Unit 1 Fundamentals of Electricity

8/8/2019 Unit 1 Fundamentals of Electricity

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Unit 1 2

UUnniitt1Fundamentals of Physics/Electricity

Learning Objectives

Upon completion of this unit the studentwill be able to:

Recall the following fundamentalquantities and their SI units: mass (kg),length (m), time (s), electric current (A),temperature (K).

Recall derived quantities related toelectricity such as electric charge,resistivity, frequency, etc. and their SIunits.

Express the magnitude of fundamentaland derived quantities in exponential(scientific) notation.

Use the following prefixes and theirsymbols to indicate decimal sub-multiples and multiples of the SI units:pico (p), nano (n), micro (), milli (m),centi (c), deci (d), kilo (k), mega (M).

Distinguish between conventionalcurrent and electron flow.

State that current is a rate of flow ofcharge and is measured in amperes(A).

Recall and apply the relationship

charge (Q) = current (I) x time (t).

Distinguish between emf and potentialdifference.

This topic is an introduction to the principles

and techniques of physics utilized in the

analysis of electricity and electronics. Every

principle and technique is illustrated by an

example drawn from practical applications and

devices.

Recall and apply the relationship forresistance R = 1/G and conductanceG = 1/R.

State Ohm's law and apply Ohms lawto determine current, voltage, andresistance.

Sketch and interpret the graphical linear

relationship between current andvoltage in a purely resistive circuit.

Determine the total emf in aseries/parallel practical resistive circuitwith several sources.

Determine the total current in aseries/parallel practical resistive circuit.

Use electronics test equipment tomeasure voltage, current andresistance.

Distinguish between work and energy.

Describe the use of the heating effect ofelectric current flowing through aconductor.

Determine the efficiency of an electricaldevice.

Recall the power equations P = VI,

P = I2R and P = V

2/R and apply the

relationships P = VI and W = VIt tosolve problems.


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Unit 1 3

1.1 SI Units (fundamental and derived)

Fundamental Units

The SI (Systme International) units are sometimes also known as MKS units,

where MKS stands for "meter, kilogram, and second." At the heart of the SI is

a short list of 7 fundamental units defined in an absolute way without referring

to any other units. Table 1.1.1 summarizes 5 of the 7 fundamental units.

Table 1.1.1 The 5 SI fundamental units

Derived Units

There are generally two classes of SI units, SI fundamental units and SI

derived units. SI derived units, are defined algebraically in terms of the SI

fundamental units. Examples of such SI derived units are given in Table 1.1.2.

Table 1.1.2 The SI derived units

Derived quantity Name SymbolExpress

in terms ofother SI units

Expressin terms of

SI base units

Frequency hertz Hz - s-1

Energy, work, quantity ofheat

joule J Nm m2kgs-2

Power watt W J/s m2kgs-3

Electric charge, quantity ofelectricity

coulomb C - sA

Electric potential difference,electromotive force

volt V W/A m2kgs-3A-1

Capacitance farad F C/V m-2kg-1s4A2

Electric resistance ohm V/A m2kgs-3A-2

Electric conductance siemens S A/V m-2kg-1s3A2

Magnetic flux weber Wb Vs m2kgs-2A-1

Magnetic flux density tesla T Wb/m2 kgs-2A-1

Inductance henry H Wb/A m2kgs-2A-2

Celsius temperaturedegreeCelsius

C - K


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Unit 1 4

1.2 Standard Scientific Notation and Prefix Form

Exponential (scientific) Notation

Scientific notation also referred to as exponential notation is based on powers

of base number 10. The general format is given as:

N 10xwhere

N = number greater than 1 but less than 10 and

x = exponent or power of 10.

Placing numbers in exponential notation has the following advantages:

1. For very large numbers and extremely small ones, these numbers can be

placed in scientific notation in order to express them in a more concise

form.

2. Numbers placed in this notation can be used in computation with far

greater ease. This advantage was more obvious before the advent of

calculators.

Example 1.2.1

How do we place the number 12345 in standard scientific notation?

