SP025 FLIPBOOK 2 OF 4

PHYSICS UNIT PHYSICS UNIT

Physics Unit KMNS 2021/2022

PHYSICS UNIT, SCIENCE DEPARTMENT
NEGERI SEMBILAN MATRICULATION COLLEGE
MINISTRY OF EDUCATION MALAYSIA
72000 KUALA PILAH, NEGERI SEMBILAN

SP025 PHYSICS 2nd SEMESTER
SESSION 2021/2022

1.0 INTRODUCTION

This physics syllabus was specially prepared for Matriculation Programme as a preparation for students to achieve a
standard basic level of physics. The physics knowledge obtained will enable the students to pursue education at
university level in the various fields of sciences, engineering, ICT and other related fields.

2.0 COURSE LEARNING OUTCOMES (CLO)
At the end of the course, students should be able to:
2.1 Explain basic concepts of electric current, electronics, magnetism, optics, quantization of light, wave properties
of particles and nuclear physics.
(C2, PLO 1, MQF LOD 1)
2.2 Demonstrate manipulate skills during experiments in capacitors, electric current and direct current, magnetic
field, geometrical optics and physical optics.
(P3, PLO 2, MQF LOD 2)
2.3 Solve problems of electric current, electronics, magnetism, optics, quantization of light, wave properties of
particles and nuclear physics.
(C4, PLO 4, CTPS 3, MQF LOD 6)

3.0 ORGANIZATION

Head of Science Department : En. Mohd Anis Suryady bin Mustafha
Head of Physics Unit : En. Mohd Hafiz bin Mohd Yosop

Physics Lecturers:

1. En. Amir-Ul Mahadi Ahmad Maulana 14. Pn. Nadia Asyikin Abdul Rahman
2. Pn. Rusnah Mat Juri 15. Pn. Zahasnida Zahari
3. En. Abd. Kadir Sulaiman 16. Cik Sali Azuin Zulkefli
4. En. Zulkefli Hashim 17. Pn. Maznon Mohd Mokhtar
5. Pn. Nun Mohd Noh 18. Pn. Ema Azura Abd. Kadir
6. En. Ng Soon Lai 19. Pn. Jannatul Ar Rayan Mohd Azmi
7. Pn. Nur Baizura Zainal Abidin 20. Pn. Nurul Shaiedah Roslan
8. En. Shamsuhanizul Shamsudin 21. Cik Nur Khuzaida Kamarudin
9. Pn. Norul Huda Alias 22. Cik Azwin Adzmi
10. Pn. Sitinorsham Shamsudin 23. Pn. Nor Fatimah Az-Zahra Othman
11. Pn. Mazlinda Mazlan 24. Pn. Noor Adilah Ab Aziz
12. Pn. Heiryah Othman 25. Pn. Nurul Adibah Zainal
13. Pn Muszalinda Mustapha 26. Pn. Fitri Norshakila Muhamad

4.0 TOTAL LEARNING TIME

Total Learning Time Face-to-Face Non Face-to-Face Total
LTP A 205
L = Lecture L TPA 18 66 0 19.5
T = Tutorial
P = Practical 18 66 12 5.5
A = Assessment 5

Credit Value

5.0 ASSESSMENT STRATEGY T&L Strategy Assessment
5.1 Assessment divided into 2 parts: Lecture Ujian Penilaian
5.1.1 Continuous assessment (60%) Sumatif (UPS)
5.1.2 Examination (40%) Practical
Practical Test
Course Learning Outcomes (CLO) Tutorial
CLO 1 – Explain basic concepts of electric current, Lab Report Test
electronics, magnetism, optics, quantization of Assignment
light, wave properties of particles and nuclear
physics. Final Examination
CLO 2 – Demonstrate manipulate skills during
experiments in capacitors, electric current and
direct current, magnetic field, geometrical optics
and physical optics.
CLO 3 – Solve problems of electric current,
electronics, magnetism, optics, quantization of
light, wave properties of particles and nuclear
physics.

