Download Using equivalence resistance to calculate current

St. Joseph’s Anglo-Chinese School
F5 Physics
Notes and Supplementary Exercise
Electricity and Magnetism
Atomic Physics
0
Chapter 15
Electric Circuit
1(a)(i)
(ii)
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What is the equivalent resistance of
the two resistors?
What is the voltage across the 6 
resistor?
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The two resistors are then connected in
parallel to the battery.
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(b)(i)
What is the equivalent resistance of
the two resistors?
(ii) What is the current through the 6 
resistor?
(iii) What is the total current in the main
circuit?
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2
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Find I1 and I2.
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1
3
The resistors are connected in a network to a 12 V battery as shown.
(a) What is the total resistance of the network?
(b) What is the current through A?
(c) What is the voltage across B?
(d) What is the voltage across the parallel combination of B and C?
(e) What is the current through (i) B, (ii) C?
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2
Chapter 15
Notes Circuit Analysis
Simplify the circuit steps by steps
3
Equivalence resistance
Three resistors in series
R = R1 + R2 + R3
Three resistors in parallel
1
1
1
1



R R1 R2 R3
5
4
8
1
5V
16 
Step 1:
The 3, 4 and 1 resistors are connected in series. Therefore, we can use an 8 resistor to
replace them.
5
8
8
5V
16 
Step 2:
The two 8 resistors are in parallel. We can calculate the equivalent resistance of the two 8
resistors. Pay attention to the presentation.
Let R be the equivalent resistance of the two 8 resistors.
1 1 1
 
R 8 8
1 1

R 4
R = 4
Therefore, we can use a 4  resistor to replace the two 8 resistors. The circuit will become:
5
4
5V
16 
Step 3
Now, it is clear that the total resistance in the circuit is 5 + 4 + 16 = 25 .
3
Using equivalence resistance to calculate current
3
Ohm’s Law
V
R
voltage across the
resistor.
current through the
resistor.
V = IR
V:
I:
or
I=
4
5
8
1
16 
Question: What are the currents through the 3, 8 and 16  resistors?
Answer:
5  0.2 A
5V
4
16 
The total resistance in the circuit is 25 .
Current passing through the 16 resistor = 5/25 = 0.2 A
5
I1
0.2 A
I2
8
8
5V
I1: I2 = 8: 8
16 
I1 = I2 = 0.2/2 = 0.1 A
Current passing through the 8 resistor = I2 = 0.1 A
3
5
I1
0.2 A
I2
4
8
5V
1
16 
Current passing through the 3  resistor = I1 = 0.1 A
Question: Find the voltages across the 16, 4 and 5 resistors.
Answer:
Voltage across 16  resistor = (0.2)(16) = 3.2 V
Voltage across 4  resistor = (0.1)(4) = 0.4 V
Voltage across 5  resistor = (0.2)(5) = 1 V
4
5V
Chapter 15
Resistors in series and parallel
1
(a)
Find the equivalent resistance across XY in each of the following cases.
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(b)
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(c)
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(d)
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(e)
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(f)
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5
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2
Assume all the meters in the above circuit are ideal.
(a) Find the readings of the ammeters and voltmeter when the switch is open.
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(b) Find the readings of the ammeters and voltmeter when the switch is closed.
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(c) What is the change in brightness of L1 and L3 when the switch is closed?
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6
3
Three identical light bulbs marked “24 V, 48 W” are connected as shown below.
(a)
Name the device X and state its function.
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(b) Find the resistance of each light bulb.
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(c) Find the equivalent resistance of the resistors
(i)
when the switch S is opened.
(ii) when switch S is closed.
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(d)
Find the current flowing through each bulb when switch S is closed.
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(e)
Find the power dissipated by each of the light bulbs when switch S is closed.
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7
4
The figure above shows the front view of a socket and the earth (E), live (L) and neutral (N) wires
of the 220 V mains supply.
(a) Show how the socket is connected to the mains supply.
(b)
Model No.: CS301
220V 50 Hz
2500 W
The above figure shows the label attached to an electrical appliance. If the appliance is
switched on for 150 hours in a month, calculate the cost of electricity.
(Given: 1 kW h of electricity costs $0.87.)
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8
Chapter 16
Electricity in the Home
Questions (Q) and Answers (A)
Q1 Why is the switch fitted in the live wire?
A1
The switch is fitted in the live wire because this makes sure that no part of the electrical
appliance is at high voltage when the switch is turned off.