Solution:

1. Position the decimal point so that there is only one non-zero digit to its

left:

1.2345

2. Count the number of positions the decimal point was shifted to the left

and that will be x:x = 4

3. Multiply the results of steps 1 and 2 above for the standard form:

1.2345 104

For number less than one, we basically follow the same steps except in order

to position the decimal with only one non-zero decimal to its left, we will have

to move it to the RIGHT. The number of positions that we had moved it to the

right will be equal to -x. In other words we will end up with a negative

exponent.


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Unit 1 5

Example 1.2.2

How do we place the number 0.000123 in standard scientific notation?

Solution:

1. Position the decimal point so that there is only one non-zero digit to itsleft:

1.23

2. Count the number of positions the decimal point was shifted to the right

and that will be -x:

x = -4

3. Multiply the results of steps 1 and 2 above for the standard form:

1.23 10

-4

SI Prefixes

The 20 SI prefixes used to form decimal multiples and submultiples of SI units

are given in Table 1.2.1.

Table 1.2.1 The 20 SI prefixes

Factor Name Symbol Factor Name Symbol1024 yotta Y 10-1 deci d

1021

zetta Z 10-2

centi c

1018

exa E 10-3

milli m

1015 peta P 10-6 micro

1012

tera T 10-9

nano n

109

giga G 10-12

pico p

106 mega M 10-15 femto f

103

kilo k 10-18

atto a

102

hecto h 10-21

zepto z101 deka da 10-24 yocto y


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Unit 1 6

Example 1.2.3

Express the following values in prefix forms:

a) 0.0024 A = ? mA

b) 0.0000000062 C = ? C

c) 1 000 000 = ? M

d) 15 kHz = ? MHz

e) 0.03 ms = ? s

Solution:

a) 0.0024 A = 2.4 mA

b) 0.0000000062 C = 0.0062 C

c) 1 000 000 = 1 M

d) 15 kHz = 0.015 MHz

e) 0.03 ms = 30 s

Example 1.2.4

Express 0.0034 A in standard scientific notation and then into prefix form.

Solution:

In scientific notation:

0.0034 A = 3.4 10-3

A

In prefix form:

3.4 10-3 A = 3.4 mA


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Unit 1 7

1.3 Conventional Current and Electron Flow

Conventional current or sometime known as the flow of positive charge

assumes that current flows out of the positive terminal, through the circuit and

into the negative terminal of the DC voltage source as shown in Figure 1.3.1.

Figure 1.3.1 Conventional current flow in a series circuit

In metallic conductors like copper wires, the positive charge carriers are non-

mobile, and only the negatively charged electrons flow. Because the electron

carries negative charge, the electron flows in the direction opposite to that of

the conventional current. Therefore, electron flow is what actually happensinside a circuit and electrons flow out of the negative terminal, through the

circuit and into the positive terminal of the DC voltage source as shown in

Figure 1.3.2.

Throughout this course, conventional current is used. Therefore always

assume current flows out of the positive terminal of the DC voltage source.

Figure 1.3.2 Electron flow in a series circuit

5

1k

1kE V

I

I

I

I

1 k

1 k5 V

5

1k

1kE V

e-

e-

1 k

1 k5 V


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Unit 1 8

1.4 Charge, EMF and Potential Difference

Charge

Electric current is the flow (movement) of electric charge. The SI unit of

electric current is the ampere (A), which is equal to a flow of one coulomb of

charge per second. The amount of electric current (measured in amperes)

through some surface, example, a section of a copper conductor, is defined

as the amount of electric charge (measured in coulombs) flowing through that

surface over time.

If Q is the amount of charge that passed through the surface in the time t,

then the average current I is:

where

Q is the electric charge in coulombs (or ampere-seconds)

t is the time in seconds

It follows that:

and

1 coulomb (or 6.24 x 1018

electrons) is defined as the charge that passes a

point if 1 ampere flows for 1 second.

Example 1.4.1

A current of 1 ampere flows through a lamp for 1 minute. How much charge

passes through the lamp?