Page 1 of 4

6.0 COURSE EVALUATION

6.1 Final examination in each semester:

Physics Paper SP025 : 80 marks

Contribution to the evaluation of subject is 40%

6.2 Course work which are carried out during the whole semester: 60%
……….
Assignment : 10%
100%
Ujian Penilaian Sumatif (UPS) : 20%

Practical Test : 15%

Lab Report Test : 15%

Contribution to the evaluation of subject is

TOTAL

7.0 MARKS EVALUATION Grade Point Status
A 4.00 Excellent
Range of marks (%) A- 3.67
80 – 100 B+ 3.33 Credit
75 – 79 B 3.00 Pass
70 – 74
65 – 69 B- 2.67 Fail
C+ 2.33
60 – 64 C 2.00
55 – 59 C- 1.67
50 – 54 D+ 1.33
45 – 49 D 1.00
40 – 44 F 0.00
35 – 39
0 – 34

8.0 REFERENCE BOOKS
8.1 Cutnell J.D.Johnson k.w, “Introduction to Physics”,10th Edition, John Wiley & Sons,Inc

9.0 ADDITIONAL REFERENCE BOOKS
9.1 Serway, R. A. & Jewett, J. A. (2014). Physics for Scientists and Engineers (9th ed.). International Student
Edition. USA: Brooks/Cole Cengage Learning.
9.2 Giordano, N. J. (2013). College Physics – Reasoning & Relationships (2nded.). USA: Brook/Cole Cengage
Learning. Giancoli, D. C. (2009). Physics - Principles with Application (6th ed.). Prentice Hall.
9.3 Haliday, D. & Resnick, R. Walker, J. (2009). Fundamental of Physics, Extended (8th ed.). Tear Walker Johs
Wiley & Sons Inc.
9.4 Hewitt, P.G. (2009). Conceptual Physics (1 1th ed.). Addison-Wesley.

10.0 STUDY GUIDELINES
10.1 Maintain a positive attitude towards the subject matter
10.2 Understand the basic concepts and principles before attempting to solve assigned problems.
10.3 Read the text book and jot down points that are unclear before attending lecture on the covered material.
10.4 During class, take careful notes and ask questions about ideas that are unclear.
10.5 Set up a regular study schedule.
10.6 Read the syllabus for the course and adhere to the schedule set by the lecturer.
10.7 Devote about two hours of study time for every hour you are in class.
10.8 Seek the advice of the lecturer if you are having trouble with the course.
10.9 Avoid the practice of delaying study until a day or two before an exam.

Page 2 of 4





CONTENTS i
ii
THE GREEK ALPHABET iii
LIST OF SELECTED CONSTANT VALUES
LIST OF SELECTED FORMULAE 1
6
TOPIC 1: ELECTOSTATICS 11
TOPIC 2: CAPACITORS
TOPIC 3: ELECTRIC CURRENT AND DIRECT-CURRENT CIRCUIT 18
25
TOPIC 4: MAGNETISM 31
TOPIC 5: ELECTROMAGNETIC INDUCTION
TOPIC 6: ALTERNATING CURRENT 37
41
TOPIC 7: GEOMETRICAL OPTICS
TOPIC 8: PHYSICAL OPTICS 48
54
TOPIC 9: QUANTIZATION OF LIGHT 58
TOPIC 10: WAVE PROPERTIES OF PARTICLE
TOPIC 11: NUCLEAR AND PARTICLE PHYSICS

THE GREEK ALPHABET

A  Alpha

B  Beta

 Gamma

  Delta

  Epsilon

  Zeta

  Eta

 Theta

  Iota

  Kappa

  Lambda

 Mu

 Nu.

  Xi

  Omicron

 Pi

  Rho

  Sigma

  Tau

  Upsilon

  ,  Phi

  Chi

  Psi

  Omega

i

LIST OF SELECTED CONSTANT VALUES
SENARAI NILAI PEMALAR TERPILIH

Speed of light in a vacuum c = 3.00 x 108 m s-1
Permeability constant 0 = 4 x 10−7 H m-1
Permittivity constant 0 = 8.85 x 10-12 F m-1
Elementary charge e = 1.60 x 10-19 C
Planck's constant h = 6.63 x 10−34 J s
Electron mass me = 9.11 x 10-31 kg
= 5.49 x 10−4 u
Neutron mass mn = 1.674 x 10-27 kg
= 1.008665 u
Proton mass mp = 1.672 x 10−27 kg
= 1.007277 u
Deuteron mass md = 3.34 x 10-27 kg
= 2.014102 u
Universal gas constant R = 8.31 J K−1 mol−1
Rydberg's constant RH = 1.097 x 107 m-1
Avogadro constant NA = 6.02 x 1023 mol−1
Boltzmann's constant k = 1.38 x 10-23 J K-1
Gravitational constant G = 6.67 x 10-11 N m2 kg-2
Free-fall acceleration g = 9.81 m s−2
Atomic mass constant 1u = 1.66 x 10-27 kg
= 931.5 MeV
Electron Volt 1 ev
c2
Constant of proportionality for Coulomb's law, k = 1 = 1.6 x 10−19 J
4π
0 = 9.0 x 109 m2 C-2

