LECTURE 3 4

BS in Electrical
Engineering

Presented By:
Head of the Department
Dr. Engr. M. Idrees

Contents
 Electric Charge
 Electric current
 Voltage
 Power

 Passive Sign Convention
 Resistance
 Laws of Resistance
 Unit of Resistivity
 Conductance
 Effect of Temperature on Resistance
 Resistance in Series
 Resistance in Parallel

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Systems of UNITS

Quantity

Basic Unit

Symbol

Length

meter

m

Mass

kilogram

kg

Time

second

s

Electric current

ampere

A

Thermodynamic kelvin
Temperature

K

Luminous

intensity

cd

candela

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SI Prefixes

4

Electric Charge
 Electric charge is the physical
property of matter that causes it to
experience a force when placed in an
electromagnetic field.
 There are two types of electric
charges: positive and negative.
 Positively charged substances are repelled

from other positively charged substances,
but attracted to negatively charged
substances.
 Negatively charged substances are
repelled from negative and attracted to

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Electric Charge
 An object is negatively charged if it has an excess
of electrons, and is otherwise positively charged
or uncharged.
 The electric charge is a fundamental conserved
property of some subatomic particles, which
determines their electromagnetic interaction.
 Electrically charged matter is influenced by, and
produces, electromagnetic fields. The interaction
between a moving charge and an
electromagnetic field is the source of
the electromagnetic force, which is one of the

four fundamental forces.
 The SI derived unit of electric charge is
the coulomb (C).

6

Electric Current
 An electric current is a flow of electric
charge.
 In electric circuits this charge is often
carried by moving electrons in a wire.
 It can also be carried by ions in
an electrolyte, or by both ions and
electrons such as in a plasma.

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Electric Current
 The particles that carry the charge in an
electric current are called charge carriers.

 In metals, one or more electrons from each
atom are loosely bound to the atom, and
can move freely about within the metal.
 These conduction electrons are the
charge carriers in metal conductors.
 Electric current can be represented as the
rate at which charge flows through a given
surface as:
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SI Unit of Electric Current
 The SI unit for measuring an electric
current is the ampere, which is the flow of
electric charge across a surface at the rate
of one coulomb per second.
 Electric current is measured using a device
called an ammeter.
 The conventional symbol for current is I

9

Voltage
  The voltage between two points is equal
to the work done per unit of
charge against a static electric field to
move the charge between two points and
is measured in units
of volts (a joule per coulomb).
 It must take some work or energy for the
charge to move between 2 points in a
circuit say from point A to point B.
 The total work per unit charge associated
with the motion of a charge between 2
points is called VOLTAGE.
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Electric Potential
 An electric potential (also called the electric
field potential or the electrostatic potential) is the
amount of electric potential energy that a unitary

point electric charge would have if located at any
point in space, and is equal to the work done by
an electric field in carrying a unit positive charge
from infinity to that point
 The volt (symbol: V) is the derived
unit for electric potential, electric potential
difference (voltage), and electromotive force. The
volt is named in honour of the Italian
physicist Alessandro Volta (1745–1827), who
invented the voltaic pile, possibly the first
chemical battery.
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Electric Power
 Power is a measure of how much work can
be performed in a given amount of time.
 Power is a measure of how rapidly a
standard amount of work is done.
 Electric power is the rate of energy
consumption in an electrical circuit.

 Power = Work / Time

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Electric Power
 The unit of power is the joule per second (J/s),
known as the watt in honour of James Watt, the
eighteenth-century developer of the steam
engine.
The instantaneous electrical power P delivered to a
component is given by
where
P(t) is the instantaneous power, measured
in watts (joules per second)
V(t) is the potential difference (or voltage drop)
across the component, measured in volts
I(t) is the current through it, measured in amperes

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Electric Power
 If the component is a resistor with timeinvariant voltage to current ratio, then

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Passive Sign Convention
 The passive sign convention (PSC) is a sign
convention or arbitrary standard rule adopted
universally by the electrical engineering
community for defining the sign of electric
power in an electric circuit
 The convention defines electric power flowing
out of the circuit into an electrical
component as positive, and power flowing into
the circuit out of a component as negative.
 So a passive component which consumes
power, such as an appliance or light bulb, will
have positive power dissipation,
 while an active component, a source of power
such as an electric generator or battery, will 15

Active and passive
components
 From the standpoint of power
flow, electrical components in a circuit can
be divided into two types
 Active and
 passive components

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Passive Component
 In a load or passive component, such as a light
bulb, resistor, or electric motor, electric
current (flow of positive charges) moves through
the device under the influence of the voltage in
the direction of lower electric potential, from the
positive terminal to the negative.
 So work is done by the charges on the
component; potential energy flows out of the
charges; and electric power flows from the circuit
into the component, where it is converted to
some other form of energy such as heat or
mechanical work.

