chapter 7

LESSON 1- Analysing Example 1
electric fields and A charge of 600 C flow through a metal conductor in
charge flow every 5 minutes. What is the electric current in the
conductor?
How charges are produced? Solution

There are two kinds of charge which produce Example 2
opposite effects are called negative charge and An electric current of 3.2 mA flows through a bulb
positive charge. for 4 minutes.
Like charges always repel each other and unlike (charge in an electrons ,e =1.6 x 10-19C)
charges always attract each other. Determine,
An object becomes negatively charged when it gains (a) the electric charge
an excess of electrons. Similarly , when an object has (b) the number of electrons
some electrons removed, the deficiency of electrons Solution
makes the object positively charged.
The symbol of charge is Q and the unit is coulomb The experiment to investigate the relationship
(C). between the rate of flow of electric charge and
The charge in an electron is , e = 1.6 x 10-19C. the current
The Van de Graaff generator built a machine in which
charge continuously delivered to the inside of a
hollow metal dome by means of a rotating rubber
belt. So the generator can produce a high voltage,
usually in the megavolt range.

The definition of current, I

Current ,I is the rate of flow of charge, Q

Current = Charge
Time

Or I = Q
t

The unit of current, I , is Ampere (A)
1A= 1 C s-1

The charge in an electron is , e = 1.6 x 10-19C.
If the number of electrons is n,

Q = ne

1

Hypothesis: Electric field can be represented by arrow lines called
The current increases as the rate of flow of electric electric field line or electric lines of force.
charge increases The electric field is strongest where the electric lines
Aim of the experiment : of force are close together.
To investigate the relationship between the rate of The electric field lines of force never cross over and
flow of electric charge and the current they start on positive charges and end on negative
Variables in the experiment: charges.
Manipulated variable: rate of flow of electric charge The electric field lines of force is a vector quantity as
Responding variable: the current it has both force and direction.
Fixed variable: the number of charge
List of apparatus and materials: Making the shape of an electric field visible
Van de Graaff generator, crocodile clip,
galvanometer, microammeter, metal plate, nylon,
ping-pong ball coated with a metallic paint and metre
rule
Arrangement of the apparatus:

The procedure of the experiment which include Semolina powder is dispersed evenly on the surface
the method of controlling the manipulated of the oil.
variable and the method of measuring the The high voltage sup[ply is switched on.
responding variable. The semolina powder on the oil surface become
By using a metre rule , the distance between two aligned in the direction of electric field and thus maps
metal plate is measured = x out the electric field lines due the action of the force
The motor of the Van de Graaff is turned on for a few of the electric field.
minutes.
The ping-pong ball is touched to metal plate. Some patterns of the electric fields
The reading of microammeter is recorded = I
The experiment is repeated 5 times for with different The pattern of electric field lines of force depends on
distances between two metal plates the shape and the number of charged objects.
Tabulate the data: The following figure shows the some examples of the
electric fields:
x

I

Analysis the data:
Plot the graph I against x

Electric field
Electric field is a region around a charged object
which any other charged body experience a force.

2

Hence the ball is attracted by the negative plate. The
process is repeated caused the ball oscillates.
The speed of the ball increases as

(1) the distance between two electrode
decreases

(2) the mass of the ball decreases
(3) the voltage of the power supply increases

Effect of an Electric Field on candle flame

Effect of an Electric Field on a charge

A lighted candle is placed between to metal plates.
The voltage supply is switched on.
The flame is seen flatten and spreads out and more
to the negative plate.
It is because the heat of burning candle produces
positive and negative ions.
The positive ions which are heavier is pulled towards
negative plate with a large force occupy a larger
proportion of the flame.

A ping-pong ball is coated with a metallic paint.
The high voltage supply is switched on.
The ping-pong ball is touched the negative plate and
released.
The ping-pong oscillates between the two plates.
It is because when the ball touches the negative
plate,it receives negative charges. So the ball is
attracted by the positive plate. When the ball touches
the positive plate ,its charged is neutrallised and
immediately receives positive charge.

TUTORIAL 1

3

1 A Van de Graaff generator can produces 6 Which diagram shows the correct electric field
pattern?
A charge positive only
B charge negative only 7 Which diagram shows the correct electric field
C high voltage pattern?
D large current

2 240 C charge flows in a metal conductor for 2
minutes. What is the current in the conductor?

A 480 A B 120 A
C 2A D 1A
E 0.5 A

3 400 mA current flows for 5 second in a bulb.
What is the quantity of charge flows in the
bulb?

A 25 C B 12.5 C
C 8C D 4C
E 2C

4 A current of 6.4 A flows in a metal wire for 2
minutes. What is the number of electrons
flowing in the wire?
(e = 1.6 x 10-19 C )

A 3.2 x 1012 B 4.8 x 1012
C 8.0 x 1012 D 4.8 x 1015
E 4.8 x 1015

5 Which of the following statement is correct
about the electric field?

A Electric field is a region around a neutral
object

B The electric field lines of force always
cross over

C Electric field is a vector quantity
D The electric field lines start on positive

charges and end on negative charges.

8 The diagram shows a candle flame is placed in
an electric field .

4

The observation the shape of the flame is due …………………………………………
to (i) N

A the number of negative ions is greater than ………………………………………….
the number of positive ions (c) A microammeter is connected to M and

B the number of positive ions is greater than the another terminal is connected to pipe.
the number of negative ions When the Van de Graff is switched on for 4
minutes ,the reading of the microammeter
C negative ions is heavier than positive ions is 20 A.
D positive ions is heavier than negative ions (e= 1.6 x 10-19 C ).
Determine
9 The diagram shows a Van de Graff generator. (i) the quantity of charge

(ii) the number of electrons flows

10 The diagram shows an arrangement of the
apparatus to show the existence of an electric
field.

(a) What is a Van de Graff generator used (a) Why the olive oil is used?
for?
............................................................
.................................................................. (b) What happen the semolina powder when

.................................................................. the high voltage supply is switched on?