Atmospheric Pressure 1 atm = 1.013 x 105 Pa
= 1000 kg m−3
Density of water W

ii

LIST OF SELECTED FORMULAE
SENARAI RUMUS TERPILIH

1. F = Qq = kQq 17. C =  rC0
40r 2 r2 18. I = dQ

 dt
F
2.  =
E q0

19. Q = ne

3. E = kQ 20.  = RA
r2 l

4. V = W 21. R = R01+  (T − T0 )
q0
22. V =  − Ir
5. V = kQ 23. P = IV
r

6. V = Vfinal −Vinitial 24. P = I 2R
25. P = V 2
7. V = W
q0 R
26. W = IVt

8. U = qV  V

 q1q2 q1q3 q2q3  27. V1 = R1 + R2 R1
r12 r13 r23 + ........Rn
9. U = k + +

10. E = V 28. 1 = l1
d  2 l2

11. C = Q 29. B = 0I
V 2r

12. U = 1 CV 2 = 1 QV = 1 Q2 30. B = 0I
2 2 2C 2r

− 31. B = 0nI

13. Q = Q0e RC 32. B = 1 0nI
2
1 −   
14. Q = Q0 − e RC F =   B
qv
33.

15. r =  34. FB = Fc
0 

16. C0 = 0A 35. F = Il  B
d
36. F = 0I1I2
l 2d

iii

 58. Z = R2 + (X L − XC )2
37.  = NIA B 59.  = tan−1 (X L − XC )

38. v = E R
B 60. Pav = IrmsVrms cos


39.  = B • A = BAcos

40.  = N 61. cos = Pr = Pav
Pa I rmsVrms
41.  = − d
dt 62. R = 2 f

42.  = Blvsin 63. 1 = 1 + 1
f uv
43.  = −NA dB
dt 64. m = hi = − v
h0 u
44. ε = -NB dA
dt 65. n1 + n2 = n2 − n1
uv R
45.  = NAB sin t
46. L = −  66. 1 =  nm aterial − 1 1 − 1 
f nm edium R1 R2
 dI 
 dt 

47. L = N 67. ym = mD
I d

48. Lcoil = 0N 2 A  m + 1 D
2r 68. ym =  2
d
0N 2 A
49. Lsolenoid = l 69. y = D
d
50. U = 1 LI 2
2 70. 2nt = m

51. M = 0N1N2 A 71. 2nt =  m + 1 
l  2

52. V = V0 sin t 72. yn = nD
53. I = I0 sin t a

73. yn = (n + 1 )D
2

54. Irms = I0 a
2
74. d sin = n

55. Vrm s = V0 75. d = 1
2 N

56. XC = 1 76. E = hf = hc
2fC 

57. X L = 2fL

iv

77. 1 mvmax2 = eVs = hf − hf0 83. dN = −N
2 dt

78. W0 = hf0 84. N = N0e−t

79. Kmax = eVs = hf −W0 85. A = A0e−t

80.  = h 86. T1 = ln 2
p 
2
( )81. m = Zmp + Nmn − mnucleus

82. EB = mc2

v

Physics Unit, KMNS SP025

TOPIC 4
MAGNETISM

4.1 Magnetic field

(a) Define magnetic field.
(b) Identify magnetic field sources.

* Example:

i. Bar magnet and current carrying conductor (straight wire, circular coil,
and solenoid).

ii. Earth magnetic field.
(c) Sketch magnetic field lines for

i. Bar magnet and current carrying conductor (straight wire, circular coil,
and solenoid).

ii. Earth magnetic field.
(d) Determine the value of the horizontal component of the earth magnetic field,

BE (Experiment 4: Magnetic Field)

4.2 Resultant magnetic field produced by current-carrying conductor

(a) Sketch resultant magnetic field diagram at a point (limited to two current
carrying straight wires and 2D).

