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UNIT 17
CURRENT ELECTRICITY
Compiled by: Hussain Ahmad Madni Uppal (O, A level teacher)
Contents of this chapter in relation to syllabus 5054.

19. Current Electricity

Content
19.1 Current
19.2 Electromotive force
19.3 Potential difference
19.4 Resistance

Learning outcomes

Candidates should be able to:

(a) state that a current is a flow of charge and that current is measured in amperes.
(b) recall and use the equation charge = current × time.
(c) describe the use of an ammeter with different ranges.
(d) explain that electromotive force (e.m.f. ) is measured by the energy dissipated by a source in
driving a unit charge around a complete circuit.
(e) state that e.m.f. is work done/charge.
(f) state that the volt is given by J / C.
(g) calculate the total e.m.f. where several sources are arranged in series and discuss how this is
used in the design of batteries.
(h) discuss the advantage of making a battery from several equal voltage sources of e.m. f. arranged
in parallel.
(i) state that the potential difference (p.d.) across a circuit component is measured in volts.
(j) state that the p.d. across a component in a circuit is given by the work done in the
component/charge passed through the component.
(k ) describe the use of a voltmeter with different ranges.
(l) state that resistance = p.d./current and use the equation resistance = voltage/current in
calculations.
(m) describe an experiment to measure the resistance of a metallic conductor using a voltmeter and
an ammeter and make the necessary calculations.
(n) state Ohm’s Law and discuss the temperat ure limitation on Ohm’s Law.
(o) *use quantitatively the proportionality bet ween resistance and the length and the cross -sectional
area of a wire.
(p) calculate the net effect of a number of resistors in series and in parallel.
(q) describe the effect of temperat ure increase on the resistance of a resistor and a filament lamp
and draw the respective sketch graphs of current/ voltage.
(r) describe the operation of a light -dependent resistor.

What is electric current?

When electrons move, we say that an electric current is produced. An electric current is formed
by moving electrons.
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Conventional Current and electron flow

Figure 17.1 shows the difference between conventional current and electron flow.

 Before the discovery of electrons, scientists believed

that the electric current is caused by moving positive
charges
 Although this belief was later proven wrong, the idea is
still widely held, because the discovery of electron flow
did not effect the basic understanding of electric current,
which is the movement of charges.
 This movement of positive charges is called
conventional current.
 An electric current is actually caused by the flow of
electrons from a negatively charged terminal to a
positively charged terminal.
 This is because of the electrons are repelled by Figure 17.1 Conventional current
negatively-charged terminal and attracted to the versus electron flow
positively charged terminal.
 This movement is known as electron flow.

Note:
In O level course, current refers to conventional current, unless otherwise stated
Past paper question (June 96)
The lower part of the cloud has a positive charge. The cloud discharges in a flash of lightening.

In which direction do electrons and conventional current flow?

Electron flow Conventional current

A. Downwards downwards
B. Downwards upwards
C. Upwards downwards
D. Upwards upwards

Ans wer: C
Explanation Electrons flow from the house towards the cloud. Conventional current is
in the opposite direction to electron flow.
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Exam tip Conventional current and electron flow are always in opposite direction.
Conventional current is from positive terminal to negative terminal of the
battery (power supply).

How do we measure electric current?

Since electric current consist of moving electric charges, we measure electric current by
determining the amount of electric charge that passes through a conductor per unit time.

 An electric current I is the rate of flow of electric charge Q.

In Symbols,
I = Q/t
Where
I = current (in A);
Q = charge (in C);
t = time taken (in s).

The SI unit of electric current is the ampere (A). One ampere is the electric current produced
when one coulomb of charge passes a point in a conductor in one second.

An instrument called the ammeter (Figure 17.2) is used to measure the strength of an electric
current in an electric current.
 The ammeter should be connected in series to the rest of the circuit (Figure 17.3).
 The current should flow into the ammeter through the ‘+’ or red terminal and leave
through the negative ‘-’ or black terminal.

Figure 17.2 An analogue

ammeter Figure 17.3 An ammeter connected in series to measure the current I

Worked Example 17.1

The current in a lamp is 0.2 A. If the lamp is switched on for two hours, what is the total electric
charge that passes through the lamp?

