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FAIL KURSUS FAKULTI SAINS GUNAAN UNIVERSITI TEKNOLOGI MARA 40450 SHAH ALAM SELANGOR

FK-FSG-PHY 407

1.0 COURSE INFORMATION Course Name : PHYSICS II

Course Code : PHY407

Programmes : 1. Bachelor of Science (Hons.) Material Technology

Credit Hours : 3

Contact Hours : Lecture (2hrs/week) : Practical (2hrs/week)


UiTM


FK-FSG-PHY 407

Synopsis

:

This course will interactively engage students in the cognitive and the psychomotor (science) domain. It begins by discussing the presence of charges in matter. The presence of an electric field and how charges interact with each other and the dynamics of the charges are probed and discussed. The concept of charging, electric field, electric forces, electric flux, electric potential, work done, electrical energy, electrical power, capacitors, electric current, resistance and resistivity are then probed and discussed. The laws governing the electrical phenomena including Coulomb’s Law, Ohm;s Law and Kirchoff’s Laws are introduced and used to help discuss the electrical phenomena. Once done, the magnetic phenomena and the effect of magnetic field on charges are introduced. Then the dynamics of charges and the production of magnetic field by moving charges are introduced leading to the induced electromotive force in a coil and its applications to magnetic energy, inductors, motors, generators and its significance and applications to alternating current. The laws involved such as Ampere’s Law, Faraday’s Law and Lenz’s Law are introduced to help understand magnetic phenomena. The discussion of electromagnetic waves especially light which exhibits the ability to be reflected, refracted, diffracted and interfered through Michelson Morley’s and Young’s Double-slit experiment will be done following the discussion of light as waves. Quantum mechanics is introduced through the particle properties of electromagnetic wave and the wave properties of particles by introducing the black body radiation, the photoelectric effect, the Heisenberg uncertainty principle and the Compton effect. Finally, atomic physics through the nature of atom associated with photons such as the atomic models and the x-ray will be introduced and discussed. In addition, the course will allow students to develop their science skills through a series of laboratories (by involving the use of common scientific devices and/or computer simulation) which incorporates investigating natural phenomena and obtain some form of laws or theory.


UiTM


FK-FSG-PHY 407

Objectives

:

On completion of this course, students should be able to do the following: 1. Identify and explain the different types of charging process for

any given material. 2. Draw, explain, write the strength and determine the electric field

around a charged particle and a configuration of charged particle and the electric forces experienced by or exerted upon any charged particle or any configuration of charged particles.

3. Write, explain and obtain the electric potential and electric potential energy on any charged particle or any configuration of charged particles and apply it to capacitors connected in series or parallel.

4. Identify and distinguish the high and low potential points in a simple and complex circuit and state and use Ohm’s law and Kirchoff’s Laws to determine the current flowing in any series and/or parallel circuits.

5. Draw and write the strength of the magnetic field produced by different types of magnets and state, use and explain the first right hand rule in determining magnetic forces acting on charged particles and /or current-carrying conductors such as a long straight wire.

6. Identify, draw, write and use the algebraic representation to

determine the resultant magnetic field produced by current-carrying conductors such as long straight wires and wire loops by using the second right-hand rule and explain and obtain the forces the field exerts on charged particles and other current-carrying conductors.

7. State and use Faraday’s and Lenz’s Laws and its algebraic

representations to determine the induced electromotive force and the induced current in wire loops and how this is applied in physical devices such as inductors and the associated energy stored in the inductor.

8. Explain, draw and determine phase differences, root-mean-

squares, impedances, resonance and phasors in circuits involving resistors, capacitors and inductors connected in series to an alternating current source.

9. Explain and describe the wave properties of light such as

refraction, interferences, diffraction and Young’s Double Slit Experiment, then write and use the mathematical description of the bright and dark fringes observed in the patterns.


UiTM


FK-FSG-PHY 407

10. Discuss explain and draw the graphs of black body radiation,

the photoelectric effect, the Compton effect and eventually the wave-particle duality and the Heisenberg Uncertainty Principle.