.................................................................. .............................................................

(b) Name the part laballed ................................................................
(i) M
(c) On the following figure , draw the electric
field lines to show the electric field
between two electrodes

5

12 The figure shows an uncharged ball X coated ..........................................................
with a conducting material is by a nylon thread (iii) What happen to the motion of the ball
between two metal plates P and Q. The metal
plate P is connected to negative terminal(earth) X when the connection between the
and plate Q to positive terminal of the high plate P and the negative terminal is
voltage supply. cut off?

(a) When the ball is touched to the plate Q ..........................................................
and released the ball oscillates between
two plates. ..........................................................
(i) Explain how the oscillations (b) Why the nylon thread is.
happened?
.......................................................... ..................................................................
.......................................................... (c) When the ball is replaced by the candle
..........................................................
flame , what happen to
(i) flame of the candle

..........................................................

..........................................................
(ii) give the reason for your answer in

..........................................................
(d) The ball X is charged by positive charges

and is placed near a metal plate a shown
in the following figure .Draw the electric
field lines to show the electric field
between the ball and the metal plate.

(ii) Give two suggestions to increase to
speed of the ball X?

..........................................................

6

LESSON 2 The potential difference across a conductor is
Analysing the relationship work (energy) to carry a unit charge
between electric current
and potential difference Potential difference = work = energy
charge charge
Current,I
Or V = E
From Lesson 1, Q
Current ,I is the rate of flow of charge, Q
The unit of potential difference, V = Volt(V)
Current = Charge
Time 1 V = 1 J C-1

Or I = Q Potential difference is said “ A potential
t difference across......"
The potential difference is measured by a
The unit of current, I , is Ampere (A) voltmeter and it must be connected in parallel
1A= 1 C s-1 with the component which we want to find the
potential difference between the component.
Current is said “ A current flows through......." For example, if we want to measure the
The current is measured by an ammeter and it difference across a bulb :
must be connected in series with the
component which we want to find the current
through the component.
For example, if we want to measure the current
through a bulb :

Potential difference (Voltage) , V
An electric circuit must have a cell or some
source of electrical energy ,if there is to be a
current. The energy to move the electrons or to
produce current we call “ voltage or potential
difference”

7

Example 1 The relationship between potential difference,V
and current,I in a metal conductor – Ohm’s Law
A battery is switched on for a few moments. In that
time 40 C pass through the battery and they carry The relationship between voltage, V and current ,I in
away 240 J of electrical energy . What is the a metal conductor is discovered by George Ohm is
potential difference across the battery? called as Ohm’s law.

Solution Ohm’s law state” The potential across a metal
conductor is directly proportional to the current
Example 2 flowing through the conductor , provided that its
temperature remains constant.
A current of 8 A flowing through an electric heater for
50 minutes convert 5.76 X 10 6 J of electrical energy Or V α I , if T remains constant
into heat energy.
Calculate The experiment to investigate the relationship
(a) the total charge circulated through the heater between the potential difference ,V and the
(b) the potential difference across the heater current,I in a metal conductor

Solution Hypothesis:
The potential difference across a metal conductor
increases as the current in the metal conductor
increases.
Aim of the experiment :
To investigate the relationship between the potential
difference ,V and current, I in a metal conductor
Variables in the experiment:
Manipulated variable: the current
Responding variable: the potential difference
Fixed variable: temperature
List of apparatus and materials:
Ammeter, voltmeter, rheostat, conductor wire,
connection wires ,dry cells and switch.
Arrangement of the apparatus:

8

The procedure of the experiment which include Resistance, R
the method of controlling the manipulated Based on the Ohm’s law,
variable and the method of measuring the
responding variable. VαI
The switch is closed. V=kI
The reading of the voltmeter ,V and the ammeter, I is k=V
recorded.
The experiment is repeated 5 times for with different I
value of, I, by adjusting the rheostat k is replaced by R
Tabulate the data:
I Hence definition of resistance is ;
V
Analysis the data: Resistance is the ratio of the potential difference to
Plot the graph V against I the current.
Or Resistance = Potential difference
The Ohmic conductors and non-Ohmic conductor
Current
Conductors which obey the Ohm’s law is called Or
Ohmic conductors.
R= V
I

The S.I. unit is Ohm (Ω)

1 Ω = 1 V A-1

Note : For a metal conductor ,if the temperature and
the other physical properties are remain unchanged ,
the resistance of the conductor not depend on the
current ,I and the potential difference, V.

9

The factors affect the resistance of a conductor Resistivity , ρ
(a) The length of the conductor( l)
R α I and R α 1
The resistance is directly proportional to the A
Length of the conductor
R αl ⇒ R=ρl
(RαI) AA

(b) The cross-sectional area of the conductor (A) ρ = RA
The resistance is inversely proportional l
to the cross-sectional area of the conductor
(R α1 ) As ρ increases , R increases.
A
S.W.G ( Standard Wire Gauge ) of a conductor
(c) The type of the material of the conductor wire
Different material of the conductors have the
resistance . When the number of S.W.G. higher the thickness of
the wire decreases .
For good conducting material such as silver and
cooper have low resistance. The experiment to investigate the relationship
For good insulating material such as rubber has between the resistance and the length of a metal
high resistance. conductor
(d) Temperature
For metal conductors such as cooper ,iron , the Hypothesis:
resistance is increases linearly to the The resistance of metal conductor increases as the
temperature. length increases
For alloys such as constantan and nichrome Aim of the experiment :
the temperature not affected the resistance. To investigate the relationship between the resistance
For semiconductor materials such silicon and and the length of a metal conductor.
germanium an also termistor the resistance Variables in the experiment:
decreases when its temperature is decreased. Manipulated variable: the length of the metal
conductor
Responding variable: the resistance
Fixed variable: temperature, the cross-sectional area
and type of material
List of apparatus and materials:
Ammeter, voltmeter, conductor wire, connection wires
,dry cells, metre rule and switch.

