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Chapter
2
INTRODUCTION TO ELECTRICITY &
DC ELECTRIC C IRCUITS
Objectives
After completing this chapter, you should be able to
1. Demonstrate evidence for the existence of two types of charges.
2. State the Coulombs law of electrostatics and use the Coulombs relation to find electrostatic force
3. Define the electric field, electric potential, emf, and electric current
4. Describe resistance of the conductors and state the Ohms law.
5. Recall and use the relation V = IRto solve its related problems.6. Recall the basic electricity relationships, and equations for Resistances in series and parallel circuits.
7. Construct the voltage and current divider circuits.
8. Compare voltage and current in series and parallel circuits.
9. Investigate and describe qualitatively the relationship among current, voltage, and resistance in a simple
electric circuit
10. State the Kirchhoffs laws and finding currents by applying them.
Outline
Electric charges 25 30
Electric field 31 33
Basics of DC electricity 34 53
Summary of Chapter 2 54 55
Problems and Short Questions 56 59
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2.1 Introduction .......................................................................................................................................... 25
2.2 Electric Charges .................................................................................................................................... 26
2.2.1 Behaviour of electric charges ........................................................................................................ 27
2.3 Coulombs law ...................................................................................................................................... 27
2.3.1 Sample Problems .......................................................................................................................... 29
2.4 Electric Field ......................................................................................................................................... 31
2.4.1 Electric lines of forces ................................................................................................................... 31
2.4.2 Properties of lines of forces .......................................................................................................... 32
2.4.3 Electric field intensity or strength ................................................................................................. 32
2.4.4 Sample problem ............................................................................................................................ 33
2.5 Electric Potential .................................................................................................................................. 34
2.6 Electric current ..................................................................................................................................... 35
2.6.1 Mechanism of flow of currents ..................................................................................................... 36
2.7 Potential Difference ............................................................................................................................. 362.8 Electromotive force (EMF) ................................................................................................................... 37
2.9 Voltage and Current Sources ................................................................................................................ 37
2.9.1 Independent Sources .................................................................................................................... 38
2.9.2 Dependent Sources ....................................................................................................................... 38
2.10 Resistance ........................................................................................................................................... 38
2.10.1 Ohms Law ............................................................................................................................... 39
2.10.2 Resistivity (or) Specific Resistance .............................................................................................. 40
2.10.3 Temperature Coefficient of Resistance ...................................................................................... 41
2.11 Power and Energy .............................................................................................................................. 41
2.12 Resistors ............................................................................................................................................. 43
2.12.1 Fixed type resistors .................................................................................................................... 43
2.12.2 Variable type resistors ............................................................................................................... 43
2.12.3 Special resistors .......................................................................................................................... 44
2.13 Ressitors in DC Ciricuits ...................................................................................................................... 45
2.13.1 Resistors in Series ............................................................................................................................ 45
2.13.1.1 Characteristics of series circuit ................................................................................................ 46
2.13.1.2 Voltage (potential) divider ....................................................................................................... 47
2.13.2 Resistors in Parallel ......................................................................................................................... 48
2.13.2.1 Characteristics of parallel circuit .............................................................................................. 49
2.13.2.2 Current Divider ......................................................................................................................... 49
2.13.2.3 Advantages of parallel circuits ................................................................................................. 50
2.13.3 Resistors in Series and Parallel ........................................................................................................ 50
2.14 Kirchhoffs law .................................................................................................................................... 512.14.1 Kirchhoffs Current Law (KCL) .......................................................................................................... 52
2.14.2 Kirchhoffs Voltage Law (KVL) ......................................................................................................... 53
Summary .................................................................................................................................................... 54
Problems for Chapter 2 .............................................................................................................................. 56
Short Questions for Chapter 2 ................................................................................................................... 59
References .................................................................................................................................................. 60
CONTENTS
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CHAPTER 2 | 2.1 Introduction 25
Engineering Physics (MASC 10002)
2.1 INTRODUCTION
During the period of 624 BC, Thales of Miletus who was a
Greek philosopher and mathematician discovered that when an
amber rod is rubbed with fur, the rod has the amazing
characteristic of attracting some very light objects such as bits of
paper and shavings of wood. This phenomenon became even
more remarkable when it was found that identical materials, after
having been rubbed with their respected cloths, always repelled
each other. After all, none of these objects was visibly altered by
the rubbing, yet they definitely behaved differently than before
they were rubbed. Whatever change took place to make these
materials attract or repel one another was invisible.
Some experimenters speculated that invisible fluids were
being transferred from one object to another during the process ofrubbing, and that these fluids were able to produce a physical
force over a distance. Charles Dufay was one the early
experimenters who demonstrated that there were definitely two
different types of changes produced by rubbing certain pairs of
objects together. The fact that there was more than one type of
change manifested in these materials was evident by the fact that
there were two types of forces produced: attraction and repulsion.
The hypothetical fluid transfer became known as a charge.
Benjamin Franklin, who was an American Statesman,inventor, and philosopher, came to the conclusion that there was
only one fluid exchanged between rubbed objects, and that the
two different charges were nothing more than either an excess
or a deficiency of that one fluid. If there is a deficiency of fluid in
the objects after being rubbed, the objects are said to be negatively
charged; if there is an excess of fluid in the objects then the
objects are termed aspositivelycharged.
It was discovered much later that this fluid was actually
composed of extremely small bits of matter called electrons, sonamed in honor of the ancient Greek word for amber.
In the 1780s, Precise measurements of electrical charge
were carried out by the French Physicist Charles Augustin de
Coulomb, using a device called a torsional balancemeasuring the
force generated between two electrically charged objects. This
Fig. 2.1 Static cling, shows the charcomb attracts neutral bits of paper
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26 CHAPTER 2 | 2.2 Electric Charges
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work led to the development of a unit of electrical charge named
in his honor, the coulomb. One Coulomb is defined as the amount of
charge flowing through a conductor in one second when one ampere of
current is flowing through that conductor.
Nowadays, electrostatics has many applications rangingfrom the analysis of phenomena such as thunderstorms to the
study of the behaviour of electron tubes. That is, it plays an
important role in modern design of electromagnetic devices
whenever a strong electric field appears. For example, an electric
field is of paramount importance for the design of X-ray devices,
lightning protection equipment and high-voltage components of
electric power transmission systems. In the area of solid-state
electronics, dealing with electrostatics is inevitable. Electrostatics
can also be used in relation to transport and holding of particles to
surfacesfor example: electrostatic precipitation, paint spraying,electrostatic clamping, fly-ash collection in chimneys, laser
printing, photocopying, and particle alignment (ex. flocking).
