06-07 CE Physics/Ch 15 Electrostatics
Chapter 15 Circuits and Domestic Electricity
電路和家居電學
15.1 Electric circuit
 Electric current
 Circuit diagram
15.2 Electrical energy and voltage
 Electrical energy transformation
 Voltage
15.3 Ohm’s law and resistance
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Ohm’s law 歐姆定律
Definition of resistance
Factors affecting the resistance of wire
Resistor and rheostat
15.4 Series and parallel circuits

Series circuit 串聯電路
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Parallel circuit 並聯電路
Effects of resistance of ammeter, voltmeter
and cell
15.5 Electrical power
 Heating effect of current
 Electrical power
15.6 Domestic electricity
 Power rating of electrical appliance
 Electrical energy
 Electric bill
 Domestic wiring and electrical safety
 Choice of power cable and fuse
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15.1 Electric circuit (p. 37)
1. Electric circuit (p. 38)
(a) An electric circuit is the conducting path in
which electric charges (carried by electrons)
flow through.
(b) In an electric circuit, a light bulb will shine
under two conditions:
(i) a power source
(ii) a closed circuit
(c) Open circuit: Fig. 15.2(a) (p. 38)
(i) A light bulb is connected to a battery (power
source) and a switch by connecting wires.
(ii) If the switch is open, the light bulb remains
unlit.
Reason:
As the electrons in the circuit move randomly,
no electric current is produced.
(d) Closed circuit: Fig. 15.2(b) (p. 38)
If the switch is closed, the light bulb lights up.
Reason:
As the electrons have a tendency to move in one
direction, an electric current is produced.
動，形成電流。
2. Electric current (p. 39) Fig. 15.3 (p. 39)
(a) An electric current is a flow of electric
charges.
Proof:
(i) The dome of a Van de Graaff generator is
connected to the earth socket through a
light-beam galvanometer 光束電流計.
(ii) Turn on the generator. The galvanometer
registers an electric current flowing between the
dome and the earth.
(b) Explanation: Fig. 15.4(a) (p. 39)
(i) In a closed circuit, negative electric charges,
which are carried by electrons, are “pushed”
from the negative terminal of the cell.
(ii) These electrons go through the circuit and
back to the positive terminal of the cell.
(iii)This flow of electric charges forms an
electric current.
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(c) Definition of electric current:
A measure of the rate of quantity of electric
charges flowing in a circuit.
(d) Mathematically:
Quantity of charge flow
Electric current =
Time taken
I= Q
t
Unit: Ampere (A)
(e) Example:
(i) 1 A = 1 C s1
(ii) A charge of 10 C flows through a point
in 2 s,
I = Q = 10 = 5 A
2
t
3. Conventional current 傳統電流(p. 39) Fig. 15.4(b) (p.
39)
(a) Conventional current flows from the positive
terminal of the cell to the negative terminal. It is
opposite to the direction of electrons flow.
(b) The wrong concept in the past:
The conduction of electricity was due to a flow
of positive charges from the positive terminal to
the negative terminal through the circuit.
(c) Reason why it is still in used: Fig. 15.5 (p. 40)
The flow of negative charges in one direction is
equivalent to that of positive charges in the
opposite direction.
4. Measuring electric current (p. 40)
(a) An electric current can be measured by:
Fig. 15.6 (p. 40)
(i) an ammeter
(ii) a milliammeter
(iii)a microammeter
(b) To measure the current passing through a light
bulb: Fig. 15.7 (p. 41)
An ammeter is connected in series with the light
bulb, with its positive terminal (in red colour)
connected close to the positive terminal of the
battery.
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(c) Typical currents in some electrical appliances.
Table 15.1 (p. 41)
5. Circuit diagram (p. 41) Table 15.2 (p. 42)
(a) (i) An electric circuit is the path along which
electric charges move.
(ii) It consists of a source of electrical energy,
connecting wires and one or more electrical
components.
(b) A circuit diagram is drawn to represent a real
circuit connection for convenience.
(c) Circuit symbols are drawn to represent the
electrical components.
