EP025 Note #KMKK

ACKNOWLEDGEMENTS

Unit Fizik, Kedah Engineering Matriculation College wish to thank everyone who has
contributed in shaping and writing this Physics 2, EP 025. Special thanks go to those for their
many valuable suggestions and conscientiousness in completing this book.

1. En. Khairul Nizam Bin Ab Hamid
2. En. Amar Shah Bin Ali
3. En. Mohd Hailmy Bin Razali
4. En. Mohd Husaine Bin Mukhtar
5. En. Ismail Bin Yaacob
6. Pn. Raziah Binti Mohd Noor
7. Pn. Jamilah Binti Morad
8. Pn. Roosaniza Binti Ramli
9. Pn. Normadiah Binti Shafie
10. Pn. Rahayu Binti Yahaya
11. Pn. Syazlina Binti Abdul Rasid
12. Pn. Fatin Azimah Binti Saad
13. Pn. Siti Aishah Binti Tahir

1

2

CONTENTS

TITLE PAGE

CHAPTER 1: ELECTROSTATICS 4
CHAPTER 2: CAPACITOR AND DIELECTRICS 19
CHAPTER 3: ELECTRIC CURRENT AND DIRECT-CURRENT 34
CIRCUITS
CHAPTER 4: MAGNETISM 46
CHAPTER 5: ELECTROMAGNETIC INDUCTION 73
CHAPTER 6: GEOMETRICAL OPTICS 91
CHAPTER 7: PHYSICAL OPTICS 106
CHAPTER 8: QUANTIZATION OF LIGHT 132
CHAPTER 9: WAVE PROPERTIES OF PARTICLE 144
CHAPTER 10: NUCLEAR AND PARTICLE PHYSICS 151

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4

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CHAPTER 1

ELECTROSTATICS

LEARNING OUTCOMES
At the end of this chapter, students should be able to:

1.1 Coulomb’s law

a) State Coulomb’s law, F  Qq  kQq .
4 or 2 r2

b) Sketch the electric force diagram
c) Apply Coulomb’s law for a system of point charges.

1.2 Electric field

a) Define and use electric field strength, E  F .
q0

b) Use E=kQ/r2 for point charge.
c) Sketch the electric field strength diagram
d) Determine electric field strength, E for a system of charges.

16.3 Electric Potential

a) Define electric potential, =
0

b) Define and sketch equipotential lines and surfaces of an isolated charge in a uniform

electric field

c) Use V  k Q for a point charge and a system of charges. Maximum four charges in
r

2D

d) Calculate potential difference between two points.
 V = Vfinal – Vinitial
V  W
qo

.
e) Deduce the change in potential energy, U between two points in electric field

U  qV

f) Calculate potential energy of a system of point charges. Up to maximum three
charges

U  k q1q2  q1q3  q2q3 
r12 r13 r23

1.4 Charge in a uniform electric field

(a) Explain quantitatively with the aid of a diagram the motion of a charge in a uniform

electric field.

(b) Use = ∆ for uniform E in:


i. Stationary charge

ii. Charge moving perpendicularly to the field

iii. Charge moving parallel to the field

iv. Charge in dynamic equilibrium

13

1.1 Coulomb’s Law

1 When the magnitude of two charges is increased by a factor of 2, the electrical forces
between these charges is
A. Doubled.
B. Quadrupled.
C. Reduced by a factor of 3.
D. Reduced by a factor of 4.

2 Two spheres are fixed near each other as shown. Each holds an identical charge +q and
experiences an electric force F. When a third sphere with a charge +q is placed in the middle
between them, it will experience a force of magnitude.

+q +q
A. 0

F
B.

4
C. F
D. 2F
3 Two small plastic spheres are given positive electrical charges. When they are 15.0 cm apart,
the repulsive force between them has the magnitude of 0.22 N. What is the charge on each
sphere

(a) if the two charges are equal
(b) if one sphere has four times the charge of the other ?
4 Three point charges are arranged on a line. Charge q3 = + 5.00 nC and is at the origin. Charge
q2 = - 3.00 nC and is at x = + 4.00 cm. Charge q1, is at x = + 2.00 cm. What is q1 (magnitude
and sign) if the net force on q3 is zero?
5 The FIGURE 1.1 below diagram shows point charges q1 = +10 C, q2 = -15 C and q3 = +5
C are placed at the corners of a triangle, as shown in the figure. Determine the resultant
electric force that acts on charge q3.