2.2 ELECTRIC CHARGES
A spark will be produced if your finger were kept closer to
the metal doorknob while walking across a carpet during dry
weather. Television advertising has alerted us to the problem of
Static cling in clothing. Besides that, lightning is familiar to
everyone. Each of these phenomena indicates a tiny glimpse ofthe vast amount of electric charge that is stored in the familiar
objects that surround us and in our own bodies. Electric charge is
an intrinsic characteristic of the fundamental particles like electrons and
protons in the atoms which making up those objects; that is, it is a
characteristic that automatically accompanies those particles
wherever they exist.
Usually, huge amount of charge in an everyday object is
hidden because the object contains equal amount of the two kinds
of charge: positive charge and negativecharge. When such charges
are balanced, it contains no net charge and the object is said to be
electrically neutral. On the other hand, if the two types of charge
are not in balance, then there is a net charge and the object is said
to be charged. The imbalance is always very small compared to
the total amounts of positive and negative charges existed in the
Charles Augustin de Coulomb(1736-1806)
Coulomb, French Physicist, pionee
electrical theory, born in Angoulm
W France. After serving as a militaengineer for France, he retired to a
small estate and devoted himself to
research in magnetism, friction, an
electricity. In 1777 he invented the
torsion balance for measuring the f
of magnetic and electrical attraction
With this invention, Coulomb was
to formulate the principle, now kno
as Coulomb's law, governing the
interaction between electric charge
Thecoulomb
, the unit of electricalcharge, is named after him.
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CHAPTER 2 | 2.3 Coulombs law 27
Engineering Physics (MASC 10002)
Fig. 2.2 shows the (a) repulsive and attractive forces between two same aopposite charges respectively.
Fig. 2.3 shows the conservation ofcharges. Here one neutron, one protand one pion are produced when twprotons are combined together
object.
Charged objects, which are in nearer to each other,
interact by exerting forces on one another. To demonstrate this,
we first charge a glass rod by rubbing one end with silk. During
this process, electrons will be transferred to silk and glassbecomes positively charged. We now suspend the charged glass
rod from a thread to isolate electrically it from its surrounding so
that its charge cannot be changed. If we bring a second, similarly
charged, glass rod nearby (Fig. 2.2a), the two rods repel each
other; that is, each rod experiences a force directed away from the
other rod. However, if we rub a plastic rod with fur and bring it
near the suspended glass rod (Fig. 2.2b), the two rods attracteach
other; that is, each rod experiences a force directed toward the
other rod. The reason for attracting these two rods is that
plastic rod is negatively charged while rubbing with fur aspositive charges are transferred into fur.
The above demonstrations reveal that charges with same
electrical sign repel each other, and charges with opposite electrical signs
attract each other.
2.2.1 Behaviour of electric charges
1. Charge of electron is 1.60210-19C and the protoncharge is +1.60210-19C.
2. Like charges repel each other3. Unlike charges attract each other4. Electric charge is quantised- any charge q can be written
as a integer multiple of the fundamental charge e =
1.60210-19 C. (i.e., charge of particles are either 0, 1e,
2e, 3e, 4e, etc.).
5. Charge is conserved- That is, during any process, the netelectric charge of an isolated system remains constant.
2.3 COULOMBS LAW
In 1785, Coulomb studied the electric attraction and
repulsion quantitatively and prepared the law that governs them.
This law describes the electrostatic force between two point
charges at certain distance at rest (or nearly at rest). According
to Coulomb, the magnitude of the force of attraction or repulsion
Neutron (0Proton (+e
Pion (+e)Proton (+e) + Proton (+e)
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28 CHAPTER 2 | 2.3 Coulombs law
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between any two charged particles depends on the following
three points:
1. The distance between the particles2. The magnitude of the charges3. Nature of the medium between two charges
Based on the experimental measurements of the force
between two charges, Coulomb derived the following laws,
known as the Coulombs law of electrostatics.
First law: Like charges repel each other and unlike charges
attract each other.
Second law: The force exerted between two charges directly
proportional to the product of their strength andinversely proportional to the square of the distance
between them.
Let q1 and q2 be two charged particles and r is the
distance between them as shown in Fig. 2.5, then electrostatic
force between two charged particles can be written as
orrqqF
rFandqqF
2
21
221
1
Newtonr
qqkF
r
2
21
(2.1)
where k is called proportionality constant or electrostatic constant.
The value of kis given by,
229
/1099.84
1CNmk
(2.2)
where, 0 permittivity1 of free space, and
r relative permittivity2 of the medium between two
charges
1 Permittivity is the property of a medium and affects the magnitude of force
between two point charges.
Fig. 2.4 Two charges objects, separaby distance r, repel each other if the
charges are (a) both positive and (b)both negative. (c) They attract eachother if their charges are of oppositesigns.
Fig. 2.5
Object A
Force ofA on B
Force ofB on A
Object B
(a) Repulsion
(b) Repulsion
(c) Attraction
r
Object A
Force ofA on B
Object B
(a) Repulsion
(b) Repulsion
(c) Attraction
r
q1q2
r
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CHAPTER 2 | 2.3 Coulombs law 29
Engineering Physics (MASC 10002)
The electric force F in air medium (free space) is given by
Newton
r
qqkF
2
21 (r = 1 for air) (2.3)
Generally, forces are measured in Newton; hence, the electrostatic force between two
charged particles is also measured in Newton (N).
2.3.1 Sample Problems
1. How many electrons are required to have a charge of one Coulomb?Solution:
Charge of an electron is e = - 1.60210-19C.
Hence, 1819
1024.610602.1
1
C
Cn
That is electrons are required to have a charge of one Coulomb.
2. Two charges, +0.35C and +0.2C, are embedded 2cm apart in a block of polyethylenewhose relative permittivity (r) is 2.3.
a) What is the magnitude and direction of the force acting on each charge?b) What would be the magnitude if the two charges were in vacuum?Solution (a):
As the charges are embedded in the medium of polyethylene,
N
r
qqkF
r
68.0)02.0(3.2
102.01035.0109
)(Force
2
669
2
21
2 Relative permittivity (r) ratio between absolute permittivity () of insulating
materials and the absolute permittivity of free space or vacuum (0= 8.85410-12
C2/Nm2). i.e. r= /0.
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Hence, the force acting on each charge is 0.68 N. Since both the charges are positive, force is
acting away from the other charge.