Solution:

Given: t = 1 min = 1 x 60 = 60 s

Formula: Q = It

= 1 x 60 = 60 C (60 coulombs)

An electron has a charge of 1.6 x 10-19

coulomb, so a current of 1A means

that 6.24 x 1018

electrons pass each point in each second! This is only a small

fraction of electrons in the wire!

t

Q=I

I

Qt =tQ I=


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Unit 1 9

EMF and Potential Difference

Maintaining a steady current in an electrical circuit requires a source of

electrical energy, such as an alkaline battery or electric generator. Chemical

energy in the battery, or mechanical energy in the case of the generator, is

converted into electrical energy by doing work on the charge passing through.

Figure 1.4.1 A zinc-carbon cell

Figure 1.4.2 A standby electric generator


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Unit 1 10

The electromotive force (referred to typically as EMF) is the work done per

unit charge by the battery or generator to move charge from lower to higher

potential. The unit of emf is volt (V). For a battery, the emf is also equal to the

voltage across the battery terminals when nothing is connected across them.

In an electrical circuit, the battery creates a potential difference in the circuit

due to its emf. Charge or current flows in an electrical circuit when there is a

potential difference. Remember current flows from high potential to low

potential.

The positive terminal of the battery has a higher potential than its negative

terminal. This difference in potential causes the current to flow in a circuit.

Figure 1.4.3 Digital voltmeter measuring the emf of a car battery


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Unit 1 11

G

1R =

R

1G =

1.5 Resistance and Conductance

Resistance (R) is the retarding force in a material that impedes the flow of

current. Resistors are load elements that dissipate heat when currents flow

into them. They are used in circuits to adjust voltages or limit currents.

All matters that allow the flow of electric current through them are called

conductors. Metals are known to be good conductors, with copper and silver

among the best. The conductivity of a particular material depends on the

number of free electrons present in it. So, a greater conductivity or

conductance implies lesser resistance and a lesser conductivity implies

greater resistance.

Conductance (G) is expressed in siemens (S) and resistance (R) is expressed

in ohms (). They are said to be reciprocal, or inverse of each other, i.e.

or

Example 1.5.1

Find the total circuit resistance Rtotal.

Solution:

598.8

3101.67

1

totalG

1totalR

S3101.67

4102.134104.553101

4.7k

1

2.2k

1

1k

13

G2

G1

Gtotal

G

totalG

3R1

2R1

1R1

totalR

1

=

==

=

++=

++=++=

=++=

1k 2.2k 4.7kRtotal 4.7 k2.2 k1 kR1 R2 R3


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Unit 1 12

resistance

voltagecurrent = R

E=I

1.6 Ohms Law

George Simon Ohm was a German physicist born in Erlangen,

Bavaria, on March 16, 1787. He discovered one of the most

fundamental laws of electricity, that is, Ohm's law.

Ohm's law states that, in an electrical circuit, the current passing through a

conductor between two points is directly proportional to the potential

difference (i.e. voltage drop or voltage) across the two points, and inversely

proportional to the resistance between them. This only holds true for an ohmic

material. Non-ohmic materials do not display a direct relationship.

or

Where

Iis the current in amperes

E is the voltage in volts

R is the resistance in ohms

Whenever two of the three quantities are known, the third quantity can alwaysbe determined.

There is an easy way to remember how to solve for any one quantity, given

the other two using Triangle method. First, arrange the letters E, I, and R in a

triangle like this:

I


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Unit 1 13

If you know E and I, and wish to determine R, just cross out R from the

triangle and see what's left:

If you know E and R, and wish to determine I, cross out I and see what's left:

Lastly, if you know I and R, and wish to determine E, cross out E and see

what's left:

Example 1.6.1

What is the bulb resistance?

Solution:

12E = V Bulb

I = 2 A

R = ?

I = 2 A

62

12ER ===

I


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Unit 1 14

Example 1.6.2

Given the current in each parallel branch and bulb 1 resistance, determine the

emf E and bulbs resistances R2, R3 and R4?

Solution:

Note that voltages across the parallel branches are the same.