FIGURE 1.1

14

1.2 Electric Field

6 Electric Field strength at a point in space is defined as electric force experienced by
A. One proton at that point.
B. One electron at that point.
C. One coulomb positive charge at that point
D. One coulomb negative charge at that point

7 FIGURE 1.2 shows three negative point charges (–q, –q,and –2q) and one positive point
charge (+4q), along with some electric field lines drawn between the charges.

FIGURE 1.2

a) There are three things wrong with this drawing. What are they?
b) Sketch the correct representations of the electric field lines for the four charges.

8 A point charge q1 = -4.00 nC is at the point x = 0.600 m, y = 0.800 m, and a second point
charge q2 = +6.00 nC is at the point x = 0.600 m, y = 0 .Calculate the magnitude and direction
of the net electric field at the origin due to these two point charges.

9 Based on FIGURE 1.4. What is the electric field at the centre of the square ?

Q1 = -2C Q4 = -2C

Q2 = -2C Q3 = -2C

FIGURE 1.4

15

1.3 Electric Potential

10 The electric field strength at a distance of 120 mm from a point charge is 5.0 105 N C 1 .

What is the electric potential at that point?

A. 6.0104V
B. 4.2106V
C. 3.6107V
D. 6.0107V

11 FIGURE 1.5 shows a cross sectional view of two spherical equipotential surfaces and two
electric field lines that are perpendicular to these surfaces. When an electron moves from
point A to point B (against the electric field), the electric force does +3.2x10−19 J of work.

FIGURE 1.5
What are the electric potential differences
i. VB − VA,
ii. VC − VB
iii. VC − VA ?
12 A particle of charge 22.4 mC and mass 57.2 mg is initially held at rest in a constant electric
field of 133Vm-1. If the particle is released and accelerates through a distance of 14.9 m,
determine
(a) The change in potential energy.
(b) The change in electrical potential
(c) The final Speed.
13 Find the electric potential energy for the array of charges shown in FIGURE 1.6. Charge
q1=+4.0μC, is located at (0.0, 0.0) m; charge q2 = +2.0 μC, is located (3.0, 4.0) m and charge
q3=-3.0 μC is located at (3.0, 0.0) m.

FIGURE 1.6

16

14 (a) Find the potential at a distance of 1.00 cm and 2.00 cm from a proton.
(b) What is the potential difference between two points that are 1.00 cm and 2.00 cm from a
proton?

1.4 Charge in a Uniform Electric Field

15 The electric field strength at a distance of 120 mm from a point charge is 5.0 105 N C 1

What is the electric potential at that point?

A. 6.0104V
B. 4.2106V
C. 3.6107V
D. 6.0107V

16 An electron enters a uniform electric field with a speed v in the direction as shown below.
Which of the following statements is correct ?
A. The electrons is deflected in the direction of the electric field E.
B. The horizontal component of velocity remain unchanged.
C. The speed of the electron remains unchanged.

17 FIGURE 1.7 shows two parallel plates X and Y with a separation distance of 20 cm.
Potential difference between the plate is 20 V.

FIGURE 1.7
i) Sketch the electric field between the plates.
ii) Calculate electric field strength between the plates.
iii) If an electron is held at mid point between the plates, determine the magnitude and the

direction of force exerted on the electron.
iv) If the electron in (iii) is released, calculate the velocity for it to reach the plate.

17

18 A uniform electric field is established by connecting the parallel plates of a capacitor to a 12
V battery as shown in FIGURE 1.8.

FIGURE 1.8
(a) If the plates are separated by 0.75 cm, what is the magnitude of the electric field in the

capacitor ?
(b) A charge of +6.24 x 10-6 C moves from the positive plate to the negative plate. Find the

change in electric potential energy for this charge.

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23

24

25

26

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CHAPTER 2

CAPACITOR AND DIELECTRICS

LEARNING OUTCOMES

2.1 CAPACITANCE AND CAPACITORS IN SERIES AND PARALLEL.

a) Define and use capacitance, C  Q .
V

b) Determine the effective capacitors in series and parallel.

c) Use energy stored in a capacitor.