Solution (b):
As both the charges were in the vacuum, its relative permittivity (r) is 1. (r is 1 for air and
vacuum).
Therefore, Force (F) =2
21
r
qqk
N6.1)02.0(
102.01035.01092
669
3. What would be the force of attraction between two 1 C charges separated by distance of (a)1 m and (b) 1 km?
Solution (a):
N
r
qkqFForce
9
2
9
2
21
1091
1109
)(
Solution (b):
N
r
qkqFForce
3
23
9
2
21
109)101(
1109
)(
4. Calculate the electrostatic force between an -particle and a proton separated by a distanceof 5.1210-15m.
Solution:
Charge of proton is Cq 191 10602.1
An -particle is made up of two protons and two neutrons and hence its charge is
CCq 19192 10204.310602.12
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(a)
(b)
Fig.2.6 shows the direction of electrlines of forces in (a) a positive chargand (b) a negative charge.
The force of attraction between the proton and -
particle is
Nr
qqkF 5.17
1012.5
10204.310602.11099.8
215
19199
2
21
2.4 ELECTRIC FIELD
The concept of electric field was introduced by the British
Physicist and Chemist, Michael Faraday. The electric field force
acts between two charges, in the same way that the gravitational
field force acts between two masses, which could be explained by
Newtons law of gravitation3.
We all know that force acting on a particle changes itsmotion. In some cases, a particle experiences a force when
another body comes in contact, while in other cases; the particle
experiences a force due to a field such as electric, magnetic and
gravitational fields. Hence, electric field is defined asthe space
in which an electric charge experiences a force. That is the
space between and around the charged bodies in which their
influence is felt is called an electric field orelectric field of force.
2.4.1 Electric lines of forces
When a small positively charged body is placed in an
electric field, it experiences a force in a field direction. If the
charged body is less in weight and free to move, it will start
moving in the direction of force and the path in which this
charged body moves is called line of force.
Therefore, electric line of force can be defined as the path
along which a unit positive charge would tend to move when free
in an electric field.
A charged body is generally represented by lines which
are referred to as electrostatic lines of force. These lines are
3Newtons Law of Gravitationstates that every matter that has a mass attracts
other matters with a force that is directly proportional to the product of their
masses and inversely proportional to the square of the distance between the
centers of gravity of the two matters. i.e. 221
d
mmGF
-
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32 CHAPTER 2 | 2.4 Electric Field
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(a)
(b)
Fig. 2.7 Imaginary lines with arrowheads show direction along whichhypothetical positive charges would
move (a) Two positively chargedparticles, (b) A negatively and apositively charged particles.
Fig. 2.8
imaginary and are used just to represent the direction and
strength of the field. Electric force lines originate from a positive
charge and ends at a negative charge. The number of lines of
force from a unit charge of q Coulomb will be equal to q (i.e.
equal to magnitude of the charge of the particle). The lines of
forces for a positive and negative charge are separately shown inthe Fig.2-6.
The lines of forces for two equal and similar charges and
for two equal and dissimilar charges separated by a distance are
shown in Fig.2-7.
2.4.2 Properties of lines of forces
The properties electrostatic lines of force are given below:
1. Electric force lines originate from a positive charge andterminate on a negative charge.
2. They do not cross each other.3. Lines of forces are always perpendicular to the surface of the
charged body at the point where they originate or terminate.
4. A unit positive charge, which is free to move, will movetowards the negatively charged particle along the electric line
of force.
5. Two lines of forces moving in the same direction repel eachother while moving in the opposite direction attracts eachother.
2.4.3 Electric field intensity or strength
Electric field intensity at a given point is defined as equal
to the force experienced by a positive unit charge place at that
point. It is denoted by the letter E.
Let the electric field intensity due to a charge q at a
distance r be E. If a charge Q Coulomb is placed at this point(Fig.2-8), it will experience a force
F = qE (2.4)
According to the Coulombs law, the force between the
charges Qand qat a distance r is given by
q Q
r
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CHAPTER 2 | 2.4 Electric Field 33
Engineering Physics (MASC 10002)
204 r
qQF
r
(2.5)
where, F electric field,
Q, q charges of the particles,
0 permittivity of free space = 8.8510-12C2/Nm2,
r relative permittivity which depends on nature of
the medium and
r distance between the charges.
From the equations (2.3) and (2.4), we have
CNr
QE
orr
qQqE
r
r
/4
4
20
20
(2.6)
If the medium is air (r= 1 for air),
CNr
Qk
r
QE /
4 220
(2.7)
where, k = 229
0
/1099.84
1CNm
.
To determine the electric field intensity due to a group ofpoint charges, we first calculate the electric field intensity of each
charge at the given point assuming only that charge present and
add up all these intensities vectorially, i.e.,
20
220
2
210
1
4.......
44 nr
n
rr r
Q
r
Q
r
QE
E = E1+ E2+ E3+ +En (2.8)
2.4.4 Sample problem
5. Find the electric field from a point charge of 30 C at adistance of 5 m.
To solve this question we shall consider the Fig.2-9.
p
q =3010-6
C
5 m
Fig. 2.9
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34 CHAPTER 2 | 2.5 Electric Potential
Supplementary study material prepared by Dr. R.D. Senthilkumar| Fall 2013
Fig.2.10 Electric potential due to anelectric field
Electric field from a point charge at a distance 5 m is
E = CNr
qk /
2
CN
CN
/1008.1
/)5(
1030109
4
2
69
2.5 ELECTRIC POTENTIAL
Definition: The potential at any point is defined as the amount
of work done, against the field, in moving an unit positive charge
from infinity to that point. The symbol for potential is V and
the unit is joule per coulomb (J/C) or volt (V).
When a body is charged, work is done in charging it.
This work done is stored in the body in the form of potential
energy. The charged body has the capacity to work by moving
other charges either by attraction or repulsion. The ability of
the charged body to do work is called electric potential.
Generally, electric potential is a measured as a ratio between
work done by the body and its charge. i.e.,
Electric Potential,C
J
Q
W
charge
doneworkV
The work done is measured in Joules and charge in
Coulombs. Hence, the unit of electric potential is Joules/Coulomb
or volt. If W = 1 joule, and Q= 1 Coulomb, then V = 1/1 = 1
volt. Therefore, a body is said to have an electric potential of 1
voltif 1 joule of work is done to give it a charge of 1 Coulomb.