11. Discuss explain and draw the Rutherford and Bohr’s atomic

model and the energy transitions for the Balmer, Lyman and Paschen series and use the model to discuss, explain and draw the production of X-ray and the spectrum characteristics of the X-ray.

APPENDIX 2

DO NOT TURN THIS PAGE UNTIL YOU ARE TOLD TO DO SO

This examination paper consists of 8 printed pages © Hak Cipta Universiti Teknologi MARA CONFIDENTIAL

CONFIDENTIAL

AS/OCT 2006/PHY407

UNIVERSITI TEKNOLOGI MARA FINAL EXAMINATION

COURSE : PHYSICS II

COURSE CODE : PHY407

EXAMINATION : OCT 2006

TIME : 3 HOURS

INSTRUCTIONS TO CANDIDATES 1. This question paper consists of TWO (2) parts : PART A (5 Questions)

PART B (2 Questions)

2. Answer ALL questions from PART A and B in the Answer Booklet. Start each answer on a new

page. 3. Do not bring any material into the examination room unless permission is given by the

invigilator. 4. Please check to make sure that this examination pack consists of : i) the Question Paper ii) an Answer Booklet – provided by the Faculty

CONFIDENTIAL 6 AS/OCT 2006/PHY407

© Hak Cipta Universiti Teknologi MARA CONFIDENTIAL

PART A (100 MARKS) QUESTION 1 a) Write down the factors that control the capacitance of a parallel-plate capacitor.

(3 marks)

b) Experiments have shown that the amount of charge q, deposited on capacitors is

directly proportional to the potential difference V, across the plates, or q = CV. In addition, the electric potential energy stored in a parallel-plate capacitor can be

shown to be, 2

qVEnergy = .

i) Show that the electrical potential energy can also be written as 2C

2qEnergy = .

ii) A parallel plate capacitor is charged up by a battery and then the connection to the battery is broken. Explain how capacitance changes if the separation of the plates is reduced by a factor of 2.

(7 marks) c) The figure below shows capacitors connected together in a circuit with a 12 volts

battery.

i) Obtain the total capacitance for the configuration in the figure. ii) Determine the total charge stored and the total electrical potential energy

stored by the capacitance in the configuration above. iii) Determine the potential difference between points A and B.

(10 marks)

3 µF

12 V +

-

1 µF

2 µF

4 µF

A B



QUESTION 2 a) Three particles move through a

constant magnetic field and follow the paths shown in the drawing. Determine whether each particle is positively charged, negatively charged, or neutral. Give a reason for each answer.

(5 marks)

b) The drawing below shows an end-on view of three parallel wires that are

perpendicular to the plane of the paper. All carries current I and the wires are separated from each other by a distance d. In two of the wires the current is directed into the paper, while in the remaining wire the current is directed out of the paper. The two outermost wires are held rigidly in place.

i) Draw the magnetic field lines for

the two rigid wires. ii) Write the magnitude of the

magnetic field at the position of the middle wire.

ii) Indicate the direction of the force acting on the middle wire.

(5 marks) c) For each electromagnet on the left of the bar magnet in the drawing below,

i) label the polarity of the induced magnetic field

ii) explain whether it will be attracted to or repelled from the permanent magnet at the right.

(4 marks)

d) For each electromagnet in the drawing on the right,

i) label the polarity of the induced magnetic fields.

ii) explain whether the left electromagnet in the drawing will be attracted to or repelled from the adjacent electromagnet on the right.

(6 marks)

2

1

B into paper

3

X X 0

Current



QUESTION 3 a) Briefly, explain the following:

i) induced electromotive force (emf) and induced current. ii) magnetic flux iii) Faraday’s and Lenz’s law of electromagnetic induction.