Q2
What is the purpose of connecting the metal case of an electrical appliance to the earth? /
What is the function of the earth wire?
A2
If the wire gets loose and touches the metal body of the appliance, a large current will flow
through the earth wire to earth. This prevents the user from getting an electric shock.
Common mistake:
If there is a short circuit, a large current will flow through the earth wire to earth. This
prevents the user from getting an electric shock.
Q3 What is the function of a fuse?
A3
If an excess current flows through the circuit or the circuit overloads, the fuse blows and
breaks the circuit before the cable overheats and causes a fire.
Q4 Why is the earth pin made longer than the other two pins?
A4
The earth pin is designed longer to open the shutters on the live and the neutral holes on the
sockets. These holes are normally closed so that young children cannot put their small fingers
into them.
9
Chapter 15 and 16
HKCEE Multiple Choice Past Paper
1.
In the above circuit, the reading of the ammeter is 0.4A. Find the resistance of the resistor R.
A.
3Ω
B.
5Ω
C.
6Ω
D.
9Ω
E.
12 Ω
2.
A motor is connected in series with a 10 Ω resistor and a 12 V power supply as shown above.
If the current in the circuit is 0.5 A, find the power consumed by the motor.
A.
3.5 W
B.
5W
C.
6W
D.
7W
E.
14 W
3.
An electrical appliance is connected to a power supply of voltage V by long connecting wires
of total resistance R as shown in the above circuit. It is found that the current passing through
I
the appliance is only 0 , where I0 is the current required for the appliance to work at its
2
rated value. Which of the following changes could increase the current through the appliance
to I0?
Voltage of power supply
A.
B.
increases to 2 V
increases to 2 V
C.
increases to 2 V
D.
E.
remains unchanged
remains unchanged
Total resistance of connecting wires
increases to 2 R
remains unchanged
R
reduces to
2
increases to 2 R
R
reduced to
2
10
4
Which of the following expressions represents a physical quantity which is different from the
others?
Work
A.
Time
(Voltage)
B.
C.
D.
E.
5.
Resistance
Force x velocity
(Current)2 x resistance
Mass x specific latent heat of fusion
The kilowatt-hour is a unit of
A.
B.
C.
D.
E.
6.
2
charge.
current.
energy.
voltage.
power.
Which of the following statements about the earth wire in an electric iron is/are correct?
(1) The earth wire should be connected to the metal body of the iron
(2) If the iron is working properly, no current passes through the earth wire.
(3) In case the neutral wire is broken, the earth wire provides a spare wire for the return path
to the mains socket.
A.
B.
C.
D.
E.
(1) only
(3) only
(l) and (2) only
(2) and (3) only
(1), (2) and (3)
7.
In the above circuit, X and Y are identical heaters. The ammeter has negligible resistance while
the voltmeter has very high resistance. When switch S is closed, the ammeter records a reading
but the voltmeter reading is zero. Which of the following provides a possible explanation?
A.
B.
C.
D.
E.
The heater X burns out.
The heater Y burns out.
The heater X is short-circuited.
The heater Y is short-circuited.
The battery is short-circuited
11
8.
Which of the following expressions does not represent energy?
A.
B.
C.
D.
E.
Force x displacement
1
2
x mass x (speed)2
(Current)2 x resistance
Current x voltage x time
Mass x specific latent heat of fusion
9
Figure (a)
Figure (b)
In Figure (a), the ammeter reading and the total power dissipated in the two identical resistors
are I and P respectively. The resistors are rearranged as shown in Figure (b). Find the ammeter
reading and the total power dissipated in the two resistors.
Ammeter reading
A.
B.
C.
D.
E.
2I
2I
4I
4I
4I
Total power dissipated
2P
4P
2P
4P
8P
10. Which of the following pairs of physical quantities has the same units?
A. Charge and current
B. Frequency and time
C. Kinetic energy and heat
D. Moment and momentum
E. Work and voltage
11. Which of the following values is equivalent to one kilowatt hour?
A.
B.
C.
D.
E.
1000 W
1000 J
3600 J
3.6 x 106 W
3.6 x 106 J
12
12.
A Christmas tree is illuminated with four strings of light bulbs. Each string has ten identical
light bulbs connected in series as shown above. If one light bulb suddenly bums out, which of
the following will happen?
A.
B.
C.
D.
E.
Only that light bulb will go out.
One light bulb in each string will go out.
One string of light bulbs will go out.
All the light bulbs will go out.
Half of the light bulbs will go out.
13.
Find voltage across X and Y in the above circuit.
A.