U  1 CV 2  1 QV  1 Q2
2 2 2 C

2.2 CHARGING AND DISCHARGING OF CAPACITORS.
a) State physical meaning of time constant and use , τ = RC.

b) Sketch and explain the characteristics of Q-t and I-t graph for charging and
discharging of a capacitor.

c) Use :

−
i. =
for discharging

−
ii. = (1 − ) for charging

2.3 CAPACITORS WITH DIELETRICS.

a) Define dielectric constant.   
r

o

b) Describe the effect of dielectric on a parallel plate capacitor.

c) Calculate capacitance of air filled parallel plate capacitor.

=


d) Use dielectrics constant

 
r

o

e) Use capacitance with dielectric, C = εrCo.

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2.1 CAPACITANCE AND CAPACITORS IN SERIES AND PARALLEL.

1. A capacitor consists of___________

A. Two conductors
B. Two semiconductors
C. Two dielectrics
D. Two insulators

2. Electric field lines always point toward

A. Ground
B. A region of higher potential.
C. A region of lower potential
D. Positive charge

3. Two capacitors with capacitances CA and CB are connected in parallel to a potential
difference, V. Which of the following statement is correct?

A. The potential difference across CA is larger than the other.
B. The charge on each capacitor is the same
C. The capacitance does not change in any condition
D. The capacitance decrease

4. A 3µF capacitor and a 6 µF capacitor, which are initially uncharged, are connected in
series with a 12V battery. What is the potential difference across the 6 µF capacitor?

5. The charged 400 µF capacitor is discharged through a 2.5 kΩ resistor. If the initial
charge on the capacitor is Q, what is the charge after 1.0 second?

6. The capacitance of the capacitor is 451pF, If a potential difference of 20.1 V is
supplied to the capacitor, determine the amount of charge on each plate.

7. A parallel-plate capacitor with an insulator as dielectric is first charged and then
disconnected from the voltage supply. The dielectric between the plates is then
removed. Describe and explain the changes, if any, to the

i. potential difference across the capacitor and When the dielectric is removed,

ii. energy stored in capacitor.

8. (a) Two conductors having net charges of +10.0 μC and –10.0 μC have a potential
difference of 10.0 V between them.
i. Determine the capacitance of the system.

ii. What is the potential difference between the two conductors if the
charges on each are increased to +100 μC and –100 μC?

29

FIGURE 2.1 (
9. Four capacitors are connected as shown in Figure 2.1 .

(a) Find the equivalent capacitance between points a and b.
(b) Calculate the charge on each capacitor if ΔVab = 15.0 V.

FIGURE 2.2

10. Consider the circuit shown in Figure 2.2, where C1 = 6.00 μF, C2 = 3.00 μF, and ΔV
= 20.0 V. Capacitor C1 is first charged by the closing of switch S1. Switch S1 is then
opened, and the charged capacitor is connected to the uncharged capacitor by the
closing of S2. Calculate the initial charge acquired by C1 and the final charge on each
capacitor.

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2.2 CHARGING AND DISCHARGING OF CAPACITORS.
11. Unit of capacitance is __________

A. Volts
B. Farad
C. Henry
D. Newton

12. What will happen to the capacitor when the source is removed?
A. It will not remain in its charged state
B. It will remain in its charged state
C. It will start discharging
D. It will become zero

13. (a) Sketch and explain the characteristics of the graph Q-t for
charging and discharging of a capacitor.

(b) A capacitor of 2.0 μF is charged using a 1.5 V battery. The charged capacitor
is then discharged through a 60 kΩ resistor.
i. What is the time constant of the discharge circuit?
ii. Find the time taken for the charge on the capacitor to decrease to 1
e
1
and of its initial value.
100

14. A fully charged capacitor has 12.0 µF and 6.0 mC charge. The capacitor has been
discharged through a 100 Ω resistor. Determine:
(a) potential difference across the capacitor

(b) time constant for charging circuit

(c) time taken if just 20% charge left in the capacitor,

(d) current at that respective time
15. A 3.0 μF capacitor is fully charged by a 12.0 V battery through a 25 Ω resistor. Calculate

(i) the maximum charge on the capacitor.
(ii) the time constant of the charging process.
(iii) the charge left on the capacitor after 100 μs discharge.

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2.3 CAPACITORS WITH DIELETRICS.