(10 marks) b) In the diagrams below, label the high and low potential points of the coil by the usual

symbol ‘+” and ‘-‘ and indicate the direction of the induced electromotive force (emf).

i) ii)

iii)

(6 marks)

c) During a 72-ms interval, a change in the current in a primary coil occurs. This change

leads to the appearance of a 6.0 mA current in a nearby secondary coil. The secondary coil is part of a circuit in which the resistance is 12 Ω. The mutual inductance between the two coils is 3.2 mH. Remembering Ohm’s law and the fact that the induced emf in the secondary coil is because of the change in current in the primary coil, determine the change in the primary current, ∆ip.

(4 marks)

AC source

Resistor

Secondary Coil Primary Coil Increasing current

Decreasing current

Coil

Increasing current

Coil




i) the wave-particle-duality ii) blackbody radiation iii) photons iv) Heisenberg uncertainty principle

(10 marks) b) i) Explain the photoelectric effect.

(4 marks)

ii) Draw an energy-frequency graph representing the phenomenon. Label all the axis.

(4 marks) iii) A silver surface has a work function of 4.73 eV ( 1 eV = 1.6 x 10-19 J). Find the

minimum frequency that light must have to eject electrons from this surface. (Planck’s constant, h = 6.63 x 10-34 Js)

(2 marks)


i) Rutherford’s nuclear atom ii) Bohr’s model of the hydrogen atom iii) Balmer series iv) ground state

(10 marks) b) Describe, with the help of a picture, how x-rays are produced.

(10 marks)



PART B (100 MARKS) QUESTION 1 a) Briefly, explain the following:

i) the law of electrical charge conservation ii) charging by contact and induction iii) Electric field lines iv) Electric flux

(10 marks) b) Consider three identical metal spheres, A, B, and C. Sphere A carries a charge of

+5q. Sphere B carries a charge of –q. Sphere C carries no net charge. The following process were performed on the spheres:

1. Spheres A and B are touched together and then separated. 2. Sphere C is then touched to sphere A, and then separated from it. 3. Lastly, sphere C is touched to sphere B and separated from it. i) What is the total charge on the three spheres before they are allowed to touch

each other? Explain your answer. iii) What is the total charge on the three spheres after they have touched?

Explain your answer. iii) Determine the amount of charges on each sphere after each of the process.

Explain your answer. (10 marks)

c) The figure below shows a configuration of charged particles placed at the corners of a square measuring a by a

q1 = -4e q2 = +2e

q4 = +e q3 = -4e

P a

a



i) Draw and label the electric field due to each of the four charges at position P, the center of the square, E1, E2, E3, and E4.

(4 marks)

ii) Using Pythagoras theorem, determine the distance from P to the charge at the corners.

(2 marks)

iii) Write down the electric field strength for each of the charges at position P, E1, E2, E3, and E4.

(4 marks)

iv) Obtain the electric field along the x-axis and the electric field along the y-axis, respectively, for E2 and E4 at position P.

(8 marks)

v) Use the results of part (iv) and the symmetry of the problem to obtain the total electric field acting at position P.

(8 marks)

vi) Explain what would happen to a positive test charge, q0, if it was placed at position P.

(4 marks) QUESTION 2 a) Briefly, explain the following:

i) alternating current ii) parallel wiring iii) resistance iv) electrical power v) ammeter

(10 marks)

b) Redraw each of the circuits below and identify which circuit is connected neither in series nor in parallel.

Circuit 1 Circuit 2 Circuit 3

(10 marks)



c) The figure below show plots of the electric current I through a certain cross section of a conducting wire over four different time periods. Determine the amount of net charge that pass through each cross section.

(10 marks)

d) Given the circuit below,

i) Label the ‘+’ and ‘–‘ signs at the ends of each resistor and battery to

indicate the high and low potential. ii) Using Kirchoff’s laws, and the results of part (i), determine the currents

I1, I2, and I3. Show ALL your work.

(20 marks)

-4

-2

810

4

2

4

2

i)

Current, I, A

Time t, seconds

ii)

iii)

iv)

6

END OF QUESTION PAPER

10 V

I3 I2 R=5 Ω

R=10 Ω

R=20 Ω

5 V

R=10 Ω I1

15 V

R=20 Ω



PART A (100 MARKS) QUESTION 1 a) Write down the factors that control the capacitance of a parallel-plate capacitor.