Therefore, when we say that a body has an electric
potential of 4 volts, it means that 4 joules of work has been doneto charge the body to 1 coulomb. In other words, every coulomb
of charge possesses energy of 4 joules. The greater the
joules/coulomb on a charged body, the greater is its electric
potential.
A B
r
E
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CHAPTER 2 | 2.6 Electric current 35
Engineering Physics (MASC 10002)
2.6 ELECTRIC CURRENTIt is well known that water always flows from higher pressure level to the lower
pressure level and this is called water flow. Similarly, when a conductor has different levels of
electricity at their two ends, charge also flows from one to other end of the conductor. This
charge flow is called flow of electric current.
The American physicists Tolman and Stewart experimentally confirmed that the
electric current in a conductor is carried by electrons present in that conductor. A metallic
wire contains a large number of electrons in random directions. The electrons in the outer
most orbits are loosely bound with the nucleus compared to the electrons at inner most orbits.
The outer electrons are called free electrons since they can be easily removed from the orbit.
The flow of free electrons in a definite direction in a conductor forms electric current.
Normally, an external force is required to move these free electrons in a definite
direction and this force is called electromotive force(EMF). The EMF is not a force, but it is thework done in moving an unit charge from one end to the other. Therefore, because of EMF,
different levels of electricity are found at the ends of a conductor, i.e., at different electric
potentials. The electric current will flow in a conductor as long as its two ends are at different
electric potentials.
Generally, the electric current (I) is definedasthe rate of flow of charge through any section of a
conductor. Thus,
I =
If charge dqpasses through a wire in time dt, then the current I defined as
= (2.9)In the above relation, the charge is measured in coulomb and time in second; therefore current
is measured in ampere. Hence,
= =
The unit of current ampere is defined as the current which flows through a conductor when one
coulomb of charge flows through that conductor in one second.
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2.6.1 Mechanism of flow of currents
The flow of electric current can be explained by referring
to Fig. 2.11. The copper wire has a large number of free
electrons. When the voltage or electric pressure is applied to the
copper wire, free electrons will start moving towards thepositive terminal round the circuit as shown in Fig. 2.11. This
directed flow of electrons is called electric current. The
direction in which the positive charge will flow is called
conventional current. Since the flow of electric current is
attributed to flow of electrons, the direction of electric current is
opposite to the direction of flow of electrons:
2.7 POTENTIAL DIFFERENCE
The potential difference indicates the electric state of a body.The difference in the potentials of two charged bodies is
called potential difference. If two bodies of different potentials
are connected together a redistribution of charge will takes place
and some charge will move from higher potential to lower
potential, i.e., current flows from higher potential to lower
potential.
Consider two bodies A and B having potentials of 5 volts and 3
volts respectively as shown in Fig. 3.2a. Each coulomb of charge
on body A has energy of 5 joules while each coulomb of chargeon body B has energy of 3 joules. Hence, body A is at higher
potential than the body B. If these two bodies are joined
through a conductor as shown in Fig. 3.2b, then electrons will
flow4from body B to body A. The flow of current stopped when
the two bodies attain the same potential. Hence, the current will
flow in a circuit if potential difference exists. Generally, the
potential difference is called voltage. The unit of potential
difference is volt.
The voltage, vab, between two points a and b in an electriccircuit can be mathematically described as,
= 4The conventional current flow will be in the opposite direction, i.e. from body
A to body B.
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Engineering Physics (MASC 10002)
where w is energy in joules (J) and is qcharge in coulombs (C).
The voltage vabor simply vis measured in volts (V),
Hence, 1 volt = 1 joule/coulomb = 1 newton meter/coulomb
Thus, the potential difference or voltage is the energy (w)required to move a unit charge (q) through an element,
measured in volts (V).
Figure 2.13 shows the voltage across an element connected to
points a and b. The plus (+) and minus ( ) signs are used to
define reference direction or voltage polarity. The vab can be
interpreted in two ways: (1) point a is at a potential of vab volts
higher than point b, or (2) the potential at point a with respect to
point b is vab. It follows logically that in general
= For example, in Fig. 2.14, we have two representations of the
same voltage. In Fig. 2.14(a), point a is+9Vabove point b; in Fig.
2.14(b), point b is 9 V above point a. We may say that in Fig.
2.14(a), there is a 9-V voltage drop from a to b or equivalently a
9-V voltage rise from b to a. In other words, a voltage drop from
a to b is equivalent to a voltage rise from b to a.
2.8 ELECTROMOTIVE FORCE (EMF)
The force which creates the pressure that causes the current to
flow through a conductor is called electromotive force (EMF).
The EMF of a cell is defined as equal to the potential difference
between the terminals of the cell in an open circuit, i.e., when no
current is drawn from the cell. In case, some current is drawn i.e.,
the cell is connected in a closed circuit the potential difference of
the terminals will not be equal to the EMF. The unit of EMF is
also volt.
2.9 VOLTAGE AND CURRENT SOURCES
The voltage or current sources that generally deliver power tothe circuit connected to them. There are two kinds of sources:independent and dependent sources.
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2.9.1 Independent Sources
An ideal independent source, which is an active element,
provides a specified voltage or current that is completely
independent of other circuit variables.
That is, an ideal independent voltage source delivers to the
circuit whatever current is necessary to maintain its terminal
voltage.
Physical sources such as batteries and generators are examples
for the ideal voltage sources. Figure 2.15 shows the symbols for
independent voltage sources. Notice that both symbols in Fig.
2.15(a) and (b) can be used to represent a dc voltage source, but
only the symbol in Fig. 2.15(a) can be used for a time-varying
voltage source.
An ideal independent current source is an active element that
provides a specified current completely independent of the
voltage across the source. The symbol for an independent current
source is displayed in Fig. 1.12, where the arrow indicates the
direction of current i.
2.9.2 Dependent Sources
An ideal dependent (or controlled) source is an active element inwhich the source quantity is controlled by another voltage or
current.
Dependent sources are usually designated by diamond-shapedsymbols, as shown in Fig. 2.17. Since the control of thedependent source is achieved by a voltage or current of someother element in the circuit, and the source can be voltage orcurrent. Dependent sources are useful in modeling elements suchas transistors, operational amplifiers and integrated circuits.
2.10 RESISTANCE
If we apply the same potential difference between the ends of
geometrically similar rods of copper and glass, the currents
passing through these rods are varied. These variations of
currents are due to the internal characteristic of conductor called
electrical resistance.
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CHAPTER 2 | 2.10 Resistance 39
Engineering Physics (MASC 10002)
The opposition to the flow of electric current offered by a
material is called resistance.