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Active Components
 In a source or active component, such as
a battery or electric generator, current is forced
to move through the device in the direction of
greater electric potential energy, from the
negative to the positive voltage terminal.
 This increases their potential energy, so electric
power flows out of the component into the
circuit. 
 Work must be done on the moving charges by
some source of energy in the component, to
make them move in this direction against the
opposing force of the electric field E.

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Passive Sign Convention
Current direction and voltage polarity play a major
role in determining the sign of power.

The voltage polarity and current direction must conform
with those shown in Fig in order for the power to have a
positive sign. This is known as
the passive sign convention.

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Conductance
 The ease with which an electric current
passes
 Conductance (G) is reciprocal of resistance
 Whereas resistance of a conductor
measures the opposition which it offers to
the flow of current, the conductance
measures the inducement which it offers
to its flow
 The unit of conductance is siemens (S).
 Earlier, this unit was called mho.
20

Conductivity
 The conductivity is defined as the
ration of the current density of J to
the electric Field E:

21

Resistance
 It may be defined as the property of a substance
due to which it opposes (or restricts) the flow of
electricity (i.e., electrons) through it.
 Metals (as a class), acids and salts solutions are
good conductors of electricity.
 Amongst pure metals, silver, copper and
aluminium are very good conductors in the given
order.

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Resistance
 The presence of a large number of free or
loosely-attached electrons in their atoms.
 These vagrant electrons assume a
directed motion on the application of an
electric potential difference.
 These electrons while flowing pass
through the molecules or the atoms of the
conductor, collide and other atoms and
electrons, thereby producing heat.

23

Resistance
 Those substances which offer relatively greater
difficulty or hindrance to the passage of these
electrons are said to be relatively poor conductors
of electricity like
 Bakelite,
 mica,
 glass,
 rubber,
 p.v.c. (polyvinyl chloride) and
 dry wood etc.

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The Unit of Resistance
 The practical unit of resistance is ohm.
 Definition
“A conductor is said to have a resistance of
one ohm if it permits one ampere current to
flow through it when one volt is impressed
across its terminals”.

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The Unit of Resistance
 For insulators whose resistances are very
high, a much bigger unit is used i.e.,
mega-ohm = 106 ohm (the prefix ‘mega’
or mego meaning a million) or kilo-ohm =
103 ohm (kilo means thousand). In the
case of very small resistances, smaller
units like milli-ohm = 10-3 ohm or microohm = 10-6 ohm are used. The symbol for
ohm is Ω.

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Laws of Resistance
 The resistance R offered by a conductor
depends on the following factors :
 It varies directly as its length, l.
 It varies inversely as the cross-section A of
the conductor.
 It depends on the nature of the material.
 It also depends on the temperature of the
conductor.

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Laws of Resistance
 Neglecting the last factor for the time
being, we can say that
R ∝ l A or R = l A ρ ...(i)
 where ρ is a constant depending on the
nature of the material of the conductor
and is known as its specific resistance or
resistivity.

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Laws of Resistance

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Laws of Resistance
If in Eq. (i),
we put
l = 1 metre and A = 1 metre2, then R = ρ
(Fig. 1.4)
Hence, specific resistance of a material may
be defined as the resistance between the
opposite faces of a metre cube of that
material.

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Units of Resistivity
 From Eq. (i), we have ρ = AR l

 Hence, the unit of resistivity is ohm-metre
(Ω-m).

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Resistivity in Ohm-metre

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Effect of Temperature on Resistance
The effect of rise in temperature is :
 To increase the resistance of pure metals. The
increase is large and fairly regular for normal ranges of
temperature. The temperature/resistance graph is a
straight line .As would be presently clarified, metals have a
positive temperature co-efficient of resistance.
 To increase the resistance of alloys, though in their
case, the increase is relatively small and irregular. For
some high-resistance alloys like Eureka (60% Cu and 40%
Ni) and manganin, the increase in resistance is (or can be
made) negligible over a considerable range of temperature.
 To decrease the resistance of electrolytes, insulators
(such as paper, rubber, glass, mica etc.) and partial
conductors such as carbon. Hence, insulators are said to
possess a negative temperature-coefficient of resistance
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Temperature Coefficient of Resistance

34

Temperature Coefficient of Resistance

35

Temperature Coefficient of Resistance

36

Resistance in Series
 When some conductors having resistances
R1, R2 and R3 etc. are joined end-on-end,
they are said to be connected in series.
 It can be proved that the equivalent
resistance or total resistance between two
points is equal to the sum of the three
individual resistances.