Answer:Capacitance dAC ε

= ; hence the dielectric constant of the material between the

plates, ε , the area of the plates, A, and the separation of the plates, A. (3 marks)

b) Experiments have shown that the amount of charge q, deposited on capacitors is directly

proportional to the potential difference V, across the plates, or q = CV. In addition, the electric

potential energy stored in a parallel-plate capacitor can be shown to be, VqEnergy

2= .

i) Show that the electrical potential energy can also be written as C

qEnergy2

2

= .

Answer: Since average energy stored is2

qVEnergy = and the charge stored is

CVq = , then, C

qCqqEnergy

22

2

==

(3 marks) ii) A parallel plate capacitor is charged up by a battery and then the connection to the

battery is broken. Explain how capacitance changes if the separation of the plates is reduced by a factor of 2. Answer: Since the capacitance is inversely proportional to the plate separation d, then doubling the separation reduce the capacitance by 2. Mathematically,

21

2 1

1

2

1

1

2 ===d

ddd

CC

.

(4 marks)

c) The figure below shows capacitors connected together in a circuit with a 12 volts battery.

iii) Obtain the total capacitance for the configuration in the figure.

3 µF

12 V +

-

1 µF

2 µF

4 µF

A B



Answer: Since in parallel,

FFFCCC µµµ 6424224 =+=+=

(1 marks)

Since in series,

FCCC µ34

31

11111

3113

=+=+=

(2 marks)

Since the capacitances are in series,

then, Fµ2

369

68

61

34

61

==+=+

(2 marks)

Hence the total capacitance is FC µ32

2413 =

(1 mark)

iv) Determine the total charge stored and the total electrical potential energy stored by

the capacitance configuration above.

Answer: Since CVq = , then, CVFq µµ 61232

=×=

(2 marks) iii) Determine the potential difference between points A and B.

Answer: Since C24= 6 µF, and the total charge is the same, then

V FC

CqV 1

66

===µµ

.

(2 marks)

3 µF1 µF

34

31

33

31

11

=+=+

FC µ43

13 =

2 µF

4 µF

C24= 6 µF



QUESTION 2

a) Three particles move through a constant magnetic field and follow the paths shown in the drawing. Determine whether each particle is positively charged, negatively charged, or neutral. Give a reason for each answer.

Answer: Using right hand rule #1, since v & B is perpendicular, then FB points perpendicular to the path shown. Then F is as indicated for a charged particle, FB is zero for a neutral particle. Hence particle 1 is +ve, particle 2 is neutral and particle 3 is –ve.

(2+3 = 5 marks)

F

#1

#3

F

b) The drawing shows an end-on view of three parallel wires that are perpendicular to the plane

of the paper. All carries current I and the wires are separated from each other by a distance d. In two of the wires the current is directed into the paper, while in the remaining wire the current is directed out of the paper. The two outermost wires are held rigidly in place.

i) Draw the magnetic field lines for

the rigid wires. ii) Write the magnitude of the

magnetic field at the position of the middle wire.

Answer: dIB

πµ2

2 0=

v) Indicate the direction of the force acting on the middle wire. Answer: To the left or the FB shown.

(2+1+1= 5 marks) c) For each electromagnet at the left of the drawing,

i) label the polarity of the induced magnetic field ii) explain whether it will be attracted to or

repelled from the permanent magnet at the right. Answer: Top picture: Repelled because of same poles Bottom picture: Repelled because of the same poles.

(2+2 = 4 marks)

d) For each electromagnet in the drawing on the right,

S

S

FB

Current

X 0X



i) label the polarity of the induced magnetic fields.

ii) explain whether the left electromagnets in the drawing will be attracted to or repelled from the adjacent electromagnet on the right.

Answer: Top picture: Attracted because of opposite poles Bottom picture: Repelled because of the same poles.