16. Capacitance increases with ______

A. Increase in plate area
B. Decrease in plate area
C. Increase in distance between the plates
D. Increase in density of the material

17. Capacitance decreases with _________
A. Increase in distance between the plates
B. Decrease in plate area
C. Decrease in distance between the plates
D. Increase in density of the material

18. Insulator which is placed between 2 plates of capacitor is

A. electric
B. dielectric
C. inductor
D. resistor

19. A parallel-plate capacitor has plates of area 320 cm2 are separated by a distance 0.450
mm. The plates are in vacuum., determine the capacitance of the capacitor.
(Given permittivity of free space, 0 = 8.85  1012 C2 N1 m2)

20. A capacitor has parallel plates of area 2000 cm2 separated by 1 cm apart. The
capacitor is connected to a power supply and charged to a potential difference V0 =
3000 V. It is then disconnected from the power supply and a sheet of insulating plastic
material is inserted between the plates, completely filling the space between them. We
find that the potential difference decreases to 1000 V while the charge on each
capacitor plate remains constant. Compute :

i. the original capacitance C0 ,
ii. the magnitude of charge Q on each plate,
iii. the capacitance C after the dielectric is inserted,
iv. the dielectric constant and
iv. the permittivity ε of the dielectric.

21. A circular parallel-plate capacitor with radius of 1.5 cm is connected to a 12.0 V
battery. After the capacitor is fully charged, the battery is disconnected without loss of
any of the charge on the plates. If the separation between plates is 3.0 mm and the
medium between plates is air.

a. Calculate the amount of charge on each plate. If their separation is increase to 8.0
mm after the battery is disconnected, determine

b. the amount of charge on each plate.

c. the potential difference between the plates.

d. the capacitance of the capacitor.

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22. a) A parallel-plate capacitor with an insulator as dielectric is first charged and then
disconnected from the voltage supply. The dielectric between the plates is then removed.
Describe and explain the changes, if any, to the
i. potential difference across the capacitor and
ii. energy stored in capacitor.

b) A capacitor has parallel plates of area 2000 cm2 separated by 1 cm apart. The
capacitor is connected to a power supply and charged to a potential difference V0 = 3000 V. It
is then disconnected from the power supply and a sheet of insulating plastic material is inserted
between the plates, completely filling the space between them. We find that the potential
difference decreases to 1000 V while the charge on each capacitor plate remains constant.
Compute :

i. the original capacitance C0 ,
ii. the magnitude of charge Q on each plate,
iii. the capacitance C after the dielectric is inserted,

iv. the dielectric constant  r and the permittivity ε of the dielectric.

33

CHAPTER 3: ELECTRIC CURRENT AND DIRECT- If the charge move around a circuit in the
CURRENT CIRCUITS same direction at all times, the current is
called direct current (dc), which is produced
3.1 Electrical Conduction by the battery.

Learning Outcome 3.2 Ohm’s law and Resistivity
a) Describe microscopic model of current.
b) Define electric current, = . Learning Outcome
a) State and use Ohm’s law.
b) Define and use resistivity, = .

c) Use electric current, = , = .

Ohm’s law: The steady current in a metallic
conductor that is not a site of emf is directly
In a metal, electrical conduction is through proportional to the potential difference
the drift of free electrons in the metal when a across it, if physical conditions such as
potential difference is applied across the temperature remain constant.
metal.
The drift velocity v of the free electrons is the  Electrical resistance, =
mean velocity of the electrons parallel to the
direction of the electric field when a potential
difference is applied. The resistance, R and the resistivity, ρ of a
Electrical conductivity metal increase as the temperature increases.

Area, Resistivity is defined as the resistance of a
unit cross-sectional area per unit length of
ADirection of electric current: the material.

 Positive to negative terminal  Resistivity, =

Direction of electron flows:
 Negative to positive terminal  A scalar quantity and its unit is ohm

The electron accelerates because of the meter ( m)
electric force acted on it.
 A measure of a material’s ability to
Electric current is the rate of flow of charge
 Current, = oppose the flow of an electric

current.

 =  It also known as specific resistance.
 It is a base and scalar quantities.
 The S.I. unit is ampere (A).  Resistivity depends on the type of the

1 ampere of current is defined as material and on the temperature.
One coulomb of charge passing through the
surface area in one second.  Good electric conductors have a very

low resistivity and good insulators

have very high resistivity.