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Class Practice 1 (p. 42)
15.2 Electrical energy and voltage (p. 43)
6. Electrical energy transformation (p. 43)
Activity 1 Lemon voltaic cell (p. 43)
(a) In a closed circuit, a light bulb lights up when
there are electric charges flowing through it.
(b) There seems to have a pump to “push” the
electric charges through the light bulb.
(c) Process of energy transformation:
Fig. 15.8 (p. 44)
(i) The driving force is supplied by a source of
electrical energy.
(ii) The electrical energy possessed by the
electric charges is converted into heat and light
when they pass through the light bulb.
(iii)The electric charges come back to the cells
and gain the electrical energy again.
(iv)The above transformation of energy is
repeated.
(d) Sources of electrical energy: Fig. 15.9 (p. 44)
(i) dry cells
(ii) batteries
7. Voltage (p. 44)
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(a) Definition:
The voltage (V ) across two points in a circuit is
the electrical energy converted into other forms
of energy per coulomb of charge passing the
points.
(b) Mathematically:
Energy converted into other
forms between two points
Voltage =
Charge through t he points
V= E
Q
Unit: volt (V)
(c) Example:
1 V = 1 J C1
8. Measuring voltage (p. 45)
(a) Voltage can be measured by: Fig. 15.10 (p. 45)
(i) a voltmeter
(ii) a millivoltmeter
(b) To measure the voltage across a light bulb:
Fig. 15.11 (p. 45)
A voltmeter is connected in parallel with the
light bulb.
(c) Multimeter: Fig. 15.12 (p. 45)
A device that can measure voltage, current and
resistance.
15.3 Ohm’s law and resistance (p. 46)
9. Experiments to show the Ohm’s law (p. 46)
Experiment 15B Ohm’s law (p. 46)
(a) Experimental procedures: Fig. 15.13(a) (p. 46)
(i) A low voltage power supply, rheostat,
resistance box and an ammeter are connected in
series.
(ii) Connect a voltmeter across the resistance
box.
(iii) Adjust the rheostat to obtain different sets
of readings of the voltmeter (V ) and the
ammeter (I ).
(b) Result and conclusion: Fig. 15.13(b) (p. 46)
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(i) The graph of V against I of the resistance
box is a straight line passing through the origin.
(ii) That is, V  I.
Experiment 15A Ohm’s law (data-logging) (p. 47)
(c) Experimental procedures: Fig. 15.14(a) (p. 47)
(i) Connect a resistance box to the interface.
(ii) The voltage across the resistance box is
changed to obtain different sets of voltage and
current.
(iii)The respective V - I graph of the resistance
box is shown by the computer.
(iv) Then replace the resistance box by a light
bulb and repeat the experiment.
(d) Result and conclusion: Fig. 15.14(b) (p. 47)
(i) The graph of V against I of the resistance
box is a straight line passing through the origin.
(ii) That is, V  I.
10. Ohm’s law (p. 48)
(a) Ohm’s law:
The voltage across a conductor is directly
proportional to the current passing through it,
provided that the temperature and other physical
conditions remain unchanged.
That is, V  I.
(b) The conductors that obey Ohm’s law are called
ohmic conductors.
11. Definition of resistance (p. 48)
(a) Definition:
The ratio V is defined as the resistance of the
I
conductor (R).
(b) Mathematically:
Resistance = Voltage across conductor
Current th rough conductor
V
R=
I
or V = IR
Unit: ohm () and 1  = 1 V A1
(c) For an ohmic conductor:
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Resistance of the conductor
= Slope of its V - I graph
(d) Resistance of a conductor is a measure of the
opposition to the current flowing through it.
For same voltage:
The wire with the highest resistance has the
smallest current flowing through.
Example 1 (p. 49), Class Practice 2 (p. 50)
12. Factors affecting the resistance of wire (p. 51)
The resistance of a wire is affected by its:
(i) dimension
(ii) temperature
(iii)material
13. Change of resistance with dimension of wire (p. 51)
Experiment 15C Factors affecting the resistance of a wire
A. Variation of resistance of a wire with its length (p. 51)
(a) Experimental procedures: Fig. 15.15 (p. 51)
(i) The resistances of eureka wires of different
lengths and thickness are measured by a
multimeter.