S N

N S

N

N

S

S

(a)

(b)

(4+2 = 6 marks)

QUESTION 3 a) Write some scientific response about the following:

i) induced electromotive force (emf) and induced current. Answer: Induced current is produced whenever there is a flux change in a circuit. As a result of the induced current, an emf will exist between points in that circuit.

ii) magnetic flux Answer: Magnetic flux is a measure of the number of magnetic lines through a surface area in space.

iii) Faraday’s and Lenz’s law of electromagnetic induction. Answer: Faraday’s law of magnetic induction states that the emf induced in a cicuit is

proportional to the change in magnetic flux in one second. Lenz’s law states that the induced current will be in a direction opposing the the direction of current that induces the change.

(2+2+6 = 10 marks) b) In the diagrams below, label the high and low potential points of the coil by the usual symbol

‘+” and ‘-‘ and indicate the direction of the induced electromotive force (emf).

i) ii)

_

+Decrease Current

Coil

_Increasing current

Coil

+



iii)

(2+2+2 = 6 marks)

c) During a 72-ms interval, a change in the current in a primary coil occurs. This change leads to

the appearance of a 6.0 mA current in a nearby secondary coil. The secondary coil is part of a circuit in which the resistance is 12 Ω. The mutual inductance between the two coils is 3.2 mH. Remembering Ohm’s law and the fact that the induced emf in the secondary coil is because of the change in current in the primary coil, determine the change in the primary current, ∆ip.

Answer:The rate of change tI p ∆∆ / , in the primary current is related to the emf Sξ induced

in the secondary coil according to S P /M I tξ = − ∆ ∆ (Equation 22.7), where M is the mutual

inductance between the coils. We can use this expression to determine pI∆ directly. However, in doing so, we will omit the minus sign, since the direction of the current is unspecified. A value for the induced emf can be obtained from the induced current SI and

the resistance R in the secondary circuit, according to S SI Rξ = , which is Ohm’s law.

Substituting the induced emf from Ohm’s law into Equation 22.7 (without the minus sign), and solving for pI∆ gives

( ) ( )( )( )3 3SP

S S P 3

6.0 10 A 12 72 10 s or 1.6 A

3.2 10 HI R tI

I R M It M

ξ− −

−

× Ω ×∆∆= = ∆ = = =

∆ ×

(4 marks)

+ -Resistor

Secondary Coil Primary Coil Increasing current




i) the wave-particle-duality Answer: A particle can behave or exhibit wave-like properties and a wave can exhibit

particle-like properties. iii) blackbody radiation

Answer: The intensity per unit wavelength of the radiation produced by a blackbody at any given temperature varies with wavelength and the maximum intensity occurs at a shorter wavelength.

iv) Photons. Answer: Photons are particle-like quanta or packets of energy of electromagnetic waves

v) Heisenberg uncertainty principle. Answer: Heisenberg uncertainty principle states that product of the uncertainty in position that an electron wave on a screen after passing thru a slit and its momentum

change along the y-axis is probabilistic and has a minimum accuracy of π4h

;

π4hypy ≥∆∆ or

π4htE ≥∆∆

(10 marks) b) i) Explain the photoelectric

effect. Answer: The process of emission of

photoelectrons (photons) from the surface of a metal when light with energy higher than the work function of the metal shines on the surface.

(4 marks)

i) Draw an energy-frequency graph representing the phenomenon. Label all the axis.

(4 marks)

ii) A silver surface has a work function of 4.73 eV ( 1 eV = 1.6 x 10-19 J). Find the

minimum frequency that light must have to eject electrons from this. (Planck’s constant, h = 6.63 x 10-34 Js).

Answer: eVJeVhfW 19

0 106.173.4 −××== . Then

HzJs

eVJeV

hWf 15

34

19

0 1014.11063.6

106.173.4×=

×

××== −

−

.

(2 marks)




i) Rutherford’s scattering Answer: The deflection and back scattering of heavy alpha particles when bombarded onto a thin layer of gold led Rutherford to propose that the positive charge in an atom is confined to a small space and is now called the nucleus. ii) Bohr’s model of the hydrogen atom. Answer: In a hydrogen atom there can only be certain allowed energies that the electron can have when orbiting around the nucleus, larger orbits correspond to larger energies. iii) Balmer series Answer: A group of lines belonging to the visible region of the electromagnetic spectrum representing photons emitted whenever there is a transition in an atom. iv) ground state Answer: The lowest energy state in an atom

(10 marks) b) i) Describe, with the help of a picture, how x-rays are produced.

