / Current (I_P): The voltage across or current through a single winding (phase).
Line Voltage (V_L) / Current (I_L): The voltage between any two lines or the current in a single line conductor.

1.8.3 Voltage & Current Computation in Balanced Circuits

In a balanced system, the load on all three phases is identical.

Connection	Voltage Relation	Current Relation	Power (P_total)
Star (Y)	V_L = √3 V_P	I_L = I_P	√3 V_L I_L cosϕ or 3V_P I_P cosϕ
Delta (Δ)	V_L = V_P	I_L = √3 I_P	√3 V_L I_L cosϕ or 3V_P I_P cosϕ

Here, cosϕ is the power factor, which is the cosine of the angle between the phase voltage and phase current.

1.8.4 Power Measurement in Three-Phase Circuits

The total power in a three-phase circuit can be measured using the two-wattmeter method. Two wattmeters are connected such that their current coils are in two different lines and their potential coils are connected between their respective line and the third line.

The total power is the algebraic sum of the readings of the two wattmeters:

P_total = W₁ + W₂

This method works for both balanced and unbalanced loads, and for both star and delta connections.

PDF Notes

Prepared by: Asst. Prof. Shahabuddin Khan

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