B.
C.
D.
E.
0V
1V
2V
3V
4V
14.
In the above circuit, all the light bulbs are identical. What happens to the brightness of the
bulbs L1, L2 and L3 if switch S is closed?
A.
B.
C.
D.
E.
L1
decreases
decreases
decreases
remains unchanged
increases
L2
increases
increases
remains unchanged
decreases
remains unchanged
13
L3
remains unchanged
decreases
remains unchanged
increases
increases
15. Which of the following diagrams correctly shows the connection of the wires of an iron to the
2
pins of a plug? (L: Live, N: Neutral, E: Earth)
A.
B.
C.
D.
E.
16.
In the above circuit, all resistors are identical and the ammeters are of negligible resistance. If
the reading of ammeter A1 is 2 A, find the readings of ammeters A2 and A3.
A2
A3
A. 1 A
3A
B. 2A
2A
C. 2A
4A
D. 4A
2A
E. 4A
6A
17. Which of the following circuits can be used to measure the resistance of the light bulb?
A.
B.
C.
D.
E.
14
18.
In the circuit above, what happens to the readings of the three ammeters if switch S is closed?
A.
B.
C.
D.
E.
A1
increases
remains unchanged
increases
decreases
increases
A2
increases
becomes zero
becomes zero
increases
increases
A3
increases
increases
remains unchanged
becomes zero
becomes zero
19. Which of the following is/are vectors?
(1) momentum
(2) kinetic energy
(3) voltage
A. (1) only
B. (2) only
C. (1) and (3) only
D. (2) and (3) only
E. (1), (2) and (3)
20. For safety, the correct way of connecting the fuse and switch to electrical appliances should be
A.
B.
C.
D.
E.
fuse in live wire, switch in neutral wire.
fuse in earth wire, switch in live wire.
fuse in earth wire, switch in neutral wire.
both in neutral wire.
both in live wire.
15
21.
In the above circuit, P, Q and R are identical resistors. Which of the following is true when
switch S is closed?
A.
B.
C.
D.
E.
The voltage across Q increases.
The voltage across P remains unchanged.
The current through Q remains unchanged.
The current through P decreases.
The power output from the battery increases.
22.
Arrange the above networks in descending order of equivalent resistances:
A.
B.
C.
D.
E.
(1), (2), (3)
(2), (1), (3)
(2), (3), (1)
(3), (1), (2)
(3), (2), (1)
23.
In the circuit above, the voltage across X and Y is
A. zero.
B. 1.5 V.
C. 3.0 V.
D. 4.5 V.
E. 6.0 V.
16
24.
In the circuit above, L1, L2 and L3 are identical light bulbs. Which of the following statements
is/are correct when the switch S is closed?
(1) The brightness of L1 decreases.
(2) L2 and L3 are of the same brightness.
(3) L1 is brighter than L2.
A.
B.
C.
D.
E.
(1) only
(2) only
(3) only
(1) and (2) only
(2) and (3) only
25.
In the circuit above, resistors A, B and C are identical. When K is open, the power dissipated
by A is P1. When K is closed the power dissipated by A becomes P2. P1 : P2 is
A 3:2
B 2:1
C 9:4
D 4:1
E 16 : 1
26.
In the above circuit, a 4 resistor is to be connected to two of the terminals A, B, C and D to
give the greatest brightness in the lamp bulb. Which connection should be made?
A across AB
B across BC
C across CD
D across AD
E across BD
17
27
Operating voltage 220 V/50 Hz
Power
1500W
Fuse rating
30 A
The diagram above shows the label attached to an electric appliance. How much electrical
energy is supplied to the appliance in 2 hours?
A. 2.0 kWh
B. 2.5 kWh
C. 3.0 kWh
D. 6.0 kWh
E. 12.0 kWh
28.
A standard three-pin socket on the wall is shown in the figure above. Which of the following
is correct?
Pin 1
Pin 2
Pin 3
A. neutral
live
earth
B. neutral
earth
live
C. earth
live
neutral
D. earth
neutral
live
E. live
earth
neutral
29.
What should be the voltage across P and Q in the circuit shown above?
A. 0V
B.
3V
C. 6V
D. 9V
E.
12 V
30.
In the circuit shown above, which of the switches should be closed in order to get the
maximum brightness in lamp Z?
A. X only
B. Y only
C. Z only
D. X and Y only
E.
X and Z only
18
31. A 3-pin plug is connected to a boiler with a rating of "2000 W, 200 V". Which of the
following statements is/are true?