(ii) Measure the length () of a particular wire
and record the reading of the multimeter (R).
(iii)Vary the length of the wire by changing the
position of the clamp and record the respective
resistances.
(b) Result and conclusion: Fig. 15.16 (p. 51)
(i) The graph of R against  of the wire is a
straight line passing through the origin.
(ii) That is, R  .
Experiment 15C Factors affecting the resistance of a wire
B. Variation of resistance of a wire with its thickness (p. 52)
(c) Experimental procedures: Fig. 15.15 (p. 51)
(i) Record the resistances of eureka wires of
different thickness.
(ii) Keep the length of the wire unchanged in
each case for comparison.
(d) Result and conclusion:
(i) The resistance of a uniform wire (R) is
inversely proportional to its cross-sectional area
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(A).
(ii) That is, R  1 .
A
(iii)A longer wire or a thinner wire (smaller
cross-sectional area) has a greater resistance.
14. Change of resistance with temperature (p. 52)
(a) Experimental procedures: Fig. 15.17 (p. 52)
(i) Connect a light bulb in series with a power
supply, an ammeter and a switch. Also, connect
a voltmeter across the bulb.
(ii) Increase the voltage to obtain different sets
of voltage and current.
(iii)Plot the graph V against I of the filament
wire.
(b) Result and conclusion: Fig. 15.18 (p. 53)
(i) When the current is small, the resistance of
the filament wire remains unchanged.
(ii) When the current is large, the resistance
increases.
(c) Explanation:
(i) At low current, the temperature of the
filament wire is low (~30C).
(ii) At high current, the temperature of the
filament wire is high (~2 000C).
(d) Reason:
(i) As the temperature increases, the atoms of
the conductor vibrate more violently and hinder
the motion of the electrons.
(ii) The electrons are the charge carriers of the
conductor. Therefore, the resistance increases.
15. Material of wire (p. 53)
The resistance of a wire depends on the
composite material.
(a) With small resistance:
Example:
Copper and other materials with loosely held
electrons which allow an electric current to flow
easily.
(b) With high resistance:
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Example:
Silicon and other materials with tightly bound
electrons.
(c) Table 15.3 shows the resistance of a 1 m long
wire with diameter of 2 mm at 20 C made of
different materials. Table 15.3 (p. 54)
16. Resistor 電阻器 and rheostat 變阻器 (p. 54)
(a) Resistors are the basic components in a circuit
because they can change the currents flowing in
the circuit.
(b) Resistor with fixed resistance values:
Fig. 15.19(a) (p. 54)
(i) Made of thin layers of carbon or coiled
conducting wires.
(ii) Give fixed resistance values.
(c) Rheostat: Fig. 15.19(b), (c) (p. 54)
(i) Adjust the resistance of a circuit in order to
change the current and voltage.
(ii) Common types:
The sliding type and the rotary type
(iii)Potential divider: Fig. 15.20 (p. 55)
A rheostat using for adjusting the voltage across
a component.
15.4 Series and parallel circuits (p. 55)
17. Series circuit (p. 56)
(a) A series circuit is one that connects electrical
devices one by one, forming a single loop.
Fig. 15.22 (p. 56)
(b) For two resistors X and Y connected in series:
(i) Since there is only one path, the currents
passing through X and Y are the same.
(ii) The sum of the electrical energy dissipated
in X (E1) and Y (E2) is equal to the total
electrical energy supplied by the cell (E).
i.e., E = E1 + E2
E = E1 + E2
Q
Q
Q
(iii)The amount of charges (Q) passing through
the circuit is the same at any points.
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By V = E ,
Q
V = V1 + V2
18. Resistance in series circuit (p. 57)
(a) When more than one resistors are connected in
series, the equivalent resistance is related by:
R = R1 + R2 + R3 + R4 + …
(b) The equivalent resistance of resistors is always
larger than any individual resistance.