2.10.1 Ohms Law
A German Physicist, George Ohm derived an importantrelation which is known as Ohms law.
Ohms law states that at uniform temperature, current
flowing through a conductor is always proportional to the
potential difference between its two ends.
If I is the current passing through a conductor and V is
the potential difference between its ends, then
V (or)V = (2.12)where R is the proportional constant known as electrical
resistance of the conductor.
Therefore, the resistance (R) between any two points of a
conductor is,
R =
V
I (2.13)
As the current is due to the flow of free electrons, we could also
say that resistance is the opposition offered by the substance to
the flow of free electrons. This opposition occurs since atoms and
molecules of the substance block the flow of free electrons. Some
metals such as silver, copper, aluminium etc. offer very low
resistance while the substances such as glass, rubber, mica, dry
wood etc. offer high resistance to the electric current.
It may be noted that resistance is the electric friction offered by
the substance and causes heat with the flow of electric current.
The moving electrons collide with atoms or molecules of the
substance; each collision results the smaller amount of heat.
The unit of resistance is ohm and it is symbolically
represented as . A wire is said to have a resistance of 1 ohm if a
Fig. 2.18
R = 1
1 A
1 V
V
I R
Relation between voltage, curren
and resistance.
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40 CHAPTER 2 | 2.10 Resistance
Supplementary study material prepared by Dr. R.D. Senthilkumar| Fall 2013
p.d. of 1 volt across its ends causes 1 ampere of current to flow through it (Fig. 2.14).
2.10.2 Resistivity (or) Specific Resistance
The resistance R of any conductor is
i) directly proportional to its length (L),ii) inversely proportional to its area of cross-section (A),iii) depends on the nature of material, andiv) depends on the temperature.
Therefore,
R (2.14)
where (Rho) is the constant known as specific resistanceor resistivityof the material. Its value
depends on the nature of material. If l= 1 m and a = 1m2, then R = . Hence specific resistance
or resistivity of a material is the resistance offered by 1 meter length of wire of material having 1m2 area
of cross-section. The unit of resistivity is ohm-m.
. = =
The following table provides the resistivity of some materials.
Sl. No. Material Nature
Resistivity
(-m) at room
temperature
1 Copper Metal 1.7 10-8
2 Iron Metal 9.68 10-8
3 Maganin Alloy 48 10-8
4 Nichrome Alloy 100 10-8
5 Pure silicon Semiconductor 2.5 103
6 Pure germanium Semiconductor 0.6
7 Glass Insulator 1010to 1014
8 Mica Insulator 1011to 1015
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CHAPTER 2 | 41
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2.10.3 Temperature Coefficient of Resistance
Normally, temperature affects the resistance of all the substances. The value of
resistance usually decreases in insulators while increasing the temperature, but in the case of
conductors the resistance increases when its temperature increases.
Consider a conductor having resistance R0at 0C. After heating the conductor to tC,
its resistance becomes Rt. Then the change in resistance (RtR0) is
i) directly proportional to the initial resistanceii) directly proportional to the rise in temperature andiii) depends on the nature of material
Therefore,
(RtR0) (R0 t) (or)(RtR0)= (R0 t) (or)
= (2.15)
where (alpha) is a constant called temperature co-efficient of resistanceat 0C. Its value depends
on the nature of material and temperature. From the above relation the temperature coefficient
of resistance can be defined as the ratio of increase in resistance per unit rise in temperature to
the original resistance. It can also be defined as the change in resistance per unit resistance, per
unit rise in temperature. The unit of is per C.If we rearrange the above equation, we get
= + (2.16)From this equation, the resistance of a conductor at any temperature can be found.
2.11 POWER AND ENERGY
Although current and voltage are the two basic variables in an electric circuit, they are not
sufficient by themselves. Thus we need to know how much power an electric device can handle,for practical purposes. To relate power and energy to voltage and current, we recall from
physics that:
Power is the time rate of expending or absorbing energy, measured in watts (W).
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42 CHAPTER 2 | 2.11 Power and Energy
Supplementary study material prepared by Dr. R.D. Senthilkumar| Fall 2013
.
Hence, mathematically,
=
where, p is the power in watts (W), is energy in Joules (J), t isthe time in seconds (S). From eq. 2.9, 2.10and 2.17, we get,
= =
= (2.18)
or
= (2.19)
Thus, the power absorbed or supplied by an element is the
product of the voltage across the element and the current
through it. The power p in Eq. (2.18) is a time-varying quantity
and is called the instantaneous power. If the power has a
+sign, power is being delivered to or absorbed by the element.If, on the other hand, the power has a sign, power is beingsupplied by the element.
Let us look into the relationship between current i and voltage v
in Fig. 2.19(a). In Fig. 2.19 (a), current enters through thepositive polarity of the voltage. In this case, = + or implies that the element is absorbing power. As thecurrent leaves through the positive polarity of the voltage, in
Fig. 2.19 (b), = or . In other words, in Fig. 2.19(b), the element is releasing or supplying power.
According to the conservation of energy, the algebraic sum of
power in a circuit, at any instant of time, must be zero:
= (2.20)
This says that the total power supplied to the circuit is equal to
the total power absorbed.
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CHAPTER 2 | 43
Engineering Physics (MASC 10002)
(a)
(b)
Fig. 2.20 Fixed resistors: (a) Wwound resistor, (b) Carbon film resi
Fig. 2.21 Symbol of fixed resistor
Fig. 2.22 Circuit symbol for: (a) a varresistor in general, (b) Potentiometer
From Eq. (2.18), the energy absorbed or supplied by an element
from time to time is
= =
(2.21)
The electric power utility companies measure energy in watt-
hours (Wh), where
1 Wh = 3,600 J
2.12 RESISTORS
An electric resistoris a two-terminal passive component used to
oppose and limit current. A resistor works on the principle of
Ohms Law. There are two types of resistors, namely, fixed and
variable.
2.12.1 Fixed type resistors
Most resistors are of the fixed type, meaning their resistance
remains constant. The wire-wound and composition are two
common types of fixed resistors which are shown in Fig. 2.20.
The composition (carbon) resistors are used when large
resistance is needed. The circuit symbol in Fig. 2.21 is for a fixed
resistor.