10

Arrangement of the apparatus: Potentiometer
As voltage divider. When the length increases , the
resistance increases and as the result the potential
differences (voltage) increases .

The procedure of the experiment which include Thermistor :
the method of controlling the manipulated A thermistor is a resistor whose resistance changes
variable and the method of measuring the with temperature. Its decrease in resistance as the
responding variable. temperature rises.
The length of the conductor wire is measured by a
ruler = l Light dependent resistor (LDR)
The switch is closed. The resistance of LDR changes depends on the
The reading of the voltmeter ,V and the ammeter, I is brightness of light falling on it. As the brightness of
recorded. light falling on it increases the resistance decreases.
The resistance is calculated , R = V
Superconductor
I
The experiment is repeated 5 times for with different Superconductor is a metal conductor decreases when
length of the wire its temperature decreases.
Tabulate the data: The resistance decreases with temperature but the
I resistance suddenly becomes zero when it is cooled
R below a certain temperature called the critical
Analysis the data: temperature, tc
Plot the graph R against l

Types of resistor

Fixed resistor :
Common materials is used in fixed resistor are alloys
such as nichrome and constantan.

Rheostat : These materials offer no resistance to flow of current
This has a coil resistance wire wound a ceramic and act as perfect conductors with zero resistiviy.
tube. A sliding contact ca be moved to any position Once the current is set up in these materials, its need
along the coil. This changes the length of the wire and no applied voltage to persist flowing without any loss..
as a result the resistance changes. The example of superconductor materials are
aluminium (Tc= 1.2 K), Plumbum (Tc= 7.2 K),
Niobium (Tc= 9.3 K), Nb3Sn (Tc= 18 K) , Nb3Ge (Tc=
23 K) and
YBa2Cu3O2 (Tc= 100 K).

11

Its used in transportation, medicine ,industry and
army .

TUTORIAL 2

1 The potential across two points in a metal 5 The graph shows the relationship between
conductor is 1 Volt if potential difference , V and current , I for an
electrolyte.
A a current of 1 A flows in a metal conductor
1 second Which of the following is true?
A The potential difference is directly
B a power of 1 W is generated when 1 C
charge flows proportional to the current
B The electrolyte obeys the Ohm’s law
C an energy of 1 J is used to flow 1 C of C The current does not flows in the
charge
electrolyte when the potential difference
D an energy of 1 J is used to flow 1 A of lower than 1.5 V
current 6 Which graph shows the relationship between
potential difference ,V and current, I for a torch
2 When lighting strikes between two charged light bulb?
cloud , 16 C charge flows from the cloud to the
Earth and transferred 6.4 x 106 kJ. What is the
potential difference across the cloud and the
Earth?

A 6.4 x 10 8 V B 8.0 x 107 V
C 4.0 x 108 V D 2.0 x 107 V
E 1.0 x 108 V

3 The potential difference across a bulb is 4.0 V
and 36 C charge flows in the bulb. What is the
energy is dissipated in the bulb?

A 0.1 A B 5.2 J
C 9.0 J D 126 J
E 144 J

4 Which graph obeys the Ohm’s law?

7 Which of the following factor is not affect the
resistance of a metal conductor?

A the length of the conductor
B the thickness of the conductor
C the type of material of the conductor
D the current flows through the conductor

8 The resistance of a conductor increases as

A the temperature decreases

12

B the length decreases 12 Which of the following V-I graph shows the
C the thickness decreases resistance increasing as the current rises?

9 Which circuit could be used to find the
resistance of the resistance?

13 Which of the following has the highest
resistance?

10 An electronic device labelled 12V , 2A. What is Length / cm S.W.G
the resistance of the device? A 100 32
B 100 20
C 50 32
D 50 20

A 0.67Ω B 6.0 Ω 14 The figure shows an electric circuit consists a
C 4.0 Ω D 14.0 Ω cooper wire , jockey ,ammeter, voltmeter and
E 24.0 Ω dry cell.

11 The graph shows the results of an experiment
to measure the resistance of a wire.

What is the resistance of the wire?. When the jockey is touched at a length 0.5m on
the cooper wire , the reading of ammeter and
voltmeter are 4A and 12 V respectively.
What is the reading of the ammeter when the
jockey is touched at a length 0.2m on the cooper
wire?

A 500 Ω B 1000 Ω A 3A B 10 A
C 2000 Ω D 4000 Ω C 12 A D 24 A
E 8000 Ω E 36 A

13

14 A piece of wire has diameter d and resistance C Critical temperature
R. When diameter of the wire is 2d , what is the D Virtual temperature
resistance of the wire. 18 The following graph shows a graph current, I
against potential difference, V represent three
AR BR conductors P, Q and R.
4 2
(a) Which conductor obeys the Ohm’s
CR D 2R Law?
.........................................................
E 4R
(b) (i) Which conductor has the
15 Which of the following changes to wire will highest resistance when the
double its resistance? current increases?
.................................................
Cross-sectional area Length
(ii) Give a reason for your answer
A Double Double in b(ii).
B Double No change …………………………………….
C No change Halve …………………………………….
D Halve No change …………………………………….

16 Which of the following is the symbol of a (c) Calculate the resistance of the
thermistor? conductor Q.

17 The graph resistance – temperature represents
a graph for a superconductor material.

What is the name of point P?

A Absolute temperature
B Basic temperature

14

where m is the gradient of the graph.
Calculate the value of ρ.

19 The graph the potential difference, V against
the length , L is the result of the experiment to

determine the resistivity, ρ, and the resistance
,R of a wire.

(a) Based on the graph in the figure above, ρ = ………………………….Ωm.