37

Resistance in Series
 Being a series circuit, it should be
remembered that
a) current is the same through all the three
conductors
b) But voltage drop across each is different
due to its different resistance and is
given by Ohm’s Law and
c) sum of the three voltage drops is equal to
the voltage applied across the three
conductors
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Resistance in Series
 V = V1 + V2 + V3 = IR1 + IR2 + IR3 —
Ohm’s Law
 But V = IR where R is the equivalent
resistance of the series combination. ∴ IR
= IR1 + IR2 + IR3 or
 R= R1 + R2 + R3

39

Main Characteristics of Series
Circuit
 The main characteristics of a series circuit
are :
a) same current flows through all parts of
the circuit.
b) different resistors have their individual
voltage drops.
c) voltage drops are additive.
d) applied voltage equals the sum of
different voltage drops.
e) resistances are additive.
f) powers are additive.
40

Resistance in Parallel
 A parallel circuit is a circuit in which the
resistors are arranged with their heads
connected together, and their tails
connected together.
 The current in a parallel circuit breaks up,
with some flowing along each parallel
branch and re-combining when the
branches meet again.
 The voltage across each resistor in parallel
is the same.

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Resistance in Parallel
 Three resistances, as joined in Fig are said
to be connected in parallel. In this case
 p.d. across all resistances is the same
 current in each resistor is different and is
given by Ohm’s Law
 the total current is the sum of the three
separate currents

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Resistance in Parallel

 The total resistance of a set of resistors in parallel is found by adding up the
reciprocals of the resistance values, and then taking the reciprocal of the total:
 equivalent resistance of resistors in parallel: 1 / R = 1 / R1 + 1 / R2 + 1 / R3 +...

43

Main characteristics of a Parallel Circuit

The main characteristics of a parallel circuit
are :
 same voltage acts across all parts of the
circuit
 different resistors have their individual
current.
 branch currents are additive.
 conductance's are additive.
 powers are additive.

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Kirchhoff’s Laws
 These laws are more comprehensive than
Ohm’s law and are used for solving
electrical networks which may not be
readily solved by the latter. Kirchhoff’s
laws, two in number, are particularly
useful
 In determining the equivalent resistance of
a complicated network of conductors and
 For calculating the currents flowing in the
various conductors.

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Kirchhoff’s Point Law or Current Law
(KCL)

 It states as follows :
“In any electrical network, the algebraic sum
of the currents meeting at a point (or
junction) is zero”
 Put in another way, it simply means that
the total current leaving a junction is equal
to the total current entering that junction.
 It is obviously true because there is no
accumulation of charge at the junction of
the network.
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(KCL)
 Consider the case of a few conductors
meeting at a point A as in Fig
 Some conductors have currents leading to
point A, whereas some have currents
leading away from point A.

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KCL
 Assuming the incoming currents to be
positive and the outgoing currents
negative, we have
I1 + (− I2) + (− I3) + (+ I4) + (− I5) = 0
or I1 + I4 − I2 − I3 − I5 = 0
or I1 + I4 = I2 + I3 + I5
or incoming currents = outgoing currents
 Similarly, in Fig (b) for node A
+ I + (− I1) + (− I2) + (− I3) + (− I4) = 0
or I= I1 + I2 + I3 + I4
We can express the above conclusion thus :
48

Kirchhoff’s Mesh Law or Voltage Law
(KVL)

 It states as follows :
“The algebraic sum of the products of
currents and resistances in each of the
conductors in any closed path (or mesh) in a
network plus the algebraic sum of the
e.m.fs. in that path is zero”.
In other words,
 Σ IR + Σ e.m.f. = 0 ...round a mesh
 It should be noted that algebraic sum is
the sum which takes into account the
polarities of the voltage drops.
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KVL
 The basis of this law is this :
If we start from a particular junction and go
round the mesh till we come back to the
starting point, then we must be at the same
potential with which we started.
 Hence, it means that all the sources of
e.m.f. met on the way must necessarily be
equal to the voltage drops in the
resistances, every voltage being given its
proper sign, plus or minus.
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Kirchhoff’s Laws

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Examples
 What is the voltage Vs across the
open switch in the circuit

52

 We will apply KVL to find Vs.
Starting from point A in the clockwise
direction and using the sign convention
+Vs + 10 − 20 − 50 + 30 = 0
∴ Vs = 30 V

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Examples
 Find the unknown voltage V1 in the
circuit of Fig.

54

 Initially, one may not be clear regarding
the solution of this question.
 One may think of Kirchhoff’s laws or mesh
analysis etc. But a little thought will show
that the question can be solved by the
simple application of Kirchhoff’s voltage
law.
 Taking the outer closed loop ABCDEFA and
applying KVL to it, we get
 − 16 × 3 − 4 × 2 + 40 − V1 = 0 ;
∴ V1 = −16 V
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