2.12.2 Variable type resistors
Variable resistors have adjustable resistance. The symbol for avariable resistor is shown in Fig. 2.22(a). A common variable
resistor is known as a potentiometer or pot for short, with the
symbol shown in Fig. 2.22(b). The pot is a three-terminal
element with a sliding contact or wiper. By sliding the wiper, the
resistances between the wiper terminal and the fixed terminals
vary. Like fixed resistors, variable resistors can either be of wire-
wound or composition type, as shown in Fig. 2.23. Although
Energy is the capacity to do work, measured in joules (J).
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44 CHAPTER 2 | 2.12 Resistors
Supplementary study material prepared by Dr. R.D. Senthilkumar| Fall 2013
resistors like those in Figs. 2.20 and 2.23 are used in circuit designs, today most circuit
components including resistors are either surface mounted or integrated, as typically shown in
Fig. 2.24.
Fig. 2. 23 Variable Resistors Fig. 2. 24 Surface Mount Resistors
(a) Composition type, (b) slider pot Surface mount resistors are soldered ontop of the circuit board and are
identified by number rather than color
bands.
2.12.3 Special resistors
Thermistorsare special resistors whose resistance changes with the temperature. There are
two types of thermistors, namely, positive temperature coefficient (PTC) and negative
temperature coefficient (NTC). In PTC, resistance increases with increase in temperature,
while in NTC, the resistance decreases with the increase in temperature.
PTCs are mostly used as current limiter for circuit protection. As the heat dissipation of
resistor increases, the resistance is increased thereby limiting the current. The NTCs are
mostly used for temperature sensing, replacement of fuses in power supply protection and for
low temperature measurements of up to 10K. An NTC can be replaced by a transistor with a
trimmer potentiometer. These are constructed using sintered metal oxides in ceramic matrix.
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CHAPTER 2 | 2.13 Ressitors in DC Ciricuits 45
Engineering Physics (MASC 10002)
Light Dependent Resistor (LDR) is another type of special
resistor. LDRs have cadmium sulfide zigzag tack whose
resistance decreases as the light intensity incident on it increases.
In the absence of light, its resistance is in mega ohms but on the
application of light, the resistance falls drastically. These resistors
are used in many consumer items such as camera light meters,
street lights, clock radios, alarms, and outdoor clocks.
2.13 RESSITORS IN DC CIRICUITS
Generally, the closed path in which Direct Current (DC.) flows
is called DC circuit.
A DC circuit basically have a DC power source (e.g.battery etc.), conductors which are used to carry current and the
load. Fig. 2.26 shows a bulb connected to a battery through the
conducting wires. The direct current starts from the positive
terminal of the battery and comes back to the same terminal
through the bulb as shown in Fig. 3.4. In this circuit, bulb is the
load. The path ABCDA is a DC circuit. Generally, resistances
act as load in a DC circuits and these may be connected in series
or parallel or series parallel. According to the connection of
resistances in the circuits, it can be classified as:
1) Series circuits2) Parallel circuits3) Seriesparallel circuits
2.13.1 RESISTORS IN SERIES
The circuit in which elements are connected end-to-end is called
series circuit.
Consider two resistors R1and R2are connected in series across abattery of V volts as shown in Fig. 2.27 a. The equivalent
resistance circuit is shown in Fig. 2.27b. By current
conservation, the same current (I) is flowing through each
resistor and the voltage (V) across each resistor is different.
Therefore, the total voltage drop from a to c across both
Bulb
V
A
B
I
Fig. 2.26
V2V1
V
R1 R2a b c
I
Fig. 2.27a shows the resistors R1an
R2are connected in series circuit
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46 CHAPTER 2 | 2.13.1 Resistors in Series
Supplementary study material prepared by Dr. R.D. Senthilkumar| Fall 2013
resistors is the sum of the voltage drops across the individual
resistors.
According to Ohms law, the voltage drop across the each resistor
is
V1= IR1 and V2= IR2. Therefore,
V = V1+ V2 or
V = IR1 + IR2= I (R1 + R2) or
V
I12
The two resistors in series can be replaced by one
equivalent resistor RTwith the identical voltage drop V = I RTwhich implies that
RT = R1 + R2
Hence, when a number of resistances are connected in
series, the total resistance is equal to the sum of individual
resistances.
The above argument can be extended to N resistors
connected in series. The equivalent resistance is just the sum ofthe individual resistances,
R=R+R+ +R= R=
2.13.1.1 Characteristics of series circuit
A series resistive network has the following
characteristics:
1.
Total resistance is equal to the sum of individual resistanceacross the each resistor.
2. Current flows through all the resistors are same.3. Voltage drop across each resistor is different.4. Sum of voltage drops is equal to the voltage supplied.5. Sum of power supplied by the source is equal to the power
dissipated in the components.
V
RT
a cI
Fig. 2.27b shows the circuit with
total resistance
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CHAPTER 2 | 2.13.1 Resistors in Series 47
Engineering Physics (MASC 10002)
2.13.1.2 Voltage (potential) divider
Two resistors that are connected in series can be used as voltage
divider. A Voltage divider circuit is shown in Fig. 2.28. It
consists of a battery which is connected with two resistors R1andR2 in series. The output voltage (divided voltage) is taken
between the two points B and C. The total resistance (RT) in the
circuit is
RT= R1+ R2
Then, I = VR+R =VR (since, V I, Ohms law)
Therefore, Vout= V2 = I R2(i.e. voltage across the resistor R2)
V = VR R ( I =VR)
The above relation is called voltage divider formula. Therefore in
a voltage divider circuits, the input voltage (Vin) is divided into
two parts one part across the resistor R1 and the other part
across the resistor R2. The output taken across the resister R2is
just a fraction of the input voltage and that fraction being
completely determined by the values of the resistances R1and R2.
For example,
If Vin= 12V, R1= 10kand R2 = 20k, then
Vout= (2/3) (12)= 8V.
If R1= 2kand R2= 680for the same input voltage,
then
Vout= (0.25) (12) = 3V.
Voltage dividers are widely used in electric meter circuits, where
specific combinations of series resisters are used to divide a
voltage into accurate values.
Fig. 2.28 Voltage divider
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48 CHAPTER 2 | 2.13.2 Resistors in Parallel
Supplementary study material prepared by Dr. R.D. Senthilkumar| Fall 2013
2.13.2 RESISTORS IN PARALLEL
A parallel circuit is a branched arrangement in which two or
more resistors are connected side by side across as shown in
figure 2.29. Parallel connections are also called multipleor shunt
connections.
Consider two resistors R1and R2are connected in parallel
across a battery of V volts as shown in Fig. 2.29 (a). By current
conservation, the current (I) across the resistors is not same and
must be divided into I1 (current through the resistor R1) and I2
(current through the resistor R2). But, the voltage across each
resistor is the same.