(i) what happen when L increases? (c) (i) From the graph, state the value of
L when V = 1.5V
…………………………………………… Show on the graph how you
determine the value of L.
…………………………………………… …………………………………………
(ii) determine the value of the potential …………………………………………

difference , V, when the length (ii) The resistance , R, is given by
L = 0 cm. R = ρL
Show on the graph , how you A
determine V
If the cross-sectional area, A of the
………………………………………… wire is 1.0 X 10-7 m2 and using the
value of ρ from (b), calculate the
……………………………………….. value of R when V = 1.5V.
(b) The resistivity , ρ, of the wire is given
(d) State one precaution that should be taken
by during this experiment.
ρ = 4.3 X 10-5 m …………………………………………………
…………………………………………………

15

20 The figure shows a bulb 12 V ,12 W is
connected to a power supply 12. The reading of
the ammeter is 1.0 A. A few minutes later, the
reading of the ammeter decreasing to 0.9 A and
the bulb becomes hot.

Based on the observations:
(a) State one suitable inference that can be

made.
(b) State one appropriate hypothesis for an

investigation.
(c) With the use of apparatus such as cooper

coils , beaker ,water and other apparatus,
describe an experimental framework to test
your hypothesis.
In your description, state clearly the
following:
(i) Aim of the experiment
(ii) Variables in the experiment
(iii) List of apparatus and materials
(iv) Arrangement of the apparatus
(v) The procedure of the experiment

which include the method of
controlling the manipulated variable
and the method of measuring the
responding variable
(vi) Way you would tabulate the data
(vii) Way you would analysis the data

16

LESSON 3- Analysing Resistors in parallel
series and parallel
circuits

Resistors in series

Resistors connected in series :
The same current flows through each resistors.
The potential difference across each resistors is
different.

Resistors connected in parallel :
The same potential difference across each
resistors.
The current flow through each resistors is
different.

17

Conclusion Hint 3

CURRENT POTENTIAL RESISTANCE
DIFFERENCE

SERIES

PARALLEL

Hints of a circuit Hint 4
Hint 1

Hint 2

18

Work example for series and parallel circuits Solution

Example 1

Determine the effective resistance for the following
circuits :-

Solution

Example 3

What is the reading of the voltmeter for the
following circuits:-

Example 2

What is the reading of the ammeter for the following
circuits:-

Solution

19

TUTORIAL 3 5 When four identical resistors are connected in

1 The figure shows ammeter reading in a circuit. series , the effective resistance is 20 Ω.
Which ammeter is showing a faulty reading? What is the effective resistance if the four
resistors are connected in parallel?
2 A battery lights all four lamps as shown in the
following figure. A 0.8Ω B 1.25 Ω
Which lamp, if removed ,would cause all the C 5.0Ω D 20.0Ω
lamps to go out? E 80.0Ω

3 Which of the bulbs in the following figure is the 6 When two identical resistors are connected in
brightest ?
Given that all the bulbs are identical. parallel , the effective resistance is 4 Ω.
What is the effective resistance if the two
resistors are connected in series?

A 2Ω B 4Ω
C 8Ω D 16Ω
E 20 Ω

7 The figure show the resistor combinations
P,Q and R.

4 Which of the following combination of switches Which resistor combination has the lowest
should be closed to make only bulb P,Q and R and the highest resistance?
light?
Lowest Highest
A1 2 3
B1 2 4 resistance resistance
C1 3 5 AQ P
D1 4 5 BR P
CR Q
DP R

20

8 Which resistor combination gives the effective 11 A current flows towards the junction of two
resistance 8 Ω ? resistors connected in parallel as shown in the
following figure. A1 and A2 are the readings
on ammeter V1 and V2 are the readings on
the voltmeters.

Which of the following is correct?

Ammeter reading Voltmeter reading

9 The figure a circuit consisting of 3 resistors A A1 < A2 V1 > V2
10 Ω and a resistor 1 Ω. B A1 < A2 V1 <2
C A1 = A2 V1 < V2
D A1 >A2 V1 = V2

What is the effective resistance of resistors
combination?

A 2.5Ω B 5Ω 12 What is the reading of the ammeter in the
C 10Ω D 12.5 Ω circuit above when the switch is closed?
E 25 Ω

10 A current flows in two resistors connected in A 0.3 A B 3A
series as shown in the following figure. A1 and C 4A DA
A2 are the readings on ammeter V1 and V2 E 36 A
are the readings on the voltmeters.

Which of the following is correct?

Ammeter reading Voltmeter reading

A A1 < A2 V1 < V2 13 What is the reading of the ammeter in the
B A1 < A2 V1 > V2 circuit above when the switch is closed?
C A1 = A2 V1 < V2
D A1 = A2 V1 = V2

21

A 0.4 A B 0.5 A 16 The figure shows a circuit. When the switch ,S
C 1.0 A D 2.0 A is opened and closed the reading of the
E 2.5 A ammeter is I1 and I2 respectively.

14 The diagram shows a circuit.

What the ratio of I1 : 12 ?

What is the reading of the ammeter when the A 1: 1 B 1:2
switch, S is opened and closed? C 1: 3 D 2:1
E 3:1

Switch S Switch S is
is opened closed

A 4.0 A 6.0 A
B 2.0 A 6.0 A
C 2.0 A 3.0 A
D 2.0 A 1.2 A

15 Two resistors 4Ω is connected parallel as 17 What is the reading of the ammeter in the
circuit above when the switch is closed?
shown in Figure (a) and the current I1 flows.
Later , the resistor resistors 4Ω is connected

series l as shown in Figure (b) and the current
I2 flows.

A 2A B 4A
3
C 3A
2 D 1A

E 1A
2

18 In the following circuit the reading of the
ammeter A1 is 12 A.

What is the reading of the ammeter A2 ?

What is the ratio I1 : I2 ? A 9A B 8A
C 6A D 3A
A 1:2 B 1: 4 E 1A
C 2:1 D 4:1
E 2:3

22

19 The diagram shows a circuit. 22

What is the value of current I1 and I2 ?