Temperature coefficient of resistivity,
 = ∆

∆

Where is the resistivity at a reference
temperature, , ∆ is the change in
resistivity and ∆ is the change in
temperature.

1 ampere  1 coulomb  1 C s1
1 sec ond

34

3.3 Variation of resistance with temperature 3.4 Electromotive force (emf), internal
resistance and potential difference.
Learning Outcome
Learning Outcome
a) Explain the effect of temperature on electrical
resistance in metals. a) Define emf, ε and internal resistance, r of a
battery
b) Use R = Ro [1+ α(T – To)].
b) State the factors that influence internal
Effect of temperature on resistance resistance.

Metal c) Describe the relationship between emf of the
When the temperature increases, the battery and potential difference across the
number of free electrons per unit volume in battery terminals.
metal remains unchanged.
Metal atoms vibrate with greater amplitude d) Use terminal voltage, V =ε– Ir.
and cause the number of collisions between
the free electrons and metal atoms increase. Electromotive force (emf), is defined as the
Hence the resistance in the metal increases. energy provided by the source (battery/cell)
to each unit charge that flows through the
Superconductor external and internal resistances.
Superconductor is a class of metals and
compound whose resistance decreases to Terminal potential difference (voltage), V is
zero when they are below the critical defined as the work done in bringing a unit
temperature, Tc. (test) charge from the negative to the positive
When the temperature of the metal terminals of the battery through the external
decreases, its resistance decreases to zero at resistance only.
critical temperature.
The unit for both e.m.f. and potential
Electrical resistance in metals. difference are volt (V).

 R = Ro [1+ α(T – To)]. When the current I flows naturally from the
battery there is an internal drop in potential
difference (voltage) equal to Ir. Thus the
terminal potential difference (voltage), V is
given by

V =ε– Ir

and because V = IR, We can write down

ε = I(R+r)

Internal resistance of a battery, r is defined
as the resistance of the chemicals inside the
battery (cell) between the poles.

The value of internal resistance depends on
the type of chemical material in the battery.

35

3.5 Resistors in series and parallel V. A potential divider concists of two resistors
connected in series.
Learning Outcome
a) Derive and determine effective resistance of Use 1 = ( 1 )

resistors in series and parallel. 1+ 2+ ..…

Resistors in series 3.7 Potentiometer
Characteristics of resistors in series
Learning Outcome
 The same current I flows through a) Explain principles of potentiometer and its
each resistor
applications.
I  I1  I2  I3 b) Use related equations for potentiometer,

 Assuming that the connecting wires 1 = ℓ1 .
have no resistance, the total potential
difference, V is 2 ℓ2

V  V1  V2  V3 A potentiometer is used to compare
potential differences to a high degree of
 From the definition of resistance, thus accuracy

Reff  R1  R2  R3

Resistors in parallel
Characteristics of resistors in parallel

 There same potential difference, V
across each resistor where

V  V1  V2  V3

 The charge is conserved, therefore
the total current I in the circuit is

I  I1  I2  I3

 From the definition of resistance, thus

1 111
Reff R1 R2 R3

3.6 Potential divider

Learning Outcome

a) Explain principle of potential divider.

b) Use equations of potential divider,

1 = ( 1 )

1+ 2+ ..…

A Potential divider is used to tap off a fraction  used to measure an unknown emf, ξ x
of a voltage supply V so that it can be applied by comparison with a known emf, ξ s
across a load that needs a voltage of less than

36

 point d is a sliding contact used to

vary the resistance between point a &

point b

 the sliding contact at d is adjusted

until the G reads zero ( indicating a

balanced circuit )

 under this condition, the current in

the galvanometer is zero & the

potential difference between a & d

equal the unknown emf, ξ x
=
 Next replaced the ξ x with a standard
battery of known emf, ξ s & the
procedure is repeated.

 if Rs is the resistance between a & d
when balance is achieved :

=  Knowing that:
 Thus

= = =


 Substitute into equation we have:

If the resistor is a wire of resistivity ρ, its =
resistance can be varied by using the sliding
contact to vary the length L indicating how
much of the wire is part of the circuit.

37

CHAPTER 3

ELECTRIC CURRENT AND DIRECT-CURRENT CIRCUITS

3.1 Electrical Conduction
a) Describe microscopic model of current.
b) Define electric current, = .
c) Use electric current, = , = .