According to the Ohms law, current through each
resistance is
I1V
1 and I2
V
2.
Therefore, the total current passes in the circuit is
I I1I2V
1
V
2= V ( 1
1
1
2)
The two resistors in parallel can be replaced by one
equivalent resistor RT with V = IRT (Fig. 2.29(b)). Comparing
these results, the equivalent resistance for two resistors that areconnected in parallel is given by
1
T= ( 1
1
1
2)
This result easily generalizes to N resistors connected in
parallel
R =
R +
R + +
R =
R
=
When one resistance R1 is much smaller than the other
resistance Ri, then the equivalent resistance RTis approximately
equal to the smallest resistor R1. In the case of two resistors,
R= RRR+R RR
R = R
Branches
V
Fig. 2.29(a) shows the resistances
R1and R2in parallel circuit
I1
I
R1
I2
Fig. 2.29 (b) shows the total
resistance
V
I
I
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CHAPTER 2 | 2.13.2 Resistors in Parallel 49
Engineering Physics (MASC 10002)
2.13.2.1 Characteristics of parallel circuit
The characteristics of a parallel resistive network are following:
1. Voltage across each branch is the same.2. Current through each branch is different.3. The sum of branch currents is equal to the total current in the
parallel circuit.
4. The reciprocal of the total resistance equals the sum of thereciprocals of the individual branch resistances.
5. The total power consumed in a parallel circuit is equal to thesum of the power consumed by the individual resistors.
2.13.2.2 Current Divider
The resistors connected in parallel provide the mechanismof current dividers.
Current is inversely proportional to resistance.
Therefore, current through each branch of a parallel circuit
shown in Fig. 3.8 can be determined by setting up an inverse
formula like the one given below:
From the Fig. 2.30, the total resistance in the parallel
circuit is given by
T12
12= = V
Hence, the voltage in the parallel circuit is given by
V = ITRT
The current (I1) passing through the resistor R1 is,
(since, V = ITRT )
Similarly,
In general, n
n
The above relation is called as current divider formula.
Fig. 2.30
I = 6 mA
V
I1
R1 R22K
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CHAPTER 2 | 2.14 Kirchhoffs law 51
Engineering Physics (MASC 10002)
Now the circuit becomes as serial circuit (Fig. 2.31 (b)).
In the second step, the total resistance (RT) can be found by
adding the individual resistances as we seen in the serial circuit
early. Therefore,
RT= R1+ RTP+ R4= 5 + 2 + 1 = 8
Third step is to calculate total current supplied by the
battery by using Ohms law.
IT= Vin/RT= 12 / 8 = 1.5A
Now the branch currents I1 and I2 and various voltage
drops can be calculated as follows:
I1 = = A
= = or
I2= ITI1= 1.5 1 = 0.5 A
Voltage drop across R1(V1) = IR1 = 1.5 5 = 7.5 V
Voltage drop across R2(V2) = I1 R2= 1 3 = 3V
It should be noted that the voltage drops across R2 and
R3 are same as they are connected in parallel.
Voltage drop across R4(V4) = I R4= 1.5 1 = 1.5V.
Therefore, sum of various drops = 7.5 + 3 + 1.5 = 12V
which is equal to the input voltage given to the circuit. (Since
voltage drop across the parallel circuit is same, only the drop
across the R2is considered to calculate the sum of voltage drops
in the circuit).
2.14 KIRCHHOFFS LAW
We have seen the circuits in which various components
are connected in series, parallel and in series-parallel with a
single voltage source. If a circuit has two or more batteries
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52 CHAPTER 2 | 2.14.1 Kirchhoffs Current Law (KCL)
Supplementary study material prepared by Dr. R.D. Senthilkumar| Fall 2013
connected in its different branches, rules of series and parallel
circuits are inapplicable. Such large electric circuits can be easily
solved by the Kirchhoffs Current and Voltage laws which were
formulated by the German physicist Gastav Robert Kirchhoff in
1847.
2.14.1 KIRCHHOFFS CURRENT LAW (KCL)
This is Kirchhoffs first law which is based on the law of
conservation of charge, which means the algebraic sum of
charges within a system cannot change.
According to this statement, the total current leavinga node is
equal to the total current enteringthat node.
To explain this rule, consider the network in which four currents
I1, I2, I3and I4meeting at a junction A as shown in Fig. 2.32.
Let us assume that all the currents entering the junction as
positive signwhereas those leaving as negative sign. Hence
the currents I1 and I2 will be taken as positive whereas thecurrents I3and I4will be taken as negative.
According to the KCL,
I1+ I2+ (I3) + (I4) = 0I1+ I2I3 I4= 0
I = - at a nodeAlso, I1+ I2 = I3+ I4
That is, incomingcurrents = outgoingcurrents, or
Iin= Iout at a node
A
Fig. 2.32 Currents at a node
illustrating KCL
I1
I2
I3
I4
Kirchhoffs Current Law (KCL) states that the algebraic sum
of currents meeting at a point (or node) in any electric circuit
is zero.
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CHAPTER 2 | 2.14.2 Kirchhoffs Voltage Law (KVL) 53
Engineering Physics (MASC 10002)
2.14.2 KIRCHHOFFS VOLTAGE LAW (KVL)
This is Kirchhoffs second law which is based on the principle of
conservation of energy.
To illustrate KVL, let us consider the circuit in Fig. 2.33. The
sign on each voltage is the polarity of the first terminal as we
travel around the loop. We can start with any branch and go
around the loop either clockwise or counterclockwise. Suppose
we start with the voltage source and go clockwise around theloop as shown; then voltages would be v1,+v2,+v3,v4, and +v5,
in that order. For example, as we reach branch 3, the positive
terminal is met first; hence we have+v3. For branch 4, we reach
the negative terminal first; hence, v4. Thus, KVL yields
+ + + = Rearranging terms gives
+ + = + which may be interpreted as
Sum of voltage drops = Sum of voltage rises,
which is an alternate form of KVL.
Kirchhoffs Voltage Law (KVL) states that the algebraic sum
of all voltages in a closed path (or loop or mesh) is zero.
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54 CHAPTER 2 | Summary
Engineering Physics (MASC 10002)
SUMMARY
1. Electric charge:An intrinsic characteristic of the fundamental particles in the atoms.Electric charges may be positive or negative. It is measured in the unit of Coulomb.