(b) Determine direction of B by using right hand rule.
(c) Determine the magnitude of magnetic field by using:

i. = for a long straight wire

2

ii. = µ0 at the centre of a solenoid

2

iii. = at the centre of a solenoid
iv. = at the end of a solenoid

2

4.3 Force on a moving charged particle in a uniform magnetic field

(a) Explain and use magnetic force, ⃗ = ⃗ × ⃗⃗ .
(b) Determine direction of force.
(c) Describe circular motion of a charge in a uniform magnetic field.
(d) Use relationship = .

4.4 Force on a moving current carrying conductor in a uniform magnetic field

(a) Explain and use magnetic force, ⃗ = ⃗ × ⃗⃗ .
(b) Determine direction of force.

18

Physics Unit, KMNS SP025

4.5 Forces between two parallel current-carrying conductors

(a) Explain magnetic force per unit length of two parallel current-carrying
conductors.

(b) Derive and use magnetic force per unit length, = 1 2.

2

4.6 Torque on a coil

(a) Use torque, ⃗ = ⃗ × ⃗⃗ where N=number of turns
(b) Explain briefly the working principles of a moving coil galvanometer.

4.7 Application of motion of charged particle

(a) Explain the motion of a moving charged particle in magnetic field and
electric field fo v, B and E perpendicular to each other.

(b) Use velocity, = in velocity selector. (e.g. Bainbridge mass spectrometer)



19

Physics Unit, KMNS SP025
OBJECTIVE QUESTIONS (C2, PLO 1, MQF LOD 1)

1. Which of the following statements is NOT true about a bar magnet?
A. Its magnetic flux is greater at the poles
B. Its magnetic field lines form a closed loop
C. Its magnetic fields lines do not intersect one another
D. Its magnetic field lines leave the South-pole and enter the North-pole

2. A bar magnet is divided in two pieces. Which of the following statements is true?
A. The bar magnet is demagnetized.
B. The magnetic field of each separated piece becomes stronger.
C. The magnetic poles are separated.
D. Two new bar magnets are created

3. An electric current flows into the page. What is the direction of the magnetic field?
A. To the bottom of the page.
B. To the top of the page.
C. Clockwise.
D. Counter-clockwise.

4. Which of the following magnetic fields is correct for a single bar magnet?

D.
20

Physics Unit, KMNS SP025

5. Which of the following diagrams represents the magnetic field due to a circular
current?

ANSWERS:
1. D 2. D 3. C 4. D 5. D

21

Physics Unit, KMNS SP025
STRUCTURED QUESTIONS (C4, PLO 4, CTPS 3, MQF LOD 6)

1. (a) State two examples of magnetic field sources
(b) Sketch the magnetic field lines of two examples given in (a)
(c) State two characteristics of the magnetic field lines

2. (a) A long straight wire carries a current of 5 A (upward). At what distance from
the wire is the magnetic field due to the current in the wire equal in
magnitude to strength of earth’s magnetic field of 5 × 10−5 T.

(b) A circular coil has 15 turns and a diameter of 45.0 cm. If the magnetic field
strength at the centre of the coil is 8.0 × 10−4 T, find the current flowing in
the coil.

(c) A solenoid of 50 turns is carrying a current of 10 mA. The magnetic field
strength at the centre is 1.05 × 10−6 T. Calculate the length of the solenoid.

3. Two long straight parallel wires are 20.0 cm apart and each wire carries a current
of 10 A. Find the magnitude and direction of the magnetic field at a point midway
between the wires if the current are
(a) in the same direction
(b) in the opposite direction

4. (a) Explain why a charged particle is moving in a circular path in a uniform
magnetic field.

(b) A proton moves in a circular orbit of radius 3.8 cm in a uniform magnetic
field of strength 1.2 T. The velocity of the proton is perpendicular to the
magnetic field. What is the orbital speed of the proton?

5. A proton with energy of 5.2 × 10−17 J moves at right angles to a magnetic field of
0.42 T. Calculate the velocity and force of the proton.

6.

X

~

B

FIGURE 4.1 Y

(a) A copper wire is stretched between two fixed points X and Y. An alternating
current is connected across it. A strong magnetic field B is applied at right
angle to the wire as shown in FIGURE 4.1. Show the force due to the
magnetic field on the copper wire.

22

Physics Unit, KMNS SP025

(b) A straight wire of length 5.0 cm, carrying a current of 8.6 A, is placed in a
uniform magnetic field of flux density 0.034 T. The wire is at an angle of 300
with the magnetic field. Calculate the force on the wire.

7.