3.2 Ohm’s law and Resistivity
a) State and use Ohm’s law.
b) Define and use resistivity, = .

3.3 Variation of resistance with temperature
a) Explain the effect of temperature on electrical resistance in metals.
b) Use R = Ro [1+ α(T – To)].

3.4 Electromotive force (emf), internal resistance and potential difference.
a) Define emf, ε and internal resistance, r of a battery

b) State the factors that influence internal resistance.

c) Describe the relationship between emf of the battery and potential difference across
the battery terminals.

d) Use terminal voltage, V =ε– Ir.

3.5 Resistors in series and parallel
a) Derive and determine effective resistance of resistors in series and parallel.

3.6 Potential divider

a) Explain principle of potential divider.

b) Use equations of potential divider, 1 = ( 1 )

1+ 2+ ..…

3.7 Potentiometer

a) Explain principles of potentiometer and its applications.

b) Use related equations for potentiometer, 1 = ℓ1 .
2 ℓ2

38

3.1 Electrical Conduction

1. Which of the following statements about the number of free electrons per unit volume

of copper and the drift velocity of the free electrons are correct when a piece of

copper wire carrying a current is heated

Number of free electrons per unit volume Drift velocity

A. Increases Increases

B. No change Increases

C. No change Decreases

D. Decreases Increases

2. Which of the following is the most likely order of magnitude of the drift velocity of

free electrons in copper at room temperature?
A. 10-4 m s-1
B. 103 m s-1
C. 106 m s-1
D. 108 m s-1

3. A voltage is applied across a piece of copper wire. Describe and explain how the drift
velocity of the free electrons in the copper wire changes
(a) when the voltage is increased
(b) when a thicker copper wire of the same length is connected across the same
voltage.

4. A thin carbon film has the dimensions 2.0 mm, 5.0 mm and 8.0 µm. The resistivity of
carbon is 3.5×10-5Ω m. Calculate the maximum and the minimum resistance of the

carbon film

3.2 Ohm’s law and Resistivity

5. A metal wire has a resistance of 1.0 Ω. What will be the resistanceof a wire made of

the same material but twice as long and with half the cross-sectional area?

A. 0.40 Ω
B. 2.00 Ω
C. 4.00 Ω
D. 0.02 Ω

6. Which of the following is the conductivity of a piece of wire of cross-sectional area

A, length L and resistance R?

A. 1 C.



B. D.



39

7. The dimension of a piece of metal is as shown in the figure. The resistivity of metal is
ρ.

Current

ab
c

When a current flows through the metal in the direction shown, the resistance of the

piece of metal is

A. C.


B. D.


8. State Ohm’s Law and sketch the graph of the relevant parameters

9. A light bulb has a resistance of 240 Ω when operating with a potential difference of
120 V across it. What is the current in the light bulb?

10. A 0.900-V potential difference is maintained across a 1.50 m length of tungsten wire
that has a cross-sectional area of 0.600 mm2. What is the current in the wire?
[Resistivity,ρ of tungsten = 5.60 x 10-8 Ω m ]

11. A resistor is constructed of a carbon rod that has a uniform cross-sectional area of
5.00 mm2. When a potential difference of 15.0 V is applied across the ends of the rod,
the rod carries a current of 4×10–3A. If the resistivity of the carbon rod is 4 x 10-6 Ω m
Find:
(a) the resistance of the rod and
(b) the rod’s length

12.

Figure 3.1

The rod in the Figure 3.1 is made of two materials. Each conductor has a square cross
section 3.00 mm on a side. The first material has a resistivity of 4.00 × 10–3 Ω m and
is 25.0 cm long, while the second material has a resistivity of 6×10–3 Ω m and is 40.0
cm long. What is the resistance between the ends of the rod?

40

3.3 Variation of resistance with temperature

13. Mercury becomes a superconductor at a temperature of 4.2 K. Which of the following
statements is correct?

A. Below 4.2 K, mercury does not conduct electricity.
B. Current does not flow in mercury at 4.2 K.
C. Resistivity of mercury at 4.2 K is zero.
D. Resistance of mercury at 4.2 K is infinitely large

14. An electric heater is connected to a 240 V supply. The resistance of the nichrome

heating element of the heater increases when the temperature increases. Which graph

correctly shows the variation of the power P dissipated from the heater with

temperature?

