BASIC ELECTRICAL ENGINEERING�Course code: 21ELE13/23

BASIC ELECTRICAL ENGINEERING�Course code: 21ELE13/23

Course Syllabus

3

M1. DC Circuits, Single Phase Circuits

M2. Single Phase Circuits, Three Phase Circuits

M3. DC Machines, Transformers

M4. Three Phase Induction Motors,

Three Phase Synchronous Generator

M5. Power Transmission and Distribution,

Electricity Bill,

Equipment Safety Measures

Personal Safety Measures

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Module 1�DC Circuits�Single Phase Circuits

DC Circuits

Contents

• Introduction
• Ohm’s Law and Kirchhoff’s law
• Analysis of series, Parallel and series parallel circuits.
• Power and Energy
• Maximum Power transfer Theorem and its applications.

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Introduction

• The electrical circuits may consist of one or more sources of energy and number of electrical parameters, connected in different ways.
• The different electrical parameters or elements are resistors, capacitors and inductors.
• The combination of such elements along with various sources of energy gives rise to complicated electrical circuits, generally referred as networks.

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• The terms circuit and network are used synonymously in the electrical literature.
• The DC circuits consist of only resistances and DC sources of energy.
• And the circuit analysis means to find a current through or voltage across any branch of the circuit.

Ohm’s Law

• The current flowing through the electric circuit is directly proportional to the potential difference across the circuit, provided the temperature remains constant.

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Key Point

• Ohm’s Law can be applied either to the entire circuit or to the part of a circuit.
• If it is applied to entire circuit, the voltage across the entire circuit and resistance of the entire circuit should be taken into account.
• If the Ohm’s Law is applied to the part of a circuit, then the resistance of that part and potential across that part should be used.

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Limitations of Ohm’s Law

The limitations of the Ohms law are,

• It is not applicable to the nonlinear devices such as diodes, Zener diodes, voltage regulators etc.
• It does not hold good for non-metallic conductors such as silicon carbide.

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Kirchhoff`s Laws�

Kirchhoff’s Current Law (KCL) :

• The total current flowing towards a junction point is equal to the total current flowing away from that junction point.
• The algebraic sum of all the current meeting at a junction point is always zero.
• = 0

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Kirchhoff’s Voltage Law (KVL):

• In any network, the algebraic sum of the voltage drops across the circuit elements of any closed path (or loop or mesh) is equal to the algebraic sum of the e.m.fs in the path.
• the algebraic sum of all the branch voltages, around any closed path or closed loop is always zero.

= 0

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Electrical Work

• In an electrical circuit, movement of electrons i.e. transfer of charge is an electric current. The electric work done when there is a transfer of charge. The unit of such work is Joule.
• One joule of electrical work done is that work done in moving a charge of 1 coulomb through a potential difference of 1 volt.

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Electrical Power

• The rate at which electrical work is done in an electric circuit is called an electrical power.
• Electrical Power = electrical work time

= W t = V I t t = V I J/sec

• According to Ohms law, V=IR or I = V R
• Using this power can be expressed as

P = V I = I2R = V2 R

Electrical Energy

• An electrical energy is the total amount of electrical work done in electric circuit.
• Electrical Energy E = Power * Time = V I t

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Series Circuit

• A series circuit is one in which several resistances are connected one after the other.
• Such connection is also called end to end connection or cascade connection.
• There is only one path for the flow of current.

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Characteristics of Series Circuits

• The same current flows through each resistance.
• The supply voltage V is the sum of the individual voltage drops across the resistances.

V = V1+V2+………. +Vn

• The equivalent resistance is equal to the sum of the individual resistances.
• The equivalent resistance is the largest of all the individual resistances.

i.e R > R1, R>R2, R>Rn

𝐑𝐞𝐪 = 𝐑𝟏 + 𝐑𝟐 + 𝐑𝟑

Parallel Circuit

• The parallel circuit is one in which several resistances are connected across one another in such a way that one terminal of each is connected to form a junction point while the remaining ends are also joined to form another junction point.

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Characteristics of Parallel Circuits

• The same potential difference gets across all the resistances in parallel.
• The total current gets divided into the number of paths equal to the number of resistances in parallel. The total current is always sum of all the individual currents.

I = I1 + I2 + I3 +…..+ In

• The reciprocal of the equivalent resistance of a parallel circuit is equal to the sum of the reciprocal of the individual resistances.

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• The equivalent resistance is the smallest of all the resistances. i.e R < R1, R< R2,……..R<Rn

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• The equivalent conductance is the arithmetic addition of the individual conductance.

Voltage Division in Series Circuit of Resistors

• Consider a series circuit of two resistors and connected to source of V volts. As two resistors are connected in series, the current flowing through both the resistors is same, i.e. I.

• So in general, voltage drop across any resistors or combination of resistors in a series circuit is equal to the ratio of that resistance value, to the total resistance multiplied by the source voltage .

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Current Division in Parallel Circuit of Resistors

• Consider a parallel circuit of two resistors and connected across a source of V volts. Current through is and is , while total current drawn from source is .

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Single Phase Circuits

Contents

• Introduction
• Generation of sinusoidal voltage
• Frequency of generated voltage
• Average value
• RMS value
• Peak factors
• Phasor diagram in R,L and C circuit.

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Introduction

• The resistance, inductance and capacitance are three basic elements of any electrical network. In order to analyse any electric circuit, it is necessary to understand the following three cases,
• A.C. through pure resistive circuit.
• A.C. through pure inductive circuit.
• A.C. through pure capacitive circuit.