Solution
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Given: current I = 0.2 A

60 𝑚𝑖𝑛 60 𝑠
Time t = 2h × 1ℎ × 1 𝑚𝑖𝑛

= 7200 s
Total electric charge Q = It
= (0.2 A)(7200 s) = 1440 C = 1.4 × 103 C

Drawing circuit diagrams

To help us solve problems involving electric circuits, it is useful to learn how to draw circuit
diagrams such as the one shown in Figure 17.3(b). Circuit diagrams represent electric circuits.

Figure 17.4 shows the four main components of an electric circuit.

Figure 17.4 Main components of an electric circuit

Table 17.1 shows the circuit symbols for some other common electric components.

Table 17.1 Circuit symbols

Symbols Device Symbol Device Symbol Device

Switch wires joined galvanometer

Cell wires crossed ammeter

Battery fixed resistor voltmeter

d.c power Variable Two-way

supply resistor switch
(rheostat)
a.c power Earth
supply Fuse connector
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Light bulb coil of wire Capacitor

Potentiometer Transformer Thermistor

Light Semi
dependent conductor Bell
resistor (LDR) diode

Interpreting circuit diagrams

It is important to be able to understand different arrangements of circuit symbols in circuit
diagrams. Figure 17.5 and 17.6 show how we can interpret two circuit diagrams.

Open Circuit and Short Circuit

Figure 17.5 An open circuit Figure 17.6 A short circuit

 The bulb is unable to light up as the  The circuit is closed, yet the bulb remains
switch is open, i.e. there is a break in the unlit. This is because there is an
circuit. alternative path of negligible resistance
 A break in the circuit means that current (wire X) for current to flow through.
cannot flow through it.  Therefore, the current does not flow
 Besides open switches, breaks in circuits through the bulb.
can occur due to loose connections, or  We call this a short circuit.
missing or broken wires.
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Figure 17.7 Another short circuit diagram

Note:
Short circuit does not mean ‘short’ in terms of length, short circuit means very low resistive
path for the circuit to complete so that current does not flow through the load. Its flows
through the low resistive path instead.

Understanding the use of a two-way switch

Figure 17.8 If both the switches are up – or down Figure 17.9 But if one switch is up and other is
– the circuit is complete and a current flows down, the circuit is open. Each switch reverses the
through the bulb effect of the other one

Electromotive Force and Potential Difference

The volt is the unit of measurement for the electrical properties electromotive force (e.m.f) and
potential difference (p.d). The e.m.f and p.d. cause the charges in a current to move.

What is electromotive force?

Consider the flow of water in a pipe (Figure 17.10)
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Figure 17.10 Water in a pipe

 Water does not flow through the pipe on its own.

 If a water pump is added the pressure difference it generates will make the water
move around the pipe.

Similar to how a pump is needed to make water flow around the pipe, an electrical energy source
is needed to move electric charges around a circuit. The ‘pumping’ action of the electrical energy
source is made possible by the electromotive force (e.m.f).

 The electromotive force (e.m.f.) ɛ of an electrical energy source is the work done by
the source in driving a unit charge around a complete circuit.

In symbols,
Where,
𝐖 ɛ = e.m.f. of an electrical energy source (in V);
ɛ=
𝑸 W = Work done, i.e. amount of non-electrical energy converted to electrical
energy (in J);
Q = amount of charge (in C).

The SI unit of e.m.f. is the joule per coulomb (J 𝑪−𝟏) or Volt (V). The e.m.f. of an electrical
energy source is one volt if joule of work is done by the source of drive one coulomb of charge
completely around a circuit.
There are many types of electrical energy sources. A common electrical energy source is the dry
cell. In a circuit diagram, the dry cell is represented by the symbol + - . Notice that a dry cell
has both a positive terminal and a negative terminal.

How does cell arrangement affects e.m.f.?

Most battery operated appliances use more than one dry cell. The number of dry cells and how
they are arranged determine the amount of e.m.f. supplies to an appliances. Dry cells can be
arranged in series or in parallel. Figure 17.11 shows how the arrangement of cells affects the
resultant e.m.f.

Circuit A Circuit B
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When cells are arranged in ….