19. Drawback of series circuit (p. 58)
Fig. 15.23, Fig. 15.24 (p. 58)
The drawback:
Consider several light bulbs connected in series:
(i) When one of them burns out, it causes a
breakdown of the whole circuit.
(ii) Other bulbs also go out because no current
can flow.
(iii)The series connection is seldom used for
domestic wiring.
20. Parallel circuit (p. 58)
(a) A parallel circuit is one that splits into two or
more branches with connected electrical
components.
Fig. 15.25 (p. 58)
(b) For two resistors X and Y connected in parallel:
(i) The current passing through the cell is equal
to the sum of the currents in the branches.
(ii) Since they are connected across the cell, the
voltage across each resistor is equal to the
voltage of the cell.
21. Resistance in parallel circuit (p. 59)
(a) When more than one resistors are connected in
parallel, the equivalent resistance is related by:
1 = 1 + 1 + 1 + 1 + ...
R1
R2
R3
R4
R
(b) The equivalent resistance of resistors is always
less than any individual resistance.
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22. Advantage of parallel circuit (p. 60) Fig. 15.26 (p. 60)
Consider several light bulbs connected in
parallel:
(i) There are different loops that provide
separate branches for the current to flow.
(ii) The failure of one light bulb does not affect
the others and each light bulb can be switched
on and off independently.
(iii)The parallel connection is often used for
domestic wiring.
Example 2 (p. 60), Example 3, Class Practice 3 (p. 61),
Class Practice 4 (p. 62)
23. Effects of resistance of ammeter (p. 64)
Fig. 15.27 (p. 64)
Consider an ammeter acts as a few ohm resistor
(RA) connected in series with two resistors R1
and R2.
(a) Small resistance circuit (R1 = 0.1 ):
(i) Total resistance = R1 + RA
(ii) Since R1 is comparable to RA, the total
resistance is increased.
(iii)The current passing through and the voltage
across the resistor decrease.
(b) Large resistance circuit (R2 = 1 k):
(i) Total resistance = R2 + RA
(ii) Since R2 is much larger than RA, the total
resistance has no significant changes in
comparison with that in the circuit without the
ammeter.
(iii)The current passing through R2 and the
voltage across it are roughly equal to that
without the ammeter.
(c) Conclusion:
(i) The resistance of an ammeter greatly affects
the current and voltage in a small resistance
circuit.
(ii) It has a small effect on those in a large
resistance circuit.
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24. Effects of resistance of voltmeter (p. 65)
Fig. 15.28 (p. 65)
Consider a voltmeter acts as a few hundred ohm
resistor (RV , current = IV) connected in parallel
with R1 and R2 of current I1 and I2 respectively.
(a) Small resistance circuit (R1 = 0.1 ):
(i) Total current = I1 + IV
(ii) Since RV is much larger than R1, the total
current flowing in the circuit is roughly equal to
that without the voltmeter.
(b) Large resistance circuit (R2 = 1 k):
(i) Total current = I2 + IV
(ii) Since R2 is comparable to RV, the total
current flowing in the circuit increases in
comparison with that without the voltmeter.
(c) Conclusion:
(i) The resistance of a voltmeter greatly affects
the total current flowing in a large resistance
circuit.
(ii) It has a small effect on those in a small
resistance circuit.
25. Effect of resistance of cell (p. 66) Fig. 15.29 (p. 66)
(a) (i) The resistance of a cell is called internal
resistance (r ).
(ii) It is about a few ohms.
(iii)It acts as a resistor connected in series with
the resistors as the case of ammeter.
(b) Voltage of the cell = I (R + r)
(c) Conclusion:
(i) The internal resistance of the cell greatly
affects the current and voltage in a small
resistance circuit.
(ii) It has a small effect on them in a large
resistance circuit.
15.5 Electrical power (p. 66)
26. Heating effect of current (p. 67) Fig. 15.30 (p. 67)
When a current passes through a conductor, its
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temperature increases.