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Introduction

• In each case, it is assumed that a purely sinusoidal alternating voltage given by the equation

is applied to the circuit.

• The equation of the current, power and phase shift is developed in each case. The voltage applied having zero phase angle is assumed reference while plotting the phasor diagram in each case.

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Generation of A.C. Voltage

• The machines which are used to generate electrical voltages are called generators. The generators which generate purely sinusoidal a.c. voltages are called alternators.

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• e= B l v sinƟ = E_m sinƟ

e= E_m sin𝟂t = E_m sin( 2Πf)t

• where B l v = E_m = maximum value of the emf induced. Similar equation can be written for current also , i= I_m sin(2Πf)t or I_m sinƟ.

Graphical Representation of Variation of e.m.f

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Standard Terminology Related to Alternating Quantity

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Instantaneous value

• The value of an alternating quantity at a particular instant is known as instantaneous value.

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Time Period (T)

• Time taken by an alternating quantity to complete its one cycle is known as its time period denoted by T seconds. After every T seconds, the cycle of an alternating quantity repeats.

Frequency (f)

• The number of cycles completed by an alternating quantity per second is known as its frequency. It is denoted by f and is measured in cycles/second which is known as hertz, denoted as Hz.

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Amplitude

• The maximum value attained by an alternating quantity during positive or negative half cycle is called its amplitude. It is denoted as or .

Angular Frequency (ω)

• It is the frequency expressed in electrical radians per second. As one cycle of an alternating quantity corresponds to 2π radians, the angular frequency can be expressed as (2π * cycles/sec). its unit is radians/sec.
• ω= 2 π f radians/sec

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Effective Value Or R.M.S Value�

• The effective value or r.m.s. value of an alternating current is given by that steady current which, when flowing through a given circuit for a given time produces the same amount of heat as produced by the alternating current, which when flowing through the same circuit for the same time.
• = 0.707Im

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Average Value

• The average value of an alternating quantity is defined as that value which is obtained by averaging all the instantaneous values over a period of half cycle.
• = 0.637 Im

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Form Factor ( )�

• The form factor of an alternating quantity is defined as the ratio of r.m.s. value to the average value.
• =1.11 for sinusoidally varying quantity

Crest or Peak Factor( )

• The peak value of an alternating quantity is defined as the ratio of maximum value to the r.m.s. value.
• = = 1.414

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Phasor Representation of an Alternating Quantity

Case 1: In phase

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• The equations for voltage and current are

e= E_m sin𝟂t

i= I_m sin𝟂t

Case 2: Lagging

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• Equations for voltage and current are

e= E_m sin𝟂t

i= I_m sin(𝟂t-ɸ)

Case 3: Leading

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• Equations for current and voltage are,

e= E_m sin𝟂t

i= I_m sin(𝟂t+ɸ)

A.C. Through Pure Resistance�

• Consider a simple circuit consisting of a pure resistance ‘R’ ohms connected across a voltage .

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• According to ohms law, we can find the equation for the current i as
• I = = =

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• Comparing with standard equation,

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• and Ø=0
• So, maximum value of alternating current, i is while, as Ø=0, it indicates that it is in phase with the voltage applied. There is no phase difference between the two. The current is going to achieve its maximum and zero whenever voltage is going to achieve its maximum and zero values.

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A.C. Through Pure Resistance�

• The waveform of voltage and current and the corresponding phasor diagram

A.C. Through Pure Resistance

Power

• The instantaneous power in AC circuits can be obtained by taking product of the instantaneous values of current and voltage.
• P= v*I = * =

= (1 – cos 2ωt)

= - cos 2ωt

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• = * Watts

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V,I,P for purely resistive circuit

A.C. Through Pure Inductance�

• Consider a simple circuit consisting of a pure inductance of L henries, connected across a voltage given by the equation,

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• Pure resistance has zero ohmic resistance. Its internal resistance is zero. The coil has pure inductance of L henries.

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• When alternating quantity i flows through inductance ‘L’, it sets up an alternating magnetic field around the inductance. This changing flux links the coil and due to self inductance, emf gets induced in the coil. This emf opposes the applied voltage.
• The self induced emf in the coil is given by,

e= -L

• At all instant, the applied voltage v is equal and opposite to the self induced emf

v= -e = -

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• At all instant, the applied voltage v is equal and opposite to the self induced emf
• Where, = =

• Where, = = 2 fL ohm
• The term, is called Inductive Reactance and is measured in ohms.
• The above equation clearly shows that the current is purely sinusoidal and having phase angle of - radians i.e. -90°. This means that the current lags voltage applied by 90°.

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Power

• The instantaneous power in a.c. circuits can be obtained by taking product of the instantaneous values of current and voltage.

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• It can observed from it that when power curve is positive, energy gets stored in the magnetic field established due to increasing current while during negative power curve, this power is returned back to the supply.

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AC Through Pure Capacitance

• Consider a simple circuit consisting of a pure capacitor of C-farads, connected across a voltage given by the equation
• The current i charges the capacitor C. The instantaneous charge ‘q’ on the plates of the capacitor is given by

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• The above current equation clearly shows that the current is purely sinusoidal and having phase angle of + radians i.e. +90°.
• This means current leads voltage applied by 90°. The positive sign indicates leading nature of the current.

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Power

• The instantaneous power in a.c. circuits can be obtained by taking product of the instantaneous values of current and voltage.

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