FIGURE 4.2

The same current-carrying wire is placed in the same magnetic field B in four
different orientations as shown in FIGURE 4.2. Rank the orientations according to
the magnitude of the magnetic force exerted on the wire, largest to smallest.

8. (a) Two straight wires are parallel to each other. If the currents in the wires are
in the opposite direction, will the wires attract or repel each other?

(b) 12 cm

I1 = 8.0 A I2 = 2.0 A

A 9.0 cm

Wire 1 Wire 2

FIGURE 4.3

Two long parallel wires carry currents of 8.0 A and 2.0 A as shown in
FIGURE 4.3.
(i) What is the force per unit length on wire 1?
(ii) What is the magnitude of the magnetic field midway between the

wires?
(iii) Where on a line between the wires is the magnetic field zero?

9. (a) State the underlying principle of working of a moving coil galvanometer.
(b) Write two reasons why a galvanometer cannot be used as such to measure
current in a given circuit.

23

Physics Unit, KMNS SP025

(c) Name any two factors which the current sensitivity of a galvanometer
depends on.

10.
BC
xxxxx

xxxxx

xxxxx

AD

electrons

FIGURE 4.4

FIGURE 4.4 shows a uniform magnetic field directed into the paper. Electrons
enter the region of magnetic field as shown.
(a) Show and label the path of the electrons as they pass through the region of

magnetic field and exit from the side BC. Also, label the magnetic force FB on
the figure.
(b) If the electrons enter the magnetic field with a higher velocity, show and label
the path of the electrons in the figure.
(c) State two situations in which an electron in a magnetic field does not
experience any magnetic force.
(d) A uniform electric field is applied across the region ABCD in such way that the
electrons are now undeflected. Mark on the figure the direction of the electric
field.
(e) Derive an expression for the velocity of the electron in (d) in terms of electric
field E and magnetic field B.

ANSWERS:

2. (a) 0.02 m (b) 19.1 A (c) 0.598 m

3. (a) 0 T (b) 4 × 10−5 T (out of the page)

4. (b) 4.36 × 106 m s−1

5. 2.49 × 105 m s−1, 1.67 × 10−14 N

6. (b) 7.31x10-3 N

7. B, D, A and C
8. (b) (i) 2.67 × 10−5 N/m (towards wire 2)

(ii) 2.00 × 10−5 T

(iii) 0.096 m from wire 1

24

Physics Unit, KMNS SP025

TOPIC 5
ELECTROMAGNETIC INDUCTION

5.1 Magnetic Flux

(a) Define and use magnetic flux, = ⃗ • =
(b) Use magnetic flux linkage, Φ =

5.2 Induced emf

(a) Explain induced emf by using Faraday’s experiment.

(b) State and use Faraday’s Law, = −

(c) State and use Lenz’s law to determine the direction of induced current.

(d) Derive and use induced emf in:

i. a straight conductor,

ε = θ

ii. a coil,
ε = −NA , ε = −NB



iii. a rotating coil,

ε =

5.3 Self-inductance
(a) Define self-inductance
(b) Apply self-inductance,

L = − ε for coil and solenoid, where:

dI

dt

i. =


ii. = 2

2
iii. = 2



5.4 Energy stored in inductor
(a) Derive and use the energy stored in an inductor, = 1 2

2

5.5 Mutual Inductance

(a) Define mutual inductance.
(b) Use mutual inductance, = 1 2 between two coaxial solenoids.



25

Physics Unit, KMNS SP025
OBJECTIVE QUESTIONS (C2, PLO 1, MQF LOD 1)

1. As per Faraday’s law of electromagnetic induction, an emf is induced in a
conductor whenever it
A. Lies perpendicular to the magnetic flux
B. Lies in a magnetic field
C. Cuts magnetic flux
D. Moves parallel to the direction of the magnetic field

2. Lenz’s law of electromagnetic induction is about the conservation of

A. charges. B. mass. C. energy. D. momentum.

3. A magnet bar moves into a solenoid as shown in the FIGURE 5.1. State the
direction of the deflection of the galvanometer.

vN S

A GB

FIGURE 5.1

A. From A to B.
B. From B to A.
C. To positive y axis.
D. To negative y axis.

4. The inductance of a solenoid can be increased by inserting a soft iron core into it.
The function of the soft iron core is to
A. to reduce the current in the coil.
B. increase the flux linkage in the coil.
C. reduce the resistance of the solenoid.
D. increase the mutual inductance between the coil and the soft iron core.