A I1 = 0.4A I2 = 0.4 A What is the reading of the voltmeter in the
B I1 = 2.0A I2 = 0.5 A circuit above when the switch is closed?
C I1 = 0.5A I2 = 2.5 A
D I1 = 2.5A I2 = 2.5 A A 2.0 V B 4.0 V
C 6.0 V D 12.0 V
E 24.0 V

23 The reading of the ammeter in the following
circuit is 2A.

20 What is the reading of the voltmeter in the
circuit above when the switch is closed?

A 8.0 V B 7.8 V What is the potential difference across the
C 6.8 V D 5.8 V resistor X?
E 4.8 V
A 0.5 V B 1.5 V
C 2.0 V D 3.0 V
E 6.0 V
21 The diagram shows a circuit.

24 The figure shows a battery 15 V is connected
to three resistors.

What is the potential difference across the
resistor 2 Ω ?

A 2V B 4V (a) What is the effective resistance of the
C 6V D 8V resistor 15 Ω and 10 Ω
E 10 V

23

(b) What is the effective resistance of the (b) (i) When an identical resistor is
resistors 15 Ω , 10 Ω and 1.5 Ω ? connected parallel to resistor Z ,
what happen to the reading of P
(c) What is the reading of the ammeter and Q?
(i) A1
P......................................................
(ii) A2
Q......................................................
(iii) A3
(d) What is the reading of the voltmeter (ii) Give the reason for your answer in
(b)(i).
(i) V1
25 The figure shows a circuit consisting of 3 ........................................................
(c) The resistors X, Y and Z are replaced
identical resistors X ,Y, Z and two
measurement instruments P and Q. by three identical bulb K, L and M as
shown in following figure.

Compare the brightness between the
bulb

(i) K and L

........................................................

(ii) L and M

........................................................

(a) Name the measurement instruments,
P...............................................................
Q..............................................................

24

26 The figure shows a circuit consisting of two
and a bulb.

Figure (a) Figure (b)

(a) When switch S is opened ,the reading of (a) (i) State the energy transformations
the ammeter is 1.5 A. that take place in the bulb.
Determine
(i) the resistance of the bulb. (ii) Draw a circuit diagram for each
photograph.
(ii) the reading of the voltmeter
(c) Observe the photographs in Figure (a)
(iii) charge flows in the bulb for 4 and Figure (b) to deduce a concept in
minutes. physics with regard to the potential
difference and the current flow for the
bulbs in series and parallel circuits.

(b) When the switch is closed ,
calculate
(i) the effective resistance in the
circuit.

(ii) the reading of the ammeter.

27 Figure (a) and Figure (b) show
photographs for two circuit. Each circuit
contains four identical bulbs connected
to four identical new dry cells.

25

LESSON 4- Analysing Internal resistance , r
electromotive force and
internal resistance. The reason why the potential difference across a cell
drops when it is supplying current is that cell itself
The definition and the S.I. unit of Electromotive has a resistance.
force (e.m.f), E The internal resistance ,r is the resistance within a
E.m.f is the potential across a cell or source of cell due to its electrolyte and electrodes or source of
electricity when it is on ‘ open circuit ‘ and supplying electricity.
no current. The electric current delivered to a circuit by a cell or
The S.I. unit of e.m.f is Volt (V). battery also flows through the battery itself.
The symbol of e.m.f is E Conduction inside a cell is by means of the movement
of charged atoms or groups of atoms called ions in
When the cell or source of electricity in a closed the electrolyte. There is some resistance to the flow of
circuit (current is flowing) ,the potential across the cell these ions which give a cell an internal resistance.
drops in is call the potential difference across the cell
,V The S.I. unit of r is Ohm (Ω)

Cells in batteries

When cell is joined together to form a battery , two
factors are affected by the way the cells are
connected. These are the e.m.f of the battery and
internal resistance of the battery. The figure following
shows three typical arrangements of cells that are
used.

V<E

The relationship between E,V,I,r and R

26

Potential difference Potential Potential
across cell when difference difference
no current flow = across + across
flowing external internal
resistance resistance

E =IR+Ir
E=V+Ir
V = IR

Example 1 Base on the information in the figure above,
The figure shows a circuit. calculate,
(a) the resistance f resistor R
(b) the internal resistance ,r of the cell

Solution

When the switch S is opened ,the reading of the Example 2
voltmeter is 1.5 V. When the switch S is closed the
reading of the voltmeter and ammeter are 1.35 V and An accumulator produce a current 4 A when it is
0.3 A respectively. connected to a resistor 2Ω. When the same
Determine accumulator is connected to a resistor 3Ω the current
(a) the e.m.f. of the cell is produced is 3A. Determine the e.m.f and the
(b) the internal resistance of the cell internal resistance of the accumulator.
(c) the resistance R
Solution
Solution

Example 2

27

Determination of E and r by using the graph Experiment to determine the e.m.f. and internal
method resistance a dry cell.

(1) Graph V against I

From the formula E = V + Ir When the switch is opened , the reading of the
ammeter and voltmeter is recorded .
E = .............................................................. Later, the switch is closed and the reading of the
r = .............................................................. ammeter=I and voltmeter=V is recorded.
(2) Graph R against 1 The experiment is repeated 5 times by adjusting the
rheostat.
I A graph V against I is plotted.

From the formula E = IR + Ir From the graph e.m.f is the intercept on the V-axis
and r is the gradient of the graph.

E = ........................................................
r = ........................................................

28

TUTORIAL 4 What is the internal resistance of the battery?

1 Which of the following physical quantity has the A 0.5Ω B 2.0Ω
same unit as the unit of the electromotive force? C 3.0Ω D 4.0 Ω
E 4.5Ω
A Current
B Energy
C Resistance
D Potential difference

2 When the switch S in the following figure is
opened the voltmeter reading is 1.5 V. When the
switch S is closed the readings of voltmeter and
the ammeter is 1.3 V and 0.2 A respectively.