(1) A 5A fuse should be used in the circuit.
(2) The fuse should be placed on the brown wire of the cable.
(3) The yellow and the green wire of the cable should be connected to the earth pin.
A. (1) only
B. (3) only
C. (1) and (2) only
D. (2) and (3) only
E. (1), (2) and (3)
32.
In the three-pin plug as shown above, X, Y and Z are respectively connected to the
X
Y
Z
A. earth
neutral
live
B. earth
live
neutral
C. neutral
earth
live
D. neutral
live
earth
E. live
neutral
earth
33
Four identical lamps P, Q, R and S are connected to a battery as shown above. If lamp P is
blown, which of the following would happen?
A.
B.
C.
D.
E.
Lamp R becomes brighter
Lamp Q becomes brighter.
Lamp S becomes brighter.
Lamps Q and S remain at the same degree of brightness.
Lamp R does not light.
1
2
3
4
5
C
A
B
E
C
6
7
8
9
10
C
C
C
D
C
11
12
13
14
15
E
C
C
A
A
31
D
32
B
33
A
Answer
16 E
17 B
18 E
19 A
20 E
19
21
22
23
24
25
E
C
B
E
C
26
27
28
29
30
C
C
D
D
B
Chapter 15
Resistors in series and parallel
20
21
Answer:
1
2
3
4
5
A
C
A
B
D
22 B
23 D
24 A
25 C
26 C
22
Chapter 16
Harder Exercise Electricity in the home
1
Figure 1 shows an incomplete wiring of a room.
(a) In which wire should the fuse be installed?
(b) Draw lines to complete the wiring.
(c) An electric heater marked "200 V 1 kW", a lamp marked "200 V 100 W" and an electric
fan marked "200 V 200 W" are connected to S1, S2 and S3 respectively.
(i)
What is the maximum current drawn from the mains?
(ii) Fuses marked 3 A, 5 A, 10 A and 13 A are available. Which one is the most suitable
for this circuit?
(iii) What should be done on the electric heater in order to prevent people from receiving
electric shocks if a fault has developed?
(d) State the advantages of using parallel circuit in a house.
(e) What equipment is used to measure the electrical energy dissipated in a house?
23
2
Figure 2 shows a lighting system. Three light bulbs X, Y and Z marked "24 V 36 W", "24 V
24 W" and "24 V 48 W" respectively are connected to a 24-V battery with eight long wires.
The internal resistance of the battery can be neglected and the resistance of each wire is 5.
Figure 2
(a) Find the resistance of each light bulb.
(b) Are the light bulbs connected in parallel or in series?
(c) Draw a circuit diagram for the lighting system.
(d) Find the current drawn from the battery.
(e) Explain why the power dissipated by each light bulb is not equal to the value on its label.
24
3.
Figure 3 shows a simplified domestic circuit. The voltage of the mains supply is 220 V. The
lines L and N represent live and neutral wires respectively.
Figure 3
(a) What are the colours for the live and neutral wires?
(b) What is the advantage of connecting the light bulbs in parallel?
(c) The light bulbs are labelled as "220 V 100 W". Assume that all the light bulbs are
switched on.
(i)
Find the total resistance of the circuit.
(ii) Find the total current drawn from the mains.
(d) The light is off now. How would you turn the switch in order to turn on all the light
bulbs?
(e) Suggest one use of the above circuit.
(i)
What is the function of the fuse?
(ii) What physical quantity is measured by the meter?
25
St. Joseph’s Anglo-Chinese School
F.5. Physics Solution
Supplementary Exercise (Chapter 16)
1
(a) Live wire
(b)
220 V
(c) (i)
2
Heater:
P = IV
1 000 = I (200)
I = 5A
Lamp:
P = IV
100 = I(200)
I = 0.5 A
Fan:
P = IV
200 = 1(200)
I = 1A
Maximum current drawn from the mains
= 5 + 0.5 + 1
= 6.5 A
(ii) 10 A.
(iii) The metal case of the heater should be earthed.
(d) 1. The voltage across all the electric appliances is the same.
2. When one electric appliance does not work, others can still work.
(e) Kilowatt-hour meter.
V2
(a) R 
P
24 2
X : Rx 
 16 
36
24 2
Y : Rx 
 24 
24
24 2
Z : Rx 
 12 
48
26
(b) In parallel.