5. The property of coil by which a counter emf is induced in it when the current
through the coil is changes is known as
A. Self-inductance
B. Mutual inductance
C. Series aiding inductance
D. Capacitance

26

Physics Unit, KMNS SP025

6. Mutually inductance between two magnetically-coupled coils depends on
A. Permeability of the core
B. The number of their turns
C. Cross-sectional area of their common core
D. All of the above

ANSWERS: 3. B 4. B 5. A 6. D
1. C 2. C

27

Physics Unit, KMNS SP025
STRUCTURED QUESTIONS (C4, PLO 4, CTPS 3, MQF LOD 6)

1. (a) A surface of area 100 mm2 inside a uniform magnetic field of strength 0.50 T.
The plane of the coil and the direction of the field make an angle α. Determine
the magnetic flux through the surface if
(i) α = 0o.
(ii) α = 60o.
(iii) α = 90o.

(b) A circular coil of 100 turns and diameter of 2.0 cm is placed in a uniform
magnetic field of strength 100 mT. The plane of the coil and the direction of the
field makes an angle of 600. Determine the magnetic flux linkage through the
coil.

2.

QA P

X X X X X X XX X

X X X X X X XX X S v
R

B

FIGURE 5.2

A 1.5 m conducting rod AB, rests on metal rail PQRS as shown in the FIGURE 5.2.

The rod is placed in a uniform magnetic field, B = 3.0 T perpendicular to the plane
of the paper. The rod is pulled to the right at a uniform velocity, v = 3.0 m s−1. If the
resistance of PQRS is 5 Ω, determine

(a) the magnitude of the induced emf in the rod.
(b) the magnitude and direction of the induced current in the rod.
(c) the magnitude of the magnetic force that is required to keep the rod moving to

the right at a uniform velocity, v = 3.0 m s−1.

3. A square coil of sides 15.0 cm and 300 turns has a resistance of 3.0 Ω. A uniform

magnetic field is applied perpendicular to the plane of the coil. The magnitude of this
field is increased uniformly from zero to 0.8 Wb m−2 in a time of 0.8 s. Determine

(a) the magnitude of the induced emf in the coil.

(b) the magnitude of the induced current in the coil.

NS
FIGURE 5.3
28

Physics Unit, KMNS SP025

4. FIGURE 5.3 shows a coil of 100 turns with diameter of 4.0 cm and is rotating at 100π
rad s−1 about an axis perpendicular to a uniform magnetic field of 5 × 10−5 T.
(a) Determine the maximum induced emf.
(b) If the coil is stationary and the magnetic field is rotated at the same angular
velocity as before, is there any emf induced? If there is emf induced, what is
the value of the maximum induced emf?

5. A 200 turns solenoid of length 20.0 cm has a cross sectional area of 20 cm2. A
current of 5 A flows through the solenoid. Calculate
(a) the total flux linkage passing through the solenoid.
(b) the self inductance of the solenoid.

6. (a) A 500 turns solenoid has a length of 10.0 cm and cross sectional area of 10
cm2. A coil of 100 turns is wound at the centre of the solenoid. Calculate
(i) the magnetic flux through the coil if the current of 2.0 A flows in the
solenoid.
(ii) the mutual inductance of the coil and solenoid.

(b) An inductor of self inductance of 5.0 mH is connected to a direct current source
which supplies a steady current of 3.0 A. If the current increases at a rate of 15
A s−1, calculate the magnitude of induced emf in the inductor.

7. Two coils are placed side by side and fixed to their positions. There is no current in
coil 1 and the current in coil 2 increases at a rate of 10 A s−1, the induced emf in coil
1 is 20 mV.
(a) Calculate the mutual inductance of this pair of coils.
(b) If there is no current in coil 2 and coil 1 carries a current of 3.6 A, what will the
flux linkage in coil 2 be?

8. Coil 1 has L1 = 30 mH and N1 = 150 turns. Coil 2 has L2 = 40 mH and N2 = 250 turns.
The mutual inductance is 4.0 mH. At a particular instant the current is 5.0 mA through
coil 1 and this current decreases at a rate of 4.0 A s−1. Determine
(a) the flux linkage in coil 1.
(b) the flux linkage in coil 2.
(c) the induced emf in coil 2.