12 Bulb 1 Bulb 2 Bulb 3 Bulb 4E = ? V

I1 = 2 A I2 = 1.5 A I3 = 1 A I4 = 0.5 A

R1 = 6 R2 = ? R3 = ? R4 = ?

V1262RE 11 === I

81.5

12ER

2

2 ===I

121

12ER

3

3 ===I

24

0.5

12ER

4

4 ===I


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Unit 1 15

1.7 DC Current and Voltage Measurements

Current and Voltage Relationship in a Purely Resistive Circuit

Graphical analysis provides convenient and rapid way to observe the behavior

of a circuit or the characteristics of an electronic device.

The first step to construct a graph is to obtain a table of data. The information

in the table can be obtained practically by taking measurements on the circuit

under examination, or can be obtained theoretically through computations.

To construct any graph of electrical quantities, it is standard practice to vary

one quantity in a specified way and note the changes that occur in a second

quantity. The quantity that is intentionally varied is called the independent

variable and is plotted on the horizontal or x-axis. The second quantity, which

varies as a result of changes in the first quantity, is called the dependent

variable and is plotted on the vertical or y-axis. Any other quantities involved

are held constant.

In the circuit shown in Figure 1.7.1, the resistance is held at 1 k and the

voltage is varied, the resulting changes in the current are then plotted. Theresistance is the constant, the voltage is the independent variable, and the

current is the dependent variable.

Figure 1.7.1 E, I and R in a basic circuit

I

RE

I

1 k


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Unit 1 16

Table 1.7.1 shows Resistor R is held constant at 1 k as voltage source E is

varied from 0 to 30 volts in steps of 5 volts. Through measurements make on

the circuit or the use of Ohm's law, you can find the value of current for each

value of voltage shown in the table.

Table 1.7.1

E (Volt) I (Ampere)

0 0.000

5 0.005

10 0.010

15 0.015

20 0.020

25 0.025

30 0.030

The information in the table is used to construct the graph shown in Figure

1.7.2. For example, when the voltage of 5 volts is applied across the 1 k

resistor, the current is 5 mA. These values of current and voltage determine a

point on the graph. When all 6 points have been plotted, a straight line is

drawn through these points.

Figure 1.7.2 Graph of volt-ampere characteristic

Volt-ampere characteristic

0.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

0 5 10 15 20 25 30

E in volts

Ii

namperes

R = 1 k


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Unit 1 17

Using the graph in Figure 1.7.2, the value of current through the resistor can

be quickly determined for any value of voltage between 0 and 30 volts. Since

the graph is a straight line, it shows that equal changes of voltage across the

resistor produce equal changes in current through the resistor. This fact

illustrates an important characteristic of the Ohms law - the current variesdirectly with the applied voltage when the resistance is held constant.

Resistors in Series

Figure 1.7.3 Resistors in series

Series circuit is sometimes known as cascade-coupled or daisy chain-coupled

circuit as shown in Figure 1.7.3. The current that flows in a series circuit has

to flow through every component in the circuit. Therefore, all components in a

series connection carry the same current.

The total resistance of all the resistors is obtained by adding the individual

resistance of each resistor.

1.5

2.2k

2.2k

2.2k

E

R1

R2

R3

N321T RRRRR ++++=K


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Unit 1 18

Resistors in Parallel

Figure 1.7.4 Four branches parallel circuit

Each current path in Figure 1.7.4 is called a branch. A parallel circuit is one

that has more than one branch. The voltage across any given branch of a

parallel circuit is equal to the voltage across each of the other branches in

parallel. The total resistance of the resistors connected in parallel is always

less than the value of the smallest resistor in the circuit.

The formula for total parallel resistance is:

Figure 1.7.5 Two resistors connected in parallel

For two resistors connected in parallel in Figure 1.7.5, the total resistance is

equal to the product of the two resistors divided by the sum of the two

resistors.

The notation used to indicate two or four resistors connected in parallel is

R1//R2 or R1//R2//R3//R4 respectively.