(c)
R1 
1
 11.48 
1
1

24 5  12  5
1
R2 
 9.17 
1
1

16 5  R1  5
Rtotal  10  R2  10  29.17 
The current drawn from the battery =
24
24
 0.823 A
=
29.17
Rtotal
27
(d) It is because there is voltage drop due to the connecting wire. The voltage across each
lamp is smaller than 24 V. Therefore, the power dissipated by each light bulb is not equal
to the value on its label.
3
(a) Live:
brown.
Neutral: blue.
(b) 1. The voltage across all the light bulbs are the same.
2. When one light bulb does not work, others can still work.
(c) (i) Resistance R of each light bulb
V2
=
P
220 2
=
100
= 484 
The light bulbs are connected in parallel.
1
Rtotal 
 161.33 
1
1
1


484 484 484
220
 1.364 A
(ii) I 
161.33
(d) We can turn the switch either from A to B or from D to C.
(e) Lighting system of a corridor.
(f) (i) It protects the electrical appliances by preventing a large current from flowing
through it.
(ii) Energy.
28
St. Joseph’s Anglo-Chinese School
1.
Electric Charges
A negatively charged rod is brought near an insulated metal sphere as shown below.
(a) Draw the distribution of charges on the sphere in the diagram above.
(b) Describe and explain the distribution of charges on the sphere.
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(c) If the amount of charge on the rod is -8 x 10-10 C, calculate the number of excess electrons
on the charged rod. It is given that the charge of an electron is -1.6 x 10-19 C.
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2
A small insulated metal sphere A carrying positive charges is made to touch another larger
neutral sphere B as shown below.
+
i+
+
i+
+
+
i+
+
(a) Draw the distribution of charges on both spheres when they are separated.
(b) Describe and explain the distribution of charges on both spheres.
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29
(c) What would happen if in the beginning, sphere B is replaced by a larger metal sphere C
which is made to touch sphere A. Draw and describe the distribution of charges on both
spheres.
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(d) What would happen to the charges on A if it is connected to the earth.
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3
Describe and explain the motion of the metal coated polystyrene ball when the Van de Graaff
generator is turned on.
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30
Chapter 17
Motor
1
Figure 1 shows a simple motor.
Figure 1
(a) Name the components A and B.
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(b) What is the coil’s direction of rotation as seen by the observer?
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(c) Complete the following graph to show the variation of turning effect on the coil with
different orientations.
Turing effect
Orientation of coil
(d) If both the poles of the magnet and the polarities of the cell were reversed at the same
time, what would happen to the direction of rotation of the coil?
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(e) Explain why the coil continues to rotate even the coil is vertical.
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31
2
(HKCEE 1998 Q5)
Figure 2
Figure 2 shows a type of motor. PQ and RS are solenoids. The solenoids and the coil ABCD
are connected in parallel to a battery.
(a) State
(i) the polarity at end Q of the solenoid PQ,
(ii) the direction of rotation of the coil as seen by the observer.
(2 marks)
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(b) Name the component E and explain its function.
(3 marks)
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(c) Suggest two ways of increasing the rotating speed of the coil.
(2 marks)
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________________________________________________________________________________
*
(d) A student says “If the battery in Figure 2 is replaced by a 50 Hz a.c. supply, the coil will
only oscillate to and fro. Hence the motor will not function properly.”
Explain why the student is incorrect.
(5 marks)
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
32
Chapter 17 and 18
Electromagnetism and electromagnetic induction
1
The figure below shows a simple d.c. motor.
device X
device Y
(a) What are devices X and Y?
_____________________________________________________________________________
_____________________________________________________________________________
(b) What is the direction of rotation of the coil as seen by the observer?
_____________________________________________________________________________
(c) Will the direction of rotation change if the polarities of the cell and the poles of the magnet are
reversed at the same time?
_____________________________________________________________________________
2
An a.c. generator is shown below.
Device X
(a)
Name device X.
_____________________________________________________________________________
(b)
Draw on the above figure the current induced by the a.c. generator at that instant.
33
(c)
Use a diagram to show how the a.c. generator can be converted into a d.c. generator.
(d)
Sketch the output voltage of the a.c. generator against time and indicate on the time
axis the times at which
(i)
the magnetic field is parallel to the plane of the coil,
(ii) the magnetic field is perpendicular to the plane of the coil.
Output voltage
0
time
(e) Describe the changes of the output voltage if
(i) the rotational speed of the generator is decreased.
(ii) the direction of rotation of the generator is reversed,
(iii) the number of turns of the coil is increased.
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
34
3
Two coils are wrapped on paper cylinders and connected as shown in the figure below.