9. A solenoid of length 30 cm, diameter of 4.0 cm has self inductance of 100 mH. If
there is a current of 2.0 A flowing in the solenoid, calculate
(a) the number of turns in the solenoid
(b) the energy stored in the solenoid

10. A solenoid with 1500 turns and radius of 4 cm has length of 20 cm.
(a) The current of the solenoid is decrease from 10 A to 2 A within 0.6 s. Calculate
the magnitude of emf induced in the solenoid.
(b) A second solenoid with 200 turns is wound coaxially with the first solenoid.
Calculate the mutual inductance between them.

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Physics Unit, KMNS SP025

ANSWERS: (ii) 4.33 × 10−5 Wb (iii) 5 × 10−5 Wb
(c) 0.016 V
1. (a) (i) 0 Wb (b) 2.7 A, from B to A
(b) 2.72 × 10−3 Wb
(b) 2.25 A
2. (a) 13.5 V (b) Yes, 1.97 mV
(b) 5.02 × 10−4 H
(c) 12.15 N (ii) 6.28 × 10−4 H

3. (a) 6.75 V (b) 7.2 mWb
(b) 2.0 × 10−5 Wb
4. (a) 1.97 mV (b) 0.2 J
5. (a) 2.51 × 10−3 Wb (b) 9.47 mH
6. (a) (i) 1.26 × 10−5 Wb

(b) 0.075 V
7. (a) −2.0 mH
8. (a) 1.5 × 10−4 Wb

9. (a) 4358 turns

10. (a) 0.947 V

30

Physics Unit, KMNS SP025

TOPIC 6
ALTERNATING CURRENT

6.1 Alternating Current
(a) Define alternating (AC).
(b) Sketch and interpret sinusoidal AC waveform.
(c) Use sinusoidal voltage and current equations;
= sin , = sin

6.2 Root mean square (rms)

(a) Define root mean square (rms) current and voltage for AC source.

(b) Use = , =
√2 √2

6.3 Resistance, reactance and impedance

(a) Sketch and use phasor diagram and sinusoidal waveform to show the

phase relationship between current and voltage for a single component

circuit of:

(i) Resistor, R

(ii) Capacitor, C

(iii) Inductor, L

(b) Use phasor diagram to analyse voltage, current, and impedance of series

circuit of RL, RC, RLC.

(c) Define and use:

(i) Capacitive reactance, = 1
2

(ii) Inductive reactance, = 2

(iii) Impedance, = √ 2 + ( − )2
(iv) Phase angle, ∅ = −1 −



(d) Discuss and explain graphically the dependence of , , and on

and relate it to resonance.

6.4 Power and power factor

(a) Apply in AC circuit consisting of , , and in series:

(i) Average power, = cos ∅
*Also known as power loss that only occurs in resistor.

(ii) Instantaneous power, =
(iii) Power factor, cos ∅ = =



31

Physics Unit, KMNS SP025
OBJECTIVE QUESTIONS (C2, PLO 1, MQF LOD 1)

1.




The graph shows the variation of impedance for an a.c circuit with frequency.
The circuit contains….
A. a pure capacitor
B. a pure inductor
C. a capacitor in series with a resistor
D. a inductor in series with a resistor

2. The total impedance Z of an RLC circuit driven by an ac voltage source at angular

frequency f is,

A √ 2 + ( )2 − ( )2

B √ 2 + ( − 1 2

)

1
C √ 2+( − )2

D √ 2 + ( + )2

3. The average power input to a series alternating current circuit is minimum when
A there are only a resistor and capacitor in the circuit.
B there are only a resistor and inductor in the circuit.
C there is only a capacitor in the circuit.
D = and the circuit contains a resistor, an inductor and a capacitor

4. What happen when a series circuit is in resonance?
A the maximum voltage across the resistor and inductance must be equal
B the maximum voltage across the resistor and capacitor must be equal
C the maximum voltage across the inductance and capacitor must be equal
D the maximum voltage across the resistor, capacitance and inductance
must be equal

32

Physics Unit, KMNS SP025

5. Which of the following statements about a pure resistor carrying an AC is TRUE?
A. Voltage leads current by radians.

2

B. Current leads voltage by radians.

2

C. The current and voltage are in phase.

D. The average power generated is zero.

ANSWERS:
1. B 2. B 3. C 4. C 5. C

33

Physics Unit, KMNS SP025

STRUCTURED QUESTIONS (C4, PLO 4, CTPS 3, MQF LOD 6)

I (A)

1. 5

0 20 40 60 80 t (ms)
−5 FIGURE 6.1

FIGURE 6.1 shows the variation of current with time for a sinusoidal A.C.
Determine
(a) the rms value of the current.
(b) the supply frequency.
(c) the phase in time interval of 15 ms.
(d) the expression for the graph.