2. Coulomb:One Coulomb is the amount of charge flowing through a conductor in one
second when one ampere of current is flowing through that conductor.
3. Coulombs law:(1) Like charges repel and unlike charges attract each other. (2) The
electrostatic force experienced between two charged particles is directly proportional to
the product of their strength and inversely proportional to the square of the distance
between them.
4. Electrostatic force (F) between two charged particles:
(for medium)
( r = 1 for air)
5. Electric field (E): The space in which an electric charge experiences a force.
Normally the space between and around the charged bodies is called electric field.
6. Electric lines of forces: These are the lines drawn virtually that indicates the
movement of an unit positive charge in the electric field.
7. Electric potential (V):The amount of work done in moving an unit positive charge
from infinity to a point in the opposite direction to the electric field. Its unit is J/C or
Volt (V).
8. Ohms Law:
At the uniform temperature, current flowing through a conductor is always
proportional to the potential difference between its two ends. i.e. V = I R. =
=
9. Resistivity : =
R
10. Temperature coefficient of resistance: = 11. Total Resistance in series: RT= R1+ R2+ R3+ + Rn
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56 CHAPTER 2 | Problems for Chapter 2
Engineering Physics (MASC 10002)
PROBLEMS FOR CHAPTER 2
1. Two spheres charged with equal but opposite charges experience a force of 103 Newtonswhen they are placed 10 cm apart in a medium of relative permittivity is 5. Determine the
charge on each sphere.
2. A point charge of C6100.3 is 12cm distant from a second point charge ofC6105.1 . Calculate the magnitude of the force between them.
3. What must be the distance between the point charge Cq 261 and point chargeCq 472 in order that the attractive electrical force between them has a magnitude of
5.7N?
4. The average distance r between the electron and the central proton in the hydrogen atomis m
11
103.5
. What is the magnitude of the average electrostatic force that acts betweenthese particles?
5. Two charges, q1 = +.35 C and q2 = +0.2 C are embedded 2 cm apart in a block ofpolyethylene (r= 2.3).
a) Determine the electric field due to q1on q2.
b) What would be the electric field due to q1on q2if the two charges were in vacuum?
6. A small uniformly charged sphere has a total charge of 1.4 10-8C.a) What is the electric field at a point 5 mm away from the sphere?
b) What force would act on a point charge of -110-9C at this point?
7. Two charges, q1 = 5C and q2= 7C, are located 15 cm away from the point P. Determinethe electric field at the point P by the charge A and B.
10.Determine the resistance of an electric light bulb if there is a current of 0.8A and a p.d. of120V. Ans: 150Ohms
11.The high voltage in a TV receiver is 17kV. The maximum allowable current is 150 A.Find the least permissible value of load resistance. Ans: 113.3 106.
12.What is the p.d. across a toaster of 13.7Ohms resistance when the current through it is8.75 A? Ans: 120V
13.An electric kettle takes a voltage of 12.8V and supplies a current of 3.2A. Determine theresistance of the circuit. Ans: 4.
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CHAPTER 2 | Problems for Chapter 2 57
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14.Find the current through an electric heater with a resistance of 38when the p.d. of 240V is applied. Ans: 6.3A.
15.An electromagnet of resistance 12.4requires a current of 1.5A to operate it. Calculatethe required voltage. Ans: 18.6V.
16.A tungsten lamp has a resistance of 150 at 2850C. Determine its resistance at thetemperature of 20C. Temp. Coefficient of tungsten is 0.00492C at 0C. Ans: 11.
17.The resistance of a dynamo coil is 173at 16C. After working for 6hours on full-load,the resistance of the coil increases to 212. Find the temperature of the coil. Assume
temperature co-efficient of resistance of copper is 0.004261C at 0C. Ans: 72C.
18.Three resistors, 10 , 15 and 5 are connected in series across the 90 V battery.Calculate, a) the total resistance of the circuit, and b) the current through each resistor.
Ans: 30; 3A.
19.Resistors R1 = 3, R2 = 5and R3 = 4are connected in series across a p.d. of 12V.a) What is the total resistance of the circuit? b) Determine the current through each
resistor. c) Find the voltage drop across each resistor. Ans: 12; 1A; 3 V, 5 V and 4V.
20.A 60, a 90and an unknown resistor are connected in series to a battery of 130V. Ifthe current through the circuit is 0.67A, a) find the equivalent resistance of the circuit, and
b) determine the value of unknown resistor. Ans: 195; 44.
21.Three resistors of 15 are connected in parallel to a 3V battery. a) Find the effectiveresistance of the circuit. b) Determine the current passing through each resistor and hence
total current. Ans: 5; 0.2A in each resistor, 0.6A as total.
22.A 12 , a 15 and an unknown resistance are connected in parallel. The total currentpassing through the circuit is 12 A and the current across the 15branch is 4A. i) What isthe total voltage? ii) Calculate the total resistance. iii) Find the value of unknown
resistance. Ans: 60V; 5; 20.
23.Calculate the total current. Calculate the voltage drop across the 36resistor. Calculatethe voltage drop across the 16resistor. Calculate the current through the 48resistor.
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58 CHAPTER 2 | Problems for Chapter 2
Supplementary study material prepared by Dr. R.D. Senthilkumar| Fall 2013
24.Calculate the total current. Calculate the voltage drop across the 8resistor. Calculate thevoltage drop across the 12 resistor. Calculate the current passing through the 12resistor.
25.For the circuits shown below, find the voltages, .
26.Find the currents and voltages in the circuit shown below:
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CHAPTER 2 | Short Questions for Chapter 2 59
Engineering Physics (MASC 10002)
SHORT QUESTIONS FOR CHAPTER 2
1. Define Electric charge. List the properties of electric charge.2. State the Coulombs law of electrostatics and derive the relation to find force between two
charged particles.
3. What is electric field? Write the relation of electric field intensity.4. What are the properties of electric lines of forces?5. Define the following terms:
a. Electric Potentialb. Electric Powerc. Electric energyd. Resistance
6. Define Electric currentand ampere.7. What is meant by potential difference? Write its unit.8. Explain Electromotive force.9.
What is Resistor? Explain the different types of resistor.
10.List the characteristics of resistors in series circuit.11.Write a short note on Voltage and Current divider circuits.12.What are the characteristics of resistors in parallel circuit?13.Write the formula for the equivalent resistances of two resistors in series and parallel
circuits.
14.Mention the advantages of parallel circuits.15.State and explain the Kirchhoffs current and voltage laws.
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