Series Parallel

The effect is that …

 The resultant e.m.f. is larger than the  The resultant e.m.f. is equal to that of
e.m.f of each cell. a single cell.
 Resultant e.m.f. = 1.5V + 1.5V = 3.0V  Resultant e.m.f. = 1.5V
 The cells last for a shorter time  The cells last for a longer time
compared to those in circuit B. compared to those in a Circuit A

This is because…

 The charges gain energy as they pass  The charges gain only a portion of the
through each cell. energy from each cell

Figure 17.11 How cell arrangement affects resultant e.m.f.

 When cells are arranged in series, the resultant e.m.f. is the sum of all the e.m.f. of
the cells.

 When cells of equal e.m.f. are arranged in parallel, the resultant e.m.f. is equal to
that of a single cell.

More on Cell arrangements

Here, a mistake has occurred.

These cells are connected in One of the cells is wrong way
series. The total e.m.f. is the sum around, so it cancels out one of
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of the individual e.m.f. the others The PD across parallel cells is

only the same as from one cell.
But together, the cells can deliver
a higher current.

Note:
Cells in series should be connected properly, i.e. positive terminal of one cell to the negative terminal
of the other so that their e.m.fs gets added up. If positive terminal of one cell is connected with the
positive terminal of the other, or the negative terminal of one cell is connected to the negative
terminal of the other, they will cancel each other out. Refer to the figures above.

What is potential difference?

When a dry cell is connected to a light bulb, the bulb converts the electrical energy provided by
the dry cell to light and thermal energy. For each coulomb of charge passing through the light
bulb, the amount of electrical energy converted to another form of energy is called the potential
difference (p.d.).

 The potential difference (p.d.) across a component in an electric circuit is the work
done to drive a unit charge through the component.

In symbols,
Where,
𝐖 V = potential difference or voltage across a component (in V);
𝑽= W = work done, i.e. amount of electrical energy converted to other forms (in J);
𝑸
Q = amount of charge (in C).

The SI unit of p.d. or voltage is the same as that for e.m.f. – the volt (V). The p.d. or voltage
across a component is one volt if one joule of work is done to drive a unit charge through it.

How do we measure e.m.f. and p.d.?

An instrument called the voltmeter (Figure 17.12) is used to measure the
(a) e.m.f. of a dry cell
The positive and negative terminal of the voltmeter must be connected to the positive and
negative terminals of the dry cell respectively.
(b) P.d. across a component (e.g. a bulb)
The voltmeter must be connected in parallel with the component (Figure 17.13).
A multimeter (Figure 17.12 (b)) is an instrument that can measure voltage (p.d.), current or
resistance, we will learn that resistance is in section 17.3.

When a voltmeter is used to measure e.m.f. or p.d., the positive ‘+’ or red terminal of the
voltmeter should be connected to the positive ‘+’ terminal of the cell, and the negative ‘-‘ or
black terminal of the voltmeter should be connected to the negative ‘-‘ terminal of the cell.
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a) An analogue voltmeter b) A multimeter

Figure 17.12 Different types of instruments that measure potential difference

Figure 17.13 A voltmeter connected in parallel to measure the p.d. ‘V’ across the bulb

Worked example 17.2

The e.m.f. of a dry cell is 1.5V. What is the energy provided by the cell to drive 0.4C of charge
around a circuit?

Solution
Given: e.m.f. ɛ = 1.5V
Charge Q = 0.4 C

𝐖
Using ɛ = 𝑸 , where W = energy provided by the cell,

W = ɛQ
= (1.5 V)( 0.4 C)
= 0.6 J

Worked example 17.3

A charge of 4.00 × 104 C flows through an electric heater. If the amount of electrical energy
converted into thermal energy is 9.00 MJ, calculate the potential difference across the end of the
heater.

Solution
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Given: charge Q = 4.00 × 104 C

energy W = 9.00 × 106 J
by definition,
𝐖
potential difference 𝑽 = 𝑸

9.00 × 106 J
= 4.00 × 104 C

= 225 V

Table 17.2 summarizes some devices and their roles, i.e. e.m.f or p.d

Past paper question (Nov 2000)

Why can birds stand on an overhead transmission line without suffering any harm?

A. Their bodies have a very high resistance

B. Their feet are very good insulators
C. There is no potential difference between their feet
D. The spaces between their feathers act as insulators

Ans wer: C
Explanation The two feet are at the same potential.

Exam tip if there is no potential difference, no current flows between the two points.

17.3 Resistance
What is resistance?
The resistance of a component is a measure of the opposition an electric current experiences
when it flows through the component.
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 The resistance R of a component is the ratio of the potential difference V across it

to the current I flowing through it.