1.5 2.2k 2.2k 2.2k 2.2kE R1 R2 R3 R4

IT

I1 I2 I3 I4

N321

T

R

1

R

1

R

1

R

1

1R

++++

=

K

1.5 2.2k 2.2kE R1 R2

IT

I1 I2

A

B

21

21T

RR

RRR

+

=


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Unit 1 19

Total EMF and Current in a Series/Parallel Resistive Circuit

Example 1.7.1

Determine the total emf ET, circuit current IT and its direction.

Solution:

IT flows in the clockwise direction, that is, it takes the direction of E1 and E2

polarities.

V15.51.5512E-EEE321T

=+=+=

mA4.84k3.2

15.5

k2.2k1

15.5

RR

E

21

TT ==

+=

+=I

5

1.5

12

2.2k

1k

E1= V

E2= V

E3= V

R1

R2

E1 = 12 V

E3 = 1.5 V

E2 = 5 V

1 k

2.2 k

IT


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Unit 1 20

Example 1.7.2

Determine the total current IT and branch current I1 and I2 of the series-

parallel circuit.

Solution:

Equivalent resistance of the parallel resistors:

Total resistance of the circuit:

Total circuit current:

Voltage across R1:

Current I1:

Current I2:

k2.22k10.1

M22.44

k6.8k3.3

k6.8k3.3

RR

RR//RR

32

3232 ==

+

=

+

=

mA1.46k3.42

5

R

E

T

T ===I

( ) k3.42k2.22k1.2//RRRR 321T =+=+=

V1.75k1.2101.46RV 31T1 ===

I

mA0.98k3.3

1.75-5

R

V-E

2

11 ===I

mA0.48mA0.98mA1.46

or

mA0.48k6.8

1.75-5

R

V-E

1T2

3

12

===

===

III

I

R1

R2

R3

IT

I1

I2

3.3 k

6.8 k

1.2 k

E

5 V


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Unit 1 22

A DMM in resistance mode must not be used to measure resistance in-circuit

or with a circuit connected to a power supply. If you want to measure the

resistance of a particular component, you must take it out of the circuit

altogether and test it separately as shown in Figure 1.7.7 and Figure 1.7.8.

Figure 1.7.7 Schematic showing resistance measurement

Figure 1.7.8 Practical measurement of resistance

DMM measuring resistance works by passing a small current through the

component and measuring the voltage produced. If you try this with the

component connected in-circuit or with power supply, the most likely result is

that the meter reading will be erroneous or the meter will damage.

0

0

0

E1

I1

R1

R2

10 k

6.8 k

0

0

E1

R1 10 k

0

+

6.8 kR26.81 k


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Unit 1 23

Current Measurement

When making current measurement the flow of current is monitored. The only

way to do this is to put the DMM in series with the circuit as shown in Figure

1.7.9 and 1.7.10. In fact as the same current is flowing at every point in this

circuit, it can be inserted at any convenient point.

The DMM should be set to ammeter mode. If the meter does not possess

auto ranging then the current range must be set in excess of the expected

value. The DMM probes should be inserted in the correct sockets and

connected with the correct polarity into the circuit. The positive lead should be

connected to the more positive side of the circuit. With the DMM connected,

power can be applied to the circuit.

Figure 1.7.9 Schematic showing LED current measurement

Figure 1.7.10 Practical measurement of LED current

A+

R1

E1

LED

220

8.39 mA


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Unit 1 24

Never leave a DMM set to ammeter mode except when actually taking a

reading. The greatest risk of damage to the DMM is on the ammeter mode

because ammeter has a very low resistance.

Voltage MeasurementWhen making voltage measurement, the first step is to set the DMM to

voltmeter mode. If the DMM does not possess auto ranging then the voltage

range must be set in excess of the expected value. This is to make sure there

is no chance of the meter being overloaded and damaged. In addition to this,

check that the test leads are plugged into the correct sockets. Many DMMs

have different sockets for different types of measurement so check that the

test leads are plugged into the correct sockets. Usually a DMM will be

provided with two leads, one black, and the other red. The black one

represents the negative, and it is connected to the negative or "common"

socket on the meter. The red one is connected to the positive socket.