A. P C. P

0 T(oC) 0 T(oC)

B. P D. P

0 T(oC) 0 T(oC)

15. If the resistance of aluminium wire is 50 Ω at 20 oC, determine its resistance at 80 oC

16. At a temperature of 30 oC, the resistance of a silver wire has a resistance of 170 Ω.
Find the resistance of wire if the temperature doubles.

17. A resistance thermometer, which measures temperature by measuring the change in
resistance of a conductor, is made of platinum and has a resistance of 50.0 ohms at
20.0 oC. When the device is immersed in a vessel containing melting indium, its
resistance increases to 76.8 ohms. Find the melting point of indium.
(Platinum = 3.92 x 10-3 oC-1)

3.4 Electromotive force (emf), internal resistance and potential difference.

18. Which of the following has the same unit as the potential difference?

A. Energy dissipated C. Charge
Resistance time

B. Power dissipated D. Current × time
Current

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19. A battery of emf 6.0 V with an internal resistance of 2.0 Ω is connected in series with a
resistor of 5.0 Ω. What is the potential difference across the resistor?
A. 1.7 V
B. 2.4 V
C. 4.3 V
D. 5.0 V

20. A battery of emf 12.0 V and internal resistance 0.50 Ω maintains a steady current of
1.0 A in a circuit. Find the terminal voltage of the battery.

21. Three resistors, R1 = 10 Ω, R2 = 10 Ω and R3 = 2 Ω are arranged in parallel. This
system of resistor is then connected in series with another resistor, R4 of resistance
4Ω, and a battery of emf 10 V. If the current flowing from the battery is 1.2 A,
calculate:
i. the current and voltage across the resistor R4,
ii. the internal resistance of the battery and

22. A cell of emf 1.5 V and internal resistance 0.5 Ω. Calculate the power delivered when
the cell is connected to an external 2.5 Ω resistor.

3.5 Resistors in series and parallel

23. A resistor operating at 100 V generates joule heat at a rate of 20 W. When placed across a 50
V source, it will draw
A. 0.10 A
B. 5 A
C. 20 A
D. 4.0 A

24. Three 6 Ω resistors are connected in parallel across a 3.0 V battery of neglible internal
resistance. Which of the following statements is correct?
A. The effective resistance is 2 Ω.
B. The current from the battery is 05 A.
C. The potential difference across each resistor is 1.0 V.
D. The total power dissipated is 1.5 W.

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25. Five 2 Ω resistors are connected as in the circuit diagram.

2Ω 2Ω

2Ω Y

X

2Ω 2Ω

Which of the following is the effective resistance between X and Y?

A. 0.4 Ω
B. 1.0 Ω
C. 2.0 Ω
D. 2.5 Ω

a 4 b c
+

10 15Ω

300V d

9 18 30

-e

Figure 3.2
26. For the circuit shown in the Figure 3.2, find:

i. its equivalent resistance,
ii. the current drawn from the power source,
iii. the potential differences across ab, cd, and de
iv. the current in each resistor.

27. Find the resistance of the resistor that must be connected in parallel with a 50 Ω resistor to
obtain a combined resistance of 20 Ω.

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3.6 Potential divider

28. Resistors of resistances 100 Ω and 300 Ω are connected in series with a 12.0 V battery of
negligible internal resistance. A voltmeter of resistance 600 Ω is used to measure the potential
difference across the 300 Ω resistors.

12.0 V

ΩΩ

v

Which of the following is the reading of the voltmeter?
A. 3.0 V
B. 4.0 V
C. 6.0 V
D. 8.0 V

29. A potential divider consists of R1 and R2 connected in series as shown in figure. Find the
potential difference across points A and B if R1 and R2 are 30 Ω and 50 Ω respectively

12.0 V

R1100 R2300

AB C

3.7 Potentiometer

30. Which of the following cannot be measured using potentiometer?
A. DC voltage
B. Temperature
C. Resistance
D. None of the mentioned

31. (a) State the advantages of using a potentiometer

(b) A slide wire potentiometer AB with the length of 100 cm is used to compare two

resistances R1 and R2 as shown in the diagram below. 80Ω
i) Find the length l if the voltage across AJ equal to the voltage across

resistor.

ii) Find the length l if switch S1 opened and S2 closed?

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Vo = 2.0 V

l J
A l

80 Ω G=0

20 Ω

S1

E = 1.50 V
Figure 3.3

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