2. A 300  resistor is connected in series with a 5.0  capacitor. The voltage across
the resistor is given by the expression

= 1.2 cos 2500 where VR in volts and t in seconds.

(a) Write down the equation of the current in the circuit.
(b) Determine the capacitive reactance.
(c) Write down the equation of the voltage across the capacitor, VC.

3. (a) When a certain AC of 50 Hz is connected to a bulb rated as 12 V, 6 W, the
bulb is lit up to its normal brightness. Sketch and labelled current-time graph
for this AC.

40Ω

ΔV 50.0 mH

50.0µF

FIGURE 6.2
34

Physics Unit, KMNS SP025

(b) The voltage source in FIGURE 6.2 has an output of Vrms = 100 V at
=1000 rad s-1. Determine

(i) The current in the circuit
(ii) The power supplied by the source
(iii) Show that the power delivered to the resistor is equal to the power

supplied by the source.

4.
R LC

141 V 327 V 133 V

FIGURE 6.3

FIGURE 6.3 shows the root mean square voltage across a resistor R, an inductor
L and a capacitor C.
(a) By using a phasor diagram, find the supply voltage AND the phase

angle between supply voltage and current in the circuit.
(b) Calculate the value of current flows in the circuit if the resistance of the

resistor is 68 .
(c) Calculate the inductance AND capacitance if the supply frequency

is 50 Hz.
(d) Calculate the resonance frequency of the circuit.

5. A 0.3 µF capacitor is connected to a source of alternating current with output
voltage, = 240 120 .
(a) Calculate the reactance of the capacitor.
(b) Determine the rms current flowing through the capacitor.

6. A circuit consists of a capacitor of 1000 μF which is connected in series to a lamp
of 2.5 V, 0.30 A and a 50 Hz source.
(a) Calculate
(i) reactance of the capacitor and resistance of the lamp.
(ii) impedance of the circuit.
(iii) voltage of the source.
(iv) voltage of the capacitor.

35

Physics Unit, KMNS SP025

(b) Explain why the total between the voltage across the capacitor and the lamp
is not the same as the source voltage in (a) (iii).

7. An alternating voltage V with frequency of 150 Hz is applied on a resistor of 300 Ω
which is in series with a capacitor of 2.0 μF.
(a) Calculate the reactance of the capacitor, XC.
(b) Calculate the total impedance in the circuit.
(c) With the help of the phasor diagram, determine the phase angle,  between
the current, I in the circuit and voltage applied, V.

8. A 0.7 H inductor and a 150 Ω resistor are connected in series to an AC source of
rms voltage 230 V and frequency 50 Hz. Calculate
(a) the reactance of the inductor.
(b) the impedance of the circuit.

9. A heater coil connected to a 240 V AC line has a resistance of 34 Ω.
(a) What is the average power used?
(b) What are the maximum and minimum values of the instantaneous power?

10. An AC source of 10 V (rms) and frequency 50 Hz is connected to a circuit which
consists of an inductor of inductance 2 H and a resistor of 1 kΩ.
(a) Determine
(i) the current flows in the circuit.
(ii) the voltage across the resistor and inductor.
(iii) the phase angle between the applied emf and current.
(b) What should you do so that the voltage of the circuit is in phase with the
current of the circuit?

ANSWERS:

1. (i) 3.54 A (ii) 25 Hz (iii) 2.36 rad

(iv) I = 5 sin (157t) (b) 80  (c) VC=0.32 sin 2500t
2. (a) I = 4 × 10−3 cos (2500t)

3. (b) (i) 2.00 A (ii) 160 W

4. (a) 240 V, 54 above +x axis (b) 2.07 A
(c) 0.503 H, 4.95 × 10−5 F (d) 31.9 Hz

5. (a) 8842  (b) 0.0192 A

6. (a) (i) 3.18 , 8.33  (ii) 8.92  (iii) 2.68 V (iv) 0.954 V

7. (a) 530.52  (b) 609.47  (c) 60.51o below +x axis

8. (a) 219.9  (b) 266 

9. (a) 1.69 × 103 W (b) 3.38 × 103 W, 0 W
10. (a) (i) 8.47 × 10−3 A (ii) 8.47 V, 5.32 V (iii) 32.1 above +x axis

36