State the conditions of the lamp
(a)
at the instant when the switch is closed,
_____________________________________________________________________________
(b)
when the switch remains closed,
_____________________________________________________________________________
(c)
at the instant when the switch is re-opened.
_____________________________________________________________________________
(d) What will happen to the lamp in each case when the above processes are repeated but
using an a.c. power supply instead?
_____________________________________________________________________________
4 A light rectangular conducting loop PQRS is moving at a uniform velocity from left to right
across a uniform magnetic field B (pointing out from the paper). Three subsequent positions of
the loop during its motion are shown in the figure below.
(a)
(b)
Draw the induced current in each of the three figures.
Determine if an external force is needed to keep the loop moving with uniform velocity in
each of the three cases.
_____________________________________________________________________________
_____________________________________________________________________________
35
Solution
Chapter 17 and 18
Electromagnetism and electromagnetic induction
1(a) Device X: commutator
Device Y: carbon brush
(b) Anticlockwise
(c) No
2(a) slip-ring
(b)
I
I
Device X
(c)
commutator
carbon brush
output
Output voltage
(d)
0
time
(e) (i) output voltage decreased, frequency decreased
(ii) output voltage reversed
(iii) output voltage increased
36
3(a)
(b)
(c)
(d)
flashes
does not light up
flashed
The lamp will light up in all three cases if an a.c. supply is used.
4 (a)
I
I
No current is induced
(b) Case 1: necessary
Case 2: not necessary
Case 3: necessary
37
Chapter 18
Electromagnetic Induction
1
Figure 1(a) shows a model generator which is being rotated by a hand.
water
Figure 1(a)
The force acting on the handle is 20 N. The output of the generator is connected to an
immersion heater. After rotating 150 revolutions, the temperature of the water inside the cup
has been raised by 5°C. The mass of water inside the cup and the specific heat capacity of
water are 0.2 kg and 4200 Jkg-1C-1 respectively. (Take  = 3.14.)
(a) Is the output current an a.c. or a d.c.?
(b) In Figure 1(b), sketch the variation of the current with the positions of the rotating coil.
Figure 1(b)
(c)
(d)
(e)
(f)
Find the work done by hand after rotating 150 revolutions.
Find the energy absorbed by the water.
Calculate the efficiency of the generator.
Suggest ONE way to increase the efficiency of the generator.
38
2
A village consists of 110 households. Power cables will be installed to supply electricity to
these households. The cables have a resistance of 0.1  km-1. It is estimated that each
household consumes 2 kW every day. The voltage of the domestic electricity is 220 V. The
distance between the power station and the village is 50 km.
(a) Figure 2(a) shows one of the transmission plannings.
(i)
(ii)
(iii)
(iv)
(v)
(vi)
Figure 2(a)
What is the total power consumed by the village every day?
What is the total resistance of the cables?
Calculate the current flowing through the cables.
Hence, calculate the power lost in the cables.
What should be the voltage output and the power output from the power station?
Find the efficiency of this transmission system.
(b) Figure 2(b) shows another planning in which ideal transformers are used.
(i)
(ii)
(iii)
(iv)
(v)
(vi)
Figure 2(b)
What is the voltage across AB?
Calculate the current flowing through the cables.
Hence, calculate the power lost in the cables.
What should be the voltage output and the power output from the power station?
Find the efficiency of this transmission system.
In daily life, can you find an ideal transformer? Why?
39
3
A permanent magnet is connected to a spring as shown in Figure 3. A solenoid is placed just
above the magnet.
Figure 3
(a) A current passes from A to B through the solenoid.
(i) What are the poles at the ends of the solenoid?
(ii) Describe what happens to the pointer.
(iii) Explain why this set-up can be used to measure current.
(iv) Give two disadvantages of using the set-up to measure current.
(v) Can the set-up still be used to measure current if the permanent magnet is replaced
by a soft iron bar? Why?
(b) Now a centre-zero galvanometer is connected to A and B and the magnet is set to
vibrate up and down. Describe the direction of the induced current, if any, passing
through the solenoid when
(i) the magnet is moving up,
(ii) the magnet is moving down,
(iii) the magnet is at its highest position.
40
Solution
Chapter 18
Electromagnetic Induction (Electromagnetic Induction)
1
(a) a.c.
(b)
(c) W = Fs
= (20 X 2 X 3.14 X 0.3)(150) = 5 625 J
(d)
E = mcT
= (0.2)(4200)(5) = 4200 J
Energy input
(e) Efficiency =
 100%
Energy input
4200
100%  74.3%
=
5625
(f) Add lubricating oil on the rotating axis.