When making the measurement, the positive lead should be connected to

terminal which is expected to have the more positive voltage. If the leads are

connected the wrong way round a negative voltage will be displayed. This is

acceptable for a DMM because it will just display a negative sign. However for

an analogue multimeter, the meter needle will move backwards and hit a stop.

If at all possible it is best not to allow this to happen. With the DMM

connected, power can be applied to the circuit as shown in Figure 1.7.11 and

Figure 1.7.12.

Figure 1.7.11 Schematic showing voltage measurement

0

0

0V+

E1

I1

R1

R2

10 k

12 k2.73 V


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Unit 1 25

Figure 1.7.12 Practical measurement of voltage

Oscilloscope

An oscilloscope shown in Figure 1.7.13 is the most useful instrument for

testing circuits because it allows you to see the signals at different points in

the circuit. It is widely used for measurement of time-varying signals.

The best way to investigate an electronic system is to observe the signals at

the input and output of each system block, checking that each block is

operating as expected and is correctly linked to the next block.

Figure 1.7.13 An Oscilloscope measuring a sinusoidal signal from a signal generator


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Unit 1 26

1.8 Electrical Power and Energy

Work and Energy in Electricity

The concept of Work is closely related to that of energy. In fact, the formal

definition of energy is "the capacity to perform work".

When electric current flows in a circuit with resistance, it does work. Devices

convert this work into many useful forms, such as heat (electric heaters), light

(light bulbs), motion (electric motors) and sound (loudspeaker).

Everything we do is connected to energy in one form or another. In an electric

circuit, power is the rate at which energy is used. The derived unit for power is

the watt.

1 watt = 1 joule/second

Power means strength, or force or energy. Power is the rate at which work is

done or energy is used. Electric power is a measure of the rate at which

electricity does work or provides energy.

Example 1.8.1A resistor has a potential difference of 50 V across its terminals and 120 C of

charge per minute passes a fixed point. Under these condition at what rate is

electric energy converted to heat?

Solution:

Since V.A = (J/C) (C/s) = J/s = W

I = Q/t = 120 C / 1 min = 120 C / 60 s = 2 A

P = VI = 50 x 2 = 100 W

Since 1 W = 1 J/s, the rate of energy conversion is 100 J/s


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Unit 1 27

Heating Effect of Electric Current and its Applications

Electricity is the most useful and indispensable form of energy. It is the only

form that can be conveniently converted into any other form of energy to suit

our various needs. All electrical devices depend upon one or more effects of

electric current. They are chemical effect, heating effect, lighting effect,

magnetic effect and mechanical effect.

The heating effect of electric current is used in some heating appliances, such

as a soldering iron, electric iron, toaster, oven, room heater, immersion heater

and so on as shown in Figure 1.8.1. These appliances have coils of nichrome

wire (an alloy of nickel and chromium), which are heated when current passes

through it.

The reasons for using nichrome wire in a heating coil are:

High melting point

Nichrome wire can remain red-hot for a long time

High resistance

Soldering iron Immersion heater Bread toaster

Electric iron Portable oven Room heater

Figure 1.8.1 Various domestic heating appliances


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Unit 1 28

Whenever electricity is used for heating water or other liquids, the heating

element is safely insulated and enclosed in a tube. It prevents the liquids from

becoming live and therefore dangerous. In an electric iron, the heating

element is sandwiched between two thin sheets of mica, which is highly

insulating and can withstand high temperature.

Table 1.8.1 shows some heating appliances used in our daily life. Try filling up

the column on energy change.

Table 1.8.1

Appliances Energy change

Electric Iron Electrical energy is converted to heat energy

Electric fan Electrical energy is converted to mechanical energy

Electric heater

Loudspeaker

Hair dryer

Electric bulb

Joules Law

James Prescot Joule conducted a quantitative study of the

heating effect of electric current and formulated a law

known as Joule's Law.

The quantity of heat developed in a current carrying conductor is equal to the

product of the square of the electric current, the resistance of the conductor

and the time of flow of current through the conductor.