Reason:
(i) When charges flow through the wire, they
lose some energy to the atoms in the wire due to
collisions.
(ii) The atoms vibrate more vigorously and the
wire heats up.
(iii)The electrical energy is changed to heat.
27. Electrical power (p.67)
(a) Definition:
Electrical power is defined as the rate of
electrical energy transferred of electrical
components.
(b) Mathematically:
Electrical power =
Electrical energy tra nsferred
Time taken
E
P=
t
Unit: watt (W) and 1 W = 1 J s1
(c) The power can be calculated by:
Fig. 15.31 (p. 68)
(i) P = VI
(ii) P = I2R
(iii)P =
V2
R
15.6 Domestic electricity (p. 69)
28. Power rating of electrical appliance (p. 69)
Activity 2 Power rating of electrical appliance (p. 69)
A fan heater has a rated value of
“220 V, 2 000 W”.
Fig. 15.32 (p. 69)
Meaning:
When it works at a voltage of 220 V, it
consumes electrical power of 2 000 W.
Class Practice 5 (p. 69)
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29. Electrical energy (p. 70)
(a) For an electrical appliance of power (P ), the
electrical energy consumed by it after switching
on for a certain time (t) is:
(i) E = Pt
(ii) E = VIt
(iii)E = I2Rt
(iv)E =
V2
t
R
(b) Measuring devices:
(i) a joulemeter or
(ii) a kilowatt-hour meter (kW h meter)
Fig. 15.33 (p. 70)
(c) Unit: kilowatt-hour (kW h)
(d) Example:
When an electrical appliance of power of 1 kW
is switched on for 1 hour, the electrical energy
consumed by it is 1 kW h.
30. Electrical energy and electrical power (p. 70)
Experiment 15D Electrical energy and electrical power
(p. 70)
(a) Experimental procedures: Fig. 15.34 (p. 71)
(i) Connect a hair dryer to a kW h meter and
turn it on for a time interval (t), which is
recorded with a stop watch.
(ii) The initial (Ei) and the final (Ef) readings of
the kW h meter are recorded.
(b) Result and conclusion:
(i) Electrical energy consumed by the hair dryer
= Ef  Ei
(ii) The power rating is:
P=
E f  Ei
t
where t is measured in hour.
31. Electric bill (p. 71)
Cost of electricity
= Total unit of electricity consumed (kW h)
 Cost of 1 unit of electricity
Example 4 (p. 71), Class Practice 6 (p. 72)
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32. Electricity supply (p. 73)
There are two common types of electricity
supply:
(a) Direct current (d.c.): Fig. 15.35(a) (p. 73)
Batteries provide steady d.c. voltage.
(b) Alternating current (a.c.): Fig. 15.35(b) (p. 73)
(i) Household appliances are run by the mains
supply that provides a.c. voltage.
(ii) The mains supply in Hong Kong is 220 V,
50 Hz.
33. Cable (p. 73)
(a) Electricity is generated in power stations and is
supplied to households through cables.
(b) Live wire (L) and neutral wire (N) inside each
cable are responsible for the conduction of
electricity. Fig. 15.36 (p. 73)
(c) The neutral wire:
(i) Connected to the earth at the local substation
and there is no voltage difference between them.
(ii) When a person touches the neutral wire
accidentally, the body does not get an electric
shock.
(iii)It would be dangerous touching the live wire
which is either at a positive or negative voltage
with respect to the earth.
(d) Fig. 15.37 show the directions of the flowing of
a.c. in live and neutral wires. Fig. 15.37 (p. 74)
Activity 3 You were an electrician (p. 74)
34. Domestic wiring (p. 75) Fig. 15.38 (p. 75)
(a) Typical domestic wiring circuit:
(i) Electricity is supplied from the power
station to the household through the incoming
cable, with L and N.
(ii) The cable is connected to the kW h meter
and then to the consumer unit (fuse box).
(iii)The mains supply is connected to all the
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circuits in the house through different fuses.
(iv)Each circuit starts at the fuse and ends at the
neutral wire.