In symbols,
Where,
𝐕 R = resistance of the components (in Ω);
𝑹= V = p.d. across the component (in V);
𝑰
I = current flowing through the component (in A).

From the definition of resistance, we can see that for a given p.d., the higher the resistance, the
smaller the current passing through.
The SI unit of resistance is the ohm (Ω). One ohm is the resistance of the component when a potential
difference of one volt applied across the component drives a current of one ampere through it.

Worked Example 17.4

A potential difference of 240V applied across the heating coil of an electric kettle drives a
current of 8 A through the coil. Calculate the
(a) Resistance of the coil;
(b) New current flowing through the coil if the potential difference applied is changed to 220
V.
Solution
(a) Given: voltage V = 240 V
Current I = 8 A
𝐕 𝟐𝟒𝟎 𝐕
By definition, 𝑹 = = = 30 Ω
𝑰 𝟖𝑨

(b) Given: voltage V = 220 V

From (a), resistance R is 30 Ω.
𝐕 𝟐𝟐𝟎 𝐕
Thus, 𝑰 = 𝑹 = 𝟑𝟎 Ω = 7.3 A

What are resistors?

A resistor is a conductor in a circuit that is used to control the size of the current flowing in a
circuit. Resistors can have resistances that range from a few ohms to several millions of ohms.
There are two types of resistors Fixed resistors and variable resistors (Figure 17.14).

Resistors

Fixed resistors Variable resistors

A fixed resistor has a resistance of A variable resistor has a resistance

fixed value. Common types of fixed that can be varied. It is used to vary
resistors include carbon film resisters the amount of current flowing in a
and wire wound resistors. circuit
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Figure 17.14 Types of resistors

How a variable resistor works

Figure 17.15 shows how a variable resistor works. By moving the slider along the metal rod, the
length of wire through which current flows can be varied. In turn, the resistance can be varied.

Figure 17.15 Working principle of a variable resistor

How do we measure resistance?

Circuit components other than resistors also have resistance. We can measure their resistances by
measuring the current flowing through them and the p.d. across them. Figure 17.16 shows a
current I flowing through a lamp and a potential difference V across it. With these two quantities,
V
we can apply the formula 𝑅 = to calculate the resistance of the lamp.
𝐼

Figure17.16 Circuit to determine the resistance of a lamp

Investigation 17.1 describes how an ammeter and a voltmeter can be used to determine the
resistance R of an unknown resistor.
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Ohm’s Law
In 1826, German physicist George Ohm discovered that when physical conditions (such as
temperature) are constant, the electric current in a metallic conductor is directly proportional to
the potential difference across it. This relationship is known as Ohm’s Law.

 Ohm’s Law states that a curre nt passing through a metallic conductor is directly
proportional to the potential diffe rence across it, provided that physical conditions
(such as tempe rature re main constant.

In symbols,

𝐼 ∝ 𝑉 where,
I = current (in A);
V = potential difference (in V).

𝑉
= R = constant
𝐼

Thus, according to Ohm’s Law, the resistance of metallic conductors remains constant under
steady physical conditions.

Ohmic conductors
Conductor that obey Ohm’s Law are known as Ohmic conductors. Figure 17.17 shows that
characteristics I-V graph of an ohmic conductor at a constant temperature.

The graph
 Is a straight line that passes
through the origin.
 Has a constant gradient that is
equal to inverse of the
resistance ‘R’ of the conductor.
1
Note: since 𝑅 is a constant, 𝑅 =
constant.
Figure17.17 Characteristic I-V graph of an Ohmic conductor
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Investigation 17.1
Objective
To determine the resistance of an ohmic resistor (which has how
resistance) using a voltmeter and an ammeter
Apparatus
Voltmeter, ammeter, rheostat, two 2 V dry cells, resistor R of
unknown resistance

Figure 17.18 Circuit setup to

determine resistance

Procedure
1. Set up the apparatus according to the circuit diagram in figure 17.18.
2. As a safety precaution, adjust the rheostat to the maximum resistance. This is so that the
initial current that flows in the circuit is small, to minimize the heating effect of the
circuit.
3. Record the ammeter reading I and the voltmeter reading V.
4. Adjust the rheostat to allow a large current to flow in the circuit. Again record the values
of I and V.
5. Repeat step 4 for at least five sets of I and V readings.
6. Plot V/V against I/A. Determine the gradient of the graph.