Answer:

Electrons are emitted from a heated filament and accelerated through a large voltage. When they strike the target, X-rays are emitted.

(7+3 = 10 marks)



PART B (100 MARKS) QUESTION 1 a) Write some scientific response about the following:

i) the law of electrical charge conservation Answer: Total amount of charges must be conserved in any process and the amount before and after must remain constant. ii) charging by contact and induction Answer: Charging by contact involves transfer of charges between objects whereas charging by induction involves bringing a charges object near an uncharged object to induce charges in the uncharged object to rearrange without any transfer of charges. iii) Electric field lines Answer: Electric field lines are lines in an area where a charged test charge will experience an acceleration if placed in this area due to the electrical forces exerted onto the test charge. iv) Electric flux Answer: Electric flux is the product of the parallel component of the electric field lines that pass through the surface area and the magnitude of the surface area.

(10 marks) b) Consider three identical metal spheres, A, B, and C. Sphere A carries a charge of +5q.

Sphere B carries a charge of –q. Sphere C carries no net charge. The following process were performed on the spheres:

1. Spheres A and B are touched together and then separated. 2. Sphere C is then touched to sphere A, and then separated from it. 3. Lastly, sphere C is touched to sphere B and separated from it. i) What is the total charge on the three spheres before they are allowed to touch each

other? Explain your answer. Answer: Total charge is the sum of all the charges. So, Q = q1+q2+q3 = 5q-q+0 = 4q. ii) What is the total charge on the three spheres after they have touched? Explain your

answer. Answer: Using charge conservation, the total charge must remain the same before and after

the process. Hence total charge after must be +4q. iii) Determine the amount of charges on each sphere after each of the process. Explain

your answer. Answer: When spheres A and B touch, an amount of charge +q, flows from A and

instantaneously neutralizes the charge –q on B leaving B momentarily neutral. Then, the remaining amount of charge, equal to +4q, is equally split between A and B, leaving A and B each with equal amounts of charge +2q. Sphere C is initially neutral, so when A and C touch, the +2q on A splits equally to give +q on A and +q on C. When B and C touch, the +2q on B and the +q on C combine to give a total charge of +3q, which is then equally divided between the spheres B and C; thus, B and C are



q1 = -4e q2 = +2e

q4 = +e q3 = -4e

P a

a

E4

E3

E1

E2

each left with an amount of charge +1.5q (2+2+6 = 10 marks)

c) The figure below shows a configuration

of charged particles placed at the corners of a square measuring a by a

vii) Draw and label the electric field due

to each of the four charges at position P, the center of the square, E1, E2, E3, and E4.

(4 marks)

viii) Using Pythagoras theorem, determine the distance from P to the charge at the corners.

Answer: Use Pythagoras theorem: 222 bar += . So, 222

2

222aaar =⎟

⎠⎞

⎜⎝⎛+⎟

⎠⎞

⎜⎝⎛= . Then

2ar =

(2 marks)

ix) Write down the electric field strength for each of the charges at position P, E1, E2, E3, and E4.

Answer: Since

2rqkE = , then, 21

42a

ekE = , 2222a

ekE = , 2342a

ekE = , 24 2aekE =

(4 marks)

x) Obtain the electric field along the x-axis and the electric field along the y-axis, respectively, for E2 and E4 at position P.

Answer: 2

12245cos22 222 aek

aekE x −=−= o ,

21245cos2 224 a

ekaekE x == o

212245sin22 222 a

eka

ekE y −=−= o , 2

1245sin2 224 aek

aekE x == o

(8 marks)

xi) Use the results of part (iv) and the symmetry of the problem to obtain the total electric

field acting at position P.



Ex

θ Ey

E

Answer: By symmetry, E1 and E3 add up to zero in both the x and the y directions since they have the same magnitudes but act in opposite directions.