5 The figure shows a circuit containing three
resistors 2Ω and a cell with an electromotive

force of 12 V and internal resistance of 6Ω .

What is the internal resistance of the cell?

A 0.1Ω B 0.3Ω
C 0.6 Ω D 1.0Ω
E 1.2 Ω

3 The figure shows a dry cell with an What is the current flowing through the circuit.
electromotive force of 3.0 V , and a resistor 3Ω.
A 1.1 A B 1.2 A
C 1.3 A D 1.4 A
E 1.5A

6 The figure shows a circuit containing two
resistors 6Ω and a cell with an electromotive

force of 12 V and internal resistance of 3Ω .

When the reading of the ammeter is 0.5 A,
what is the internal resistance of the cell?

A 4.0 Ω B 3.0 Ω What is the current flowing through each resistor
C 2.0 Ω D 1.0 6Ω?
E 0.5 Ω

4 The figure shows a battery is connected to a A 0.5 A B 1.0 A
C 2.0 A D 3.0 A
resistor 5Ω . When the switch S is opened the E 4.0 A
reading of the voltmeter is 10 V. When the
switched S is closed the reading of the
voltmeter is 14V.

29

7 The figure shows a circuit containing two What is the internal resistance and the
resistors 10Ω, a resistor 20 Ω , a cell with e.m.f electromotive force of the cell?

of 1.5 V and internal resistance of 2Ω.

Internal resistance E.m.f / V
/Ω
A 0.25 1.5
B 0.50 3.0
C 1.00 3.0
D 1.25 4.5
E 1.50 4.5

What is the reading of he voltmeter? 11 Which circuit can be used to determine the
electromotive force a battery?

A 0.23 V B 0.46 V
C 1.25 V D 1.50 V
E 2.00 V

8 An accumulator produce a current 0.6 A when it

is connected to a resistor 2Ω. When the same

accumulator is connected to a resistor 7Ω the
current is produced is 0.2 A.
What is the e.m.f and the internal resistance of
the accumulator.

A 1.0 V, 1.0 Ω B 1.5 V, 0.5 Ω
C 2.0 V, 0.5 Ω D 0.5 V, 1.5 Ω
E 1.0 V , 1.5 Ω

9 A cell produces a current 0.5 A when it is

connected to a resistor 2Ω. When the same

accumulator is connected to a resistor 4Ω the
current is produced is 0.4 A.
What is the e.m.f of the cell?

A 1.6 V B 2.6 V 12 Which of the following graphs relates the
C 3.0 V D 4.0 V reading of ammeter and the voltmeter in figure
E 4.5 V above?

10 Figure(a) shows a circuit to determine the e.m.f
and internal resistance of a cell. Figure (b)
shows the experiment is repeated by using the
same cell.

30

13 An experiment is carried out to determine e.m.f 15 The figure shows a circuit containing voltmeter,
and internal resistance of a cell as shown in ammeter, two switches S1 and S2 , two bulbs
Figure(a). The result of the experiment is shown M1 and M2 and a battery with internal
in Figure(b). resistance of 1Ω.

Which of the following represent the e.m.f and
the internal resistance of the cell?

e.m.f. y Internal (a) When the switches S1 and S2 is opened ,
A resistance the reading of the voltmeter is 12 V.
B p What is the e.m.f. of the cell?
C q p
D p q …………………………………………………
q y
x (b) When the switch S1 is closed and the
x switch S2 is opened , the reading of the
ammeter is 3.0 A.
p Calculate
q (i) the reading of the voltmeter?

14 The figure shows a graph potential difference,V
against current, I of a battery.

(ii) the resistance of bulb M1 ?

Which of the following is not true? (c) When the switches S1 and S2 is closed ,
the reading of the ammeter is 6.0 A .
A E.m.f of the battery is 1.5 V Calculate
B The external resistance is 1.5 Ω (i) the reading of the voltmeter?
C The internal resistance of the battery i
D As the current decreases the internal (ii) the resistance of bulb M2 ?

resistance of the battery decreases.

31

16 The graph V against I below shows the results (c) (i) From the graph , state the value of V,
of the experiment to determine the when I = 0.80 A.
electromotive force ,E, and the internal Show on the graph how you
resistance, r , of a dry cell. determine the value V.

…………………………………………..
(ii) The resistance R is given by

R=V
I

Calculate R when I = 0.80 A

(a) Based on the graph in the figure above, (d) State one precaution that should be
(i) what happen when I increases? taken during this experiment.
…………………………………………………
………………………………………………… …………………………………………………
…………………………………………………
(ii) determine the value of the potential
difference , V, when the current , 17 The figure shows a circuit to determine the e.m.f
I = 0.0 A. and internal resistance of a cell.
Show on the graph , how you
determine V. The results of the experiment is shown in the
table below.
…………………………………………………
(iii) name the physical quantity that I/ A 0.8 0.37 0.25 0.17 0.14
8 10
represents the value in (a)(ii). R/ Ω 3
1/ A-1
………………………………………………… I 13 5

(b) The internal resistance, r, of the dry cell is
given by
r = -m
where m is the gradient of the graph.
Calculate the value r.

(a) Complete the table above.
(b) Plot the graph R against 1

I

32

(c) Based on the graph determine
(i) the internal resistance of the cell.
(ii) the e.m.f of the cell.

(d) What is the charges flow in 2 minutes
when R = 6 Ω

33

LESSON 5 Analysing
electrical energy and power

Definition of electrical energy,E and the S.I. unit. Example 1
A current of 5A flows in a heating elements for 10
Based on the definition of current,, minutes. If the potential difference across the
I= Q elements is 240 V, calculate the electrical energy is
t used by the elements
Q = It ………………...(1) Solution

Based on the definition of potential difference, Example 2
V=E
Q When the switch S is closed for 5 minutes , calculate
E = V Q ………………(2) the energy is produced in the resistor 6Ω?
Solution
Substitute (1) into (2)

E = VIt …………………(3)

So the definition of ” electrical energy is the product of
the potential difference , the current and the time.”