(b) Lighting circuit :
It is connected to the ceiling lamps. Light bulbs
can be connected in parallel.
Reason:
(i) All the bulbs can be operated at the rated
voltage of 220 V.
(ii) If one bulb blows, the others can still work.
(c) Ring circuit:
With the ring circuit, the current from the
consumer unit can flow to the sockets through
two paths:
Reason:
(i) Thinner cables can be used to deliver the
current.
(ii) If there is a fault in one path, the current can
still pass to the socket through another path.
35. Safety wiring of domestic electricity (p. 76)
Activity 4 3-pin plug and 2-pin plug (p. 76),
Class Practice 7 (p. 78)
Apart from fires, electricity can cause serious
injuries.
Fig. 15.39 (p. 77)
Safety wiring of an electric iron:
Fig. 15.40 (p. 79)
(a) Main switch:
Installed at the live wire.
Reason:
Ensure that no part of the iron is at a high
voltage when the switch is open.
(b) Fuse: Fig. 15.41 (p. 79)
(i) It is a short metal wire of low melting point
and negligible resistance.
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(ii) It is installed at the live wire.
Reason:
Prevent the appliance from getting excessive
current.
(c) Earth wire:
(i) It is connected to the metal case of the iron.
Normally, no current flows through it.
(ii) When a fault occurs:
e.g. The live wire touches the metal case.
Fig. 15.42(a) (p. 80)
The case is at a high voltage. A large current
can flow to the ground through the earth wire
and the fuse is blown.
(iii)If no earth wire is installed:
Fig. 15.42(b) (p. 80)
The large current flows through the body of the
person who touches the metal case. He may get
a fatal electric shock.
Example 5 (p. 80)
36. Safety precautions of using electrical appliances
(p. 81) Fig. 15.43 (p. 81)
(a) Do not overload a socket by inserting too many
plugs into it.
(b) Make sure leads are not worn, cut or shown bare
wire at any point. Do not join extra wire to make
leads longer.
(c) Do not turn on or off an electrical appliance
when your hands are wet.
(d) Pull out plugs before changing a fuse, repairing
an appliance, filling an electric kettle or giving
first aid to a person who had gotten an electric
shock.
(e) Do not run extension leads into a bathroom.
(f) Do not poke anything into sockets or appliances.
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(g) Make sure the appliance used is correctly wired
and its fuse is of a suitable fuse value.
(h) Do not remove the earth wire and the fuse from
an appliance.
37. Choice of power cable (p. 82)
(a) Operating current of an electrical appliance is
the current flowing through it when it is
working.
Example:
Consider a fan heater of a rated value of
“200 V, 2 000 W”.
Operating current (I) = P = 2000 = 9.1 A
V
220
(b) The larger the operating current, the thicker the
power cable is used. Fig. 15.44 (p. 82)
Reason:
(i) If thin power cables (high resistance) are
used for high operating current electrical
appliances, the power loss is great ( P = I2R).
(ii) The cables become very hot because of the
heating effect of the current. The insulation that
isolates the wires may be melted.
(iii) The wires may touch each other to form a
short circuit and cause an electric leakage.
38. Choice of fuse (p. 83) Fig. 15.45 (p. 83)
(a) A fuse is installed at the live wire of an
electrical appliance.
Reason:
When a fault occurs, the current is larger than
the fuse rating. The fuse melts and breaks the
circuit before the appliance could cause any fire
and electrocute.
(b) Fuse rating:
(i) Marked on each fuse.
(ii) Shows the maximum current that can flow
through the fuse.
(c) A fuse of value slightly higher than the
operating current of the appliance should be
installed.
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Example:
For the 11 A operating current of an electric
water heater, a 13 A fuse should be installed.
(d) The figures show the power, operating current
and suitable fuse for different appliances. (p. 83)
Example 6 (p. 84)
STS Corner 1 Electric car (p. 85)
STS Corner 2 Applications of circuit (p. 86)
STS Corner 3 Electricity today (p. 87)
STS Corner 4 A brief history of electricity (p. 88)
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