214

2142

2122 22242 a

kea

eka

ekEEE xxx =+−=+−= ,

214

2142

2122 22242 a

kea

eka

ekEEE yyy =+−=+−=

Then the total E is

2

2

2

2

222 4

214

214

ake

ake

akeEEE yx =⎟

⎠

⎞⎜⎝

⎛+⎟

⎠

⎞⎜⎝

⎛=+= .

o45 is So

ake

ake

EE

x

y θθ .1

2142

14

tan

2

2

===

(8 marks)

xii) Explain what would happen to a positive test charge, q0, if it was placed at position P. Answer: A positive test charge will feel a force in the direction of the electric filed line and

hence will accelerate in that direction with a magnitude of 200 4ma

keqmEq

mFa === .

(4 marks)




i) alternating current Answer: Current that changes direction after every cycle. ii) parallel wiring Answer: A type of wiring where the potential drop in each branch is the same. iii) Resistance Answer: the opposing factor to the flow of current in a circuit. iv) electrical power Answer: Power is the amount of energy dissipated (lost) in a resistor in one second. v) ammeter Answer: Ammeter is a device (instrument) that is connected in series in a circuit and used to

measure current through that circuit..

(10 marks)

b) Redraw each of the circuits on the right and identify which circuit is connected neither in series nor in parallel.

For the first circuit,

2 3

4

5

6

7

8

1

1

2

3

4

5

6

7

8



23

4

5

6

7

8

1

234

5

6

7

8

1

2 3

4

5

6

7

8

1

The resistors can further be rearranged as shown below:

234758

6

1

2347

5

68

1

23475

68

1

Finally, the resistors can be represented as,

2347586

1

For the second circuit, redrawing can be done as shown below:

1

2

3

4

5

6

7 1

23 45 67

The last circuit could not be redrawn as was done for the first 2 circuits. Hence, this circuit does not have any resistors connected in series and in parallel.



1 2

3

45

(6+2+1+1 = 10 marks)

c) The figure below show plots of the electric current I through a certain cross section of a

conducting wire over four different time periods. Determine the amount of net charge that pass through each cross section.

(2+2+2+2+2 = 10 marks)

Answer: The amount of charge is just the area since current is the amount of charge passing through in one second. Section (i): CmsmAtIarea µ414 −=×−=∆= Section (ii): CmsmAtIarea µ422 =×=∆=

Section (iii): ( ) CmsmAtIarea µ42421

−=×−=∆=

Section (iv): By symmetry, since the amount of charge above and the axis is the same then it adds up to zero.

-4

-2

810

4

2

4

2

i)

Current, I, mA

Time t, ms

ii)

iii)

iv)

6



d) Given the circuit below,

iii) Label the ‘+’ and ‘–‘ signs at the ends of each resistor and battery to indicate the high and low potential.

iv) Using Kirchoff’s laws, and the results of part (i), determine the currents I1, I2, and I3.

Show ALL your work. Answer: Kirchoff’s current rule: Sum of currents into a junction must equal sum of current leaving.

321 III =+ Kirchoff’s voltage rule: In a loop, Sum of potential drop must equal sum of potential rise. Using clockwise motion: Left loop 211 10551520 III =+++ . Rewrite: 0102025 21 =−+ II

Right loop 510101020 233 =+++ III . Rewrite: 051030 23 =++ II

Replace I3 by I1+I2. 054030 21 =++ II ; 0102025 21 =−+ II . Multiply by 4.

04080100 21 =−+ II . Add up to remove I2. 85130 1 −=I . So, AAI 65.013085

1 −=−= .

Substitute I1 into 0102025 21 =−+ II . 210201308525 I=+− . Then,

AI 37.8101300

85252 =+−= . Finally, AI 7.735.865.03 =+−=

(20 marks)

END OF QUESTION PAPER

10 V

I3 I2 R=5 Ω

R=10 Ω

R=20 Ω

5 V

R=10 Ω I1

15 V

R=20 Ω

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