The S.I. unit of Electrical energy is Joule (J)
IJ = 1VAs

Based on the equation of the Ohm’s law
V = IR …………………..(4)

I = V ……………………(5)
R

Substitute (4) into (3)
E = I2 R t

Substitute (5) into (3)
E = V2 t
R

Conclusion:

E=VIt
E = I2 R t
E = V2 t

R

1

The definition of the Electrical Power ,P and the Solution
S.I. unit Experiment to determine the power of a bulb.

From the definition of power,
P =E
t

and from the formula of the electrical energy ,
E = V It or E = I2 Rt or E = V2 t
R
P = VIt or P = I2 Rt or P = V2 t
t t Rt

Conclusion

E=VI
E=I2R
E = V2

R

The S.I. unit f power is Watt (W)
1W=1VA

Example 3

A small laboratory immersion heater uses a 12
supply. The current through the heater is 4A. What is
the power of the heater.

Solution

Example 4 The switch is closed.
The reading of the ammeter = I and the voltmeter V
An electric kettle is labelled 3 kW,240 V. is recorded.
The power of the bulb is calculated by using the
(a) What is meant by the label 3KW,240 V? formula P = VI
(b) What is the current flows through the kettle? The experiment is repeated 5 times by adjusting the
(c) Determine the suitable fuse to use in the kettle. rheostat.
(d) Determine the resistance of the heating The average power of the bulb is calculated.

elements in the kettle.

2

Buying electrical energy Solution

Every house has an electrical meter supplied by the
Electricity board.
The units used are kilowatt-hours (kWh).

1 kilowatt - hour is the energy supplied in 1 hour to an
appliance whose power rating is 1 kW.

Energy = power x time

Kilowatt-hour kilowatts hours

1 kW j = 1000 x 3600 J = 3.6 x 106 J

Example 4

Determine how many units is used for the following
electrical appliances :

(a) 2 bulbs is used in 5 hours and each is labelled
60 W,240V

(b) An air-conditioner is rating 2kW and is used for
5 hours per day during one month

Solution

Example 6 Efficiency of Electrical Appliances

The following table shows the electrical appliances is Efficiency = Useful energy output of appliance x 100%
Energy input to appliance
used at Ahmad’s house.
Efficiency = Po x 100 %
Appliance Number Power of Time is PI

of each used for

appliance appliance a day

(W) (Hour))

Fluorescent 15 60 12

lamp

Fan 8 90 5

Iron 1 1200 0.5

Calculate the cost of using the electrical appliances

by Ahmad’s Family within 20 days.

[ The cost of electricity is 20 sen for first 100 units and

24 sen for next 900 units ]

3

Example 7 Ways of increasing energy efficiency.
An electric motor is used to lift a load of mass 2 kg to
a height 5 m in 2.5 s. If the supply voltage is 12 V and (1) Maintaining the electrical appliances in good
the flow of current in the motor is 5.0 A , calculate working condition.
(a) Energy input to the motor For example :
(b) Useful energy output of the motor Regularly cleaning and removing dust from
(c) Efficiency of the motor the air filters of air conditioners and blades of
Solution electric fans.
Cleaning regularly filter bags of vacuum
Example 8 cleaner.
An electric kettle is used to boil some water to make
tea. The kettle has a power rating of 3 kW, and is (2) Operating the appliances correctly.
filled with 0.5 kg of cold tap water at 20oC . It takes a For example :
minutes and a half to boil. How efficient is this kettle? Turn off the appliance when not in use.
[ Specific heat capacity of water = 4 200 Jkg-1 oC-1] Use full loads of washing in a washing
machine.
Solution Use free wind and sunshine instead of a
tumble-dryer whenever possible.
Do not put warm food into a fridge or freezer.
Do not put more water in a kettle than you
need for your hot drinks.
Switch off all unnecessary lights; use low-
power lamps and install fluorescent lighting
where it is acceptable.
Make full use of energy needed to heat an
oven by cooking several things at the same
time.

4

TUTORIAL 5

1 The potential difference across a resistance is A 360 J B 288 J
6.0V and the current flows to the resistance is C 72 J D 36 J
0.2 A for 2 minutes. What is the energy is E 18 J
produced in the resistance?

A 60 J B 120 J
C 144 J D 240 J
E 480 J

2 15 J of energy is produced in a torch light bulb 5 When the reading of the ammeter in the figure
when the current flows through the bulb for above is 2 AJ, calculate the energy generated in
10 s. both of the resistors for every second.
What is the potential difference across the bulb?

A 0.5 V B 1.5 V A 0.5 J B 1.5 J
C 3.0 V D 4.5 V C 3.0 J D 4.5 J
E 6.0 V E 6.0 J

3 The figure shows a circuit containing two
resistors and a battery.

6 Based on the information in the figure above

determine the energy dissipated in resistor 3 Ω
for 5 second?

What is the energy dissipated per second in the A 30 J B 40 J
resistors 4Ω and 8Ω ? C 50 J D 60 J
E 90 J
A 6J B 3J
C 1.0 J D 0.5 J 7 A bulb is labelled 6 V, 0.6 A. What is the power
E 0.1 J of the bulb?

A 0.05 W B 3.6 W
C 10 W D 20 W
E 40 W

4 Base on the figure above,what is the energy
dissipated in the resistor 8 Ω in 25 second?

5

8 A filament bulb is labelled 240 V, 60 W. 13 Four electrical appliances are left switched on
What is the current flows through the filament for different times.
and the resistance of the filament? In which appliance is the greatest amount of
energy converted?

A 0.25 A, 60Ω B 0.25 A,960Ω Appliance Time
C 4.0 A , 60 Ω D 4.0 A, 960 Ω
E 5.0 A , 160Ω
A 3 kW water heater 0.5 hour
9 A current of 2 A flows in filament bulb . The B 1.5 kW hot-plate 1.5 hours
C 1 kW fan 3 hours
resistance of the filament is 5Ω. What is the D 750 W electric iron 1 hour
power generated by the lamp?