2
(a) (i)
(ii)
(iii)
(iv)
(v)
(vi)
P = (110)(2kW)
= 220 kW
R = (2)(50)(0.1)
= 10 
P = IV
220 000 = I (220)
I = 1000 A
Power lost in the cables = I2R
= (1000)2(10)
= 10 M W
Power output from power station
= 220 000 + 107
= 1.022 x 107 W
voltage drop due to cables = IR
= (1000)(10)
= 10000 V
Voltage output from power station
= 220 + 10000 = 10220 V
220000
 100%
Efficiency =
1.022  10 7
= 2.15 %
41
(b) (i)
Np
NS

Vp
Vs
400 V AB

1
220
VAB  88000 V
(ii) From (a), current supplied to the village = 1000 A
N p Is

NS I p
400 1000

1
Ip
I p  2.5 A
The current passing through the cables is 2.5 A.
(iii) Power lost = I2R
= (2.5)2(10)
= 62.5 W
(iv) Power output from power station
= 220 000 + 62.5
= 220 062.5 W
Voltage drop due to the cables = I R
= (2.5)(10) = 25 V
VCD  88000  25 = 88 025 V
N p Vp

N S Vs
V power station
1

400
88025
V power station  220.0625 V
Voltage output from the power station is 220.0625 V.
220000
 100%
(v) Efficiency =
220062.5
= 99.97 %
(vi) No.
Energy is lost due to:
1. the resistance of the wires which dissipates heat energy,
2. the eddy current in the core,
3. the leakage of magnetic field, and
4. the magnetizing process of the core which uses energy.
3
(a) (i)
(ii)
(iii)
(iv)
(v)
Upper end: South Pole.
Lower end: North Pole.
The pointer moves to a higher position.
When a current passes through the solenoid from A to B, the solenoid becomes an
electromagnet which attracts the permanent magnet. The larger is the current, the
stronger is the electromagnet and the pointer moves to a higher point and vice versa.
Therefore, it can be used to measure current.
It is affected by the nearby magnetic field and by wind.
Yes. It is because soft iron can also be attracted by the electromagnet.
42
(b)
(i)
(ii)
(iii) There is no deflection because the magnet is momentarily at rest at its highest
position.
43
Chapter 19
Alpha, beta and gamma radiation
1
An experiment is carried out to investigate the kinds of radiation emitted by a radioactive
source S.
A G-M tube is placed at A, B, C and D in turn to obtain the count rates. The average
corrected count rate is recorded in Table 1.
Table 1
Which type(s) of radiations (,  and ) is/are emitted from the radioactive source S? Explain
briefly.
(5 marks)
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
44
2.
A radioactive source S is contained at the bottom of a lead container with a narrow passage.
The source emits radiation which passes through a weak magnetic field. A radiation detector R,
connected to a sealer, moves from M to N (Fig a).
Fig a
Fig b
Fig c
Figure b and c shows the variation of the count rate as R is moved from M to N when the
magnetic field is applied and not applied respectively. S is equidistant from M and N.
(a) What is the name of the radiation detector R?
(1 mark)
____________________________________________________________________________
(b) Why should the passage of the lead container be narrow?
(1 mark)
____________________________________________________________________________
(c) Explain briefly why the count rate is not zero even when the radiation detector R is far
away from M or N.
(1 mark)
____________________________________________________________________________
(d) What kind of radiation is detected by R? Explain briefly.
(2 marks)
____________________________________________________________________________
____________________________________________________________________________
____________________________________________________________________________
____________________________________________________________________________
45
Chapter 20 Radioactive decay and half-life
1
A radium-226 nucleus (Ra) has 88 protons and 138 neutrons. When it decays, it emits an alpha
particle and a gamma ray and changes to daughter nucleus X.
(a) Write down the equation for this decay.
________________________________________________________________________________
(b) It is known that the nucleus X will also emit an alpha particle and changes to another
nucleus Y. Write down the equation for this decay.
________________________________________________________________________________
2
Technetium-99m (Tc-99m) is the radioisotope commonly used in developing images of
internal body organs. The m indicates that it is unstable. It decays to Tc-99 in its stable state by
gamma decay. Tc-99m has a half-life of 6 hours and its atomic number is 43.
(a) Write down the equation for the decay of Tc-99m to Tc-99.
________________________________________________________________________________
(b) Explain briefly why Tc-99m is suitable for medical diagnosis.