W = I2Rt joule

Where

W = heat energy produced in joule (J)

I = current in ampere (A)

R = resistance of the conductor in ohm ()

t = time in second (s)


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Unit 1 29

Using Ohms law V = IR, the above equation becomes:

W = VIt

or

W = VQ

Can you suggest some more equations?

Show your working here:

Using Power equations:

P = VI or P = V2/R or P= I

2R

Substituting the above equations:

W = Pt = V2/Rt = I2Rt

Example 1.8.2

An electric heater works in a 230 VDC and draws a current of 3 A for 5

minutes supply. Determine the heat energy produced in the heater. Also find

out the resistance of the coil in the heater.

Solution:

V = 230 V

I = 3 A

t = 5 minute = 5 x 60 = 300 s

Heat Energy W = VIt

= 230 x 3 x 300 = 207 000 J

The resistance of the coil

76.673

230VR ===

I


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Unit 1 30

Efficiency of Electrical Device

The efficiency of an entity (a device, component, or system) in electronics and

electrical engineering is defined as useful power output divided by the total

electrical power consumed (a fractional expression).

inputpowerTotal

outputpowerUsefulEfficiency =

Efficiency should not be confused with effectiveness. A system that wastes

most of its input power but produces exactly what it is meant to is effective but

not efficient. The term "efficiency" only makes sense in reference to the

wanted effect.

A light bulb might have 2 % efficiency at emitting light yet still be 98 % efficient

at heating a room. In practice it is nearly 100 %

efficient at heating a room because the light

energy will also be converted to heat

eventually, apart from the small fraction that

leaves through the windows.

In electric kettle, the efficiency is over 90 % as comparatively little heat energy

is lost during the 3 to 5 minutes a kettle takes to boil water.


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Unit 1 31

Example 1.8.3

What is the efficiency of an electronic amplifier that delivers 10 watts of power

to the loudspeaker while drawing 20 watts of power from the source?

Solution:

%50%10020

10%100

PowerInput

PowerOutputEfficiency ===

Electrical devices having high efficiency are obviously desirable when we wish

to design portable systems that operate on batteries. Inefficiency comes with

a cost either paid to the power company or the cost of replacing the batteries.

Also, any difference in the input and output power probably produces heat

within the system and the heat must be removed from the system if it is to

remain within its operating temperature range.

Power Equations

The letter P in electrical equations represents electric power. The term

wattage is used informally to mean 'electric power in watts'.

In direct current resistive circuits, instantaneous electrical power is calculated

using Joule's Law, which is named after the British physicist James Prescott

Joule, who first showed that electrical and mechanical energies were

interchangeable.

The following relationships for power in an electric circuit can also be

developed:

P = VI

1 watt = 1 volt.ampere

= 1 (joule/coulomb)/(coulomb/second)

= 1 joule/second


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Unit 1 32

Also from Ohms law V = IR

P = I2R

1 watt = 1 ampere2.ohm

And I = V/R

P = V2/R

1 watt = 1 volt2/ohm

The power rating shown on electrical appliances gives a comparative

indication of the cost of operating those appliances (not taking efficiencies into

account).

The energy consumed by an electrical appliance depends on its power rating

and the length of time it is operating.

Energy = Power time

W = Pt

W = VIt

The joule is too small to measure electrical energy consumption. Morecommon are the mega joule (MJ), or the kilowatt-hour (kWh).

MJ3.6kWh1

kWh1MJ3101

3600

kWh3600

3101MJ1

W.s6101MJ1

J6101MJ1

=

=

=

=

=


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Example 1.8.4

a) Determine the power consumption of the resistors R1 and R2 in watts (W).

b) Find the heat energies produced by resistors R1 and R2 if they are used in

10 second in joule (J).

Solution:

a) Power consumption of resistor R1

W0.026k5.6

212

1R

2E1

P ===

Power consumption of resistor R2

W0.12k1.2

212

2R

2E2P ===

b) The heat energies are

J0.26100.026t1

P1

W ===

J1.2100.12t2

P2

W ===

1.2k

5.6k

5E

12 V

1.2 k

R2

R1

5.6 k

Documents

Unit 1 Fundamentals of Electricity