A 20.0 W B 10.0 W 14 Why is a fuse used in electrical appliance?
C 5.0 W D 2.5 W
E 0.5 W A To earth the appliance
B To protect the appliance and its cable
10 The figure shows a circuit. C To change the efficiency of the appliance
D To change the current rating of the

appliance

15 The fuse rating for a fuse used in the plug of an
electrical heater should be

Based on the circuit above , what is the reading A much less than the normal heater current
of the ammeter when the switch is closed? B just less than the normal heater current
C exactly equal to the normal heater current
D just greater than the normal heater current

A 1A B 4A 16 An electric heater marked “ 240V , 2.3 kW ”.
C 5A D 9A With fuse is most suitable to connect series to
E 12 A the heater?

11 The kilowatt - hour is a unit of A 5A B 7A
C 8A D 10 A
D 13 A

A charge B energy 17 A television is labelled 250 W , 240 V is used 5
C power D voltage hours per day in one month.
If the cost of electricity is 24 sen per unit , what
12 A 2 kW electric fire is used for hours. How long is the cost of operating the appliance in the
will it take a 100 W electric light bulb to use the month of June?
same amount of energy?

A 20 hours B 50 hours A RM5.00 B RM6.00
C 100 hours D 200 hours C RM8.00 D RM9.00
E 400 hours E RM12.00

6

18 The table shows the electrical energy 22 An electric motor is used to lift a load of mass 8
consumption tariff. kg to a height 5 m in 5 s. The flow of current in
the motor is 5.0 A .What is the potential
Electrical units Cost per unit (sen) difference across the motor if the efficiency of
First 200 units 22 the motor is 100%.
Second 500 units 25
A 10 V B 20 V
Calculate the cost in RM of using a 1.5 kW C 50 V D 80 V
refrigerator for 360 hours. E 100V

A 84.00 B 90.00 23 The figure show a circuit containing two
C 118.80 D 129.00 resistors P and Q , a bulb L, two switches S1
E 135.00 and S2, ammeter, voltmeter and a battery.

19 The table above shows the electricity tariffs for
domestic use. The reading of an electricity
meter reading in a house in the month of August
is 6020 and in the month of September is 7450.

Energy consumption Rate(sen/unit)
First 100 units 20 sen
Next 900 units 25 sen
Over 1000 units 30 sen

What is the cost of electricity is used in the
house ?

A RM420 B RM374
C RM228 D RM168
E RM 76

20 A fluorescent lamp with a power rating of 40 W (a) When the switches S1 and S2 is
produce 36 W of light energy. opened , the reading of ammeter and
What is the efficiency of the lamp? voltmeter are 0.3 A and 2.4 V
respectively.
A 4% B 72% Calculate,
C 76% D 85% (i) the resistance of the bulb?
D 90%
(ii) the resistance of the resistor P.
21 An electric motor is used to lift a load of mass 50
kg to a height 2 m in 10 s. The supply voltage is (iii) The power dissipated in P
25 V and the flow of current in the motor is 5.0 A
.What is efficiency of the motor

A 60% B 75%
C 80% D 85%
D 90%

7

(b) Compare the brightness of the bulb in the (ii) the resistance of the immersion
situation (a) when heater
(i) only the switch S1 is closed
(c) A student conducts an experiment to
.................................................................... compare the heating effect of immersion
heaters P,Q an R. The volume and initial
(ii) both the switches S1 and S2 temperature of the water is fixed. The
is closed. following table shows the result of the
experiment.
....................................................................
(c) The resistance of the resistor Q is 8Ω. Immersion Potential Current/A Time for
the water
When the switch S2 is closed and the heater difference/ 6.0 to start
switch S1 is opened, what is the reading of 5.0 boiling/
V 4.0 minute
(i) the voltmeter
P 240 8.0
(ii) the ammeter Q 240
R 240 10.0
24 Figure shows an immersion heater with 9.0
specification of 240V, 1 000 W
(i) State the energy change that occurs
when the immersion heater switched
on.

…………………………………………

…………………………………………
(ii) Calculate the energy supplied by

each of the immersion heaters P,Q
and R to start boiling the water.

(a) Name one suitable material to be used to (iii) Using your answer in (c)(ii) suggest
a heating element in the immersion heater. which immersion heater is the most
……………………………………….............. suitable to heat water. Give one
reason for your answer.
(b) The immersion heater is connected to a
240 V supply. …………………………………………
Calculate;
(i) the current that passes through the …………………………………………
immersion heater.
…………………………………………
8

26 The table shows three electrical appliances are 26 The figure shows an electric motor is used to lift
used in one month. a load.

Appliance Rating Time of use in (a) State the energy transformations that take
hour place when the switch is closed.
Air 240V, ....................................................................
conditioner 2kW 100
(b) The mass of the load is 0.8 kg and is lifted
240 V, 20 to a height 1.5 m in 4.0 second. The
Water heater 4 kW reading of the ammeter and voltmeter are
1.2 A and 5.0 V respectively.
Refrigerator 240 V, 200 Calculate
1 kW (i) useful energy output of the motor

(a) What is meant by the label 240 V, 4 kW ? (ii) Energy input to the motor?

.................................................................... (iii) the efficiency of the motor.

.................................................................... (c) When the load is removed and the switch
is closed, what happen to the
(b) (i) What is the suitable fuse is used (i) reading of ammeter?
in the refrigerator? …………………………………………..
(ii) power of the motor?
............................................................ ............................................................

(ii) Give the reason for your answer in
b(i)

............................................................

............................................................
(c) The following table shows the electrical

energy consumption tariff.

Energy consumption Rate per unit

First 100 units RM0.20
Next 100 units RM0.23
Over 200 units RM0.25

Based on the table calculate the total cost
for one month to use the electrical
appliances.

9