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
3
In carbon dating, radioactive carbon-14 is decayed into nitrogen-14.
(a) Given that the atomic number of carbon and nitrogen is 6 and 7 respectively. What kind
of radiation (,  or ) will carbon-14 emit?
________________________________________________________________________________
(b) Write down the symbolic equation of the decay process.
________________________________________________________________________________
(c) Suggest a stopping material for the radiation in (a) to verify your result. Explain briefly.
________________________________________________________________________________
(d) Suggest an application of the radiation in (a).
________________________________________________________________________________
46
4
Radon-222 ( 222
86 Rn ), which its half-life is 3.8 days, is a radioactive substance. It emits an alpha
particle to become polonium-218 ( 218
84 Po ).
(a) Write down the equation for this decay.
________________________________________________________________________________
(b) Radon-220 ( 220
86 Rn ), which its half-life is just 55 seconds, is also radioactive. It will
decay to polonium-216 ( 216
84 Po ). Which type of radiation will radon-220 emit?
________________________________________________________________________________
(c) Write down the corresponding equation for the decay in (b).
________________________________________________________________________________
5
Iodine-131 is a radioactive substance with half-life equal to 8 days. It will emit beta radiation.
The number of proton in an iodine-131 nucleus is 53.
(a) Iodine-131 is radioactive, it emits a  particle to become daughter nucleus X. Write an
equation to represent the radioactive decay in iodine-131.
________________________________________________________________________________
(b) Give two reasons why we use iodine-131 as tracers in medical diagnosis.
________________________________________________________________________________
________________________________________________________________________________
(c) Explain why we do not use an alpha source as tracers in medical diagnosis.
________________________________________________________________________________
_______________________________________________________________________________
________________________________________________________________________________
6
A sample of radioactive substance is emitting  radiation with a half-life of 5 700 years. At
the beginning, the sample has 4 000 radioactive nuclei. How many radioactive nuclei are left
after 5 half-lives?
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
47
7
A sample of radioactive substance initially has an activity of 25 000 Bq. Three days later, the
activity drops to 3 125 Bq. Find the half-life of this sample.
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
8
Radon gas (Ra-222) is a source of background radiation, which is generated naturally. It has a
half-life of 3.8 days. At the beginning, there are 400 radioactive nuclei in a sample of radon
gas. How long does it take for the number of radioactive nuclei to decrease to 50?
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
48
Chapter 20 Radioactive decay
1
Figure 1 shows a radioactive decay series.
Figure 1
(a) State what particles are emitted at each stage in the decay process.
(2 marks)
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
(b) Which nuclide is greater in mass, B or C? Explain briefly.
(3 marks)
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
49
Chapter 21
1.
Nuclear Energy
Uranium-235 is used as a fuel in the chain reaction of nuclear reactors. The figure below
shows the process which involves in the chain reaction: a uranium-235 nucleus absorbs a
neutron before breaking in half and releasing more neutrons.
before
after
(a) What is the name of the process shown in the above figure?
(1 mark)
________________________________________________________________________________
(b) Why neutrons are better 'bullets' than protons in order to cause the reaction?
(2 marks)
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
(c) If the chain reaction is under control, the energy released can be used to generate
electricity. Suggest a way how the rate of reaction can be controlled.
(1 mark)
________________________________________________________________________________
________________________________________________________________________________
50
Answers
Chapter 19
Alpha, beta and gamma radiation
1.  and  radiation
2. (a) G.M. tube
(b) To obtain a narrow beam of radiation
(c) R receives background radiation
(d)  radiation
Chapter 20
Radioactive decay and half life
226
4
218
4
1. (a) 88 Ra  222
(b) 222
86 X  84Y  2 He
86 X  2 He  
2.
3.
4.
5.
6.
7.
8.
(a)
(a)
(b)
(c)
(d)
(a)
(b)
(c)
Tc *  99
43Tc  
99
43
 radiation
14
14
0
6 C  7 N  1 e
5 mm Aluminium
Carbon-14 dating
222
218
4
86 Rn  84 Po  2 He
radiation
220
216
4
86 Rn  84 Po  2 He
131
0
(a) 131
53 I  54 X  1 e
125
t½ = 1 day
11.4 days
Chapter 20
Radioactive decay
1. (a) A→ B:  particle
B→ C:  particle
C→ D:  particle
D→ E:  particle
(b) same
Chapter 21
Nuclear energy
1. (a) fission
(c) Control rods are used to absorb excess neutrons generated from the reaction to control the
rate of reaction.
51