Results and Discussion

The gradient of the graph gives the resistance of the resistor R
(Figure 17.19). Note that the resistance of the conductor can
be found using the gradient of the graph only if it is ohmic
(i.e. it has a constant resistance).

Figure 17.19 Graph of V against I

Non-Ohmic conductors
Conductors that do not obey ohm’s Law are known as non-ohmic conductors. The current
flowing through non-ohmic conductors does not increase proportionally with the potential
difference. In other words, the resistance R of such conductors vary.
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We can differentiate between ohmic and non-ohmic conductors using their I-V graphs of non-
𝑉
ohmic conductors are not straight lines. The ratio is not a constant resistance. Table 17.3 shows
𝐼
the characteristics curved I-V graphs of non-ohmic conductors.

Table 17.3 Characteristics I-V graphs of some non-ohmic conductors

Non-ohmic Fraction I-V graph Description of graph
conductors
Filament l amp The filament lamp (or  As the current increases, the
the light bulb) devices generate more heat,
converts electrical and thus their temperatures
energy to light and increase.
heat energy.  As temperature increases, the
resistance of the filament
lamp increases.
 The I-V graph of the filament
lamp shows that the resistance
𝑉
( ) increases with the
𝐼
temperature.
Semiconductor A semiconductor  The I-V graph of a
di ode diode is a device that semiconductor diode shows
allo ws current to flow that when a p.d. is applied in
in one direction only the forward d irection, the
(the forward current flo w is relat ively
direction). large. Th is means the
resistance is low in the
forward direct ion.
 When the p.d. is applied in the
reverse direction, there is
almost no current flow. This
means the resistance is very
high in the reverse direction.

Figure 17.21 I-V characteristic of a thermistor

Figure 17.20 I-V characteristic of Ohmic

conductor

 The resistance of the metallic conductor, ohmic or mon-ohmic (e.g. filame nt lamp),
generally increases with increasing te mperature.
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We will learn more about the other factors that affect the resistance of metallic conductors in
Section 17.4.

Worked Example 17.5

Figure 17.22 shows how the current I in the filament of a
lamp depends on the potential difference V across it.
(a) Calculate the resistance of the filament when the
potential difference is 1.0 V.
(b) Describe how the resistance of the filament
changes, if at all, when the p.d across it increases.

Figure 17.22
Solution
(a) From the graph, when V = 1.0 V, I = 0.16 A
By definition,
𝑉 1.0 𝑉
Resistance R = 𝐼 = 0.16 𝐴 = 6.25 Ω = 6.3 Ω
𝑉
(b) The gradient of the graph decreases as the p.d. increases. This means that the ratio 𝐼 ,
which is the resistance R of the filament, increases when p.d. across it increases.

17.4 Resistivity
According to Ohm’s Law, the resistance R of a metallic conductor is a constant if the physical
conditions remain the same. However, if temperature increases, the resistance of the metallic
conductor will also increase.

Besides temperature, the resistance R of a conductor also depends on

1. Its length l;
2. Its cross-sectional area A (or thickness);
3. The type of material it is made of.

Table 17.4 shows the relationship between resistance and the cross-sectional area and length of a
wire.

Table 17.4 Relationship between resistance and the cross-sectional area and length of a wire.
Relationship between resistance and cross- Relationship between resistance and length
sectional area
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 Wire P and Q have the same length and are  Wire S and T have the same cross-sectional
made up of the same material. area and are made of the same material.
 The cross-sectional area of wire P is larger  Wire S is longer than wire T.
than that of the wire Q.
Experiments have shown that when the length
Experiments have shown that when the cross- of the wire increased, its resistance increases
sectional area of a wire is increased, its proportionally. In other words, the resistance R
resistance decreases proportionally. In other is directly proportional to the length l when the
words, the resistance R is inversely cross-sectional area and type of material are
proportional to the cross-sectional area A when same.
length and type of the material is the same.
R l (2)
1
R (1)
𝐴

Combining (1) and (2) from table 17.3, we obtain

𝑙 Where, R = Resistance of the wire (in Ω);

𝑅= 𝜌 𝜌 (a constant) = resistivity, a fixed property of the wire’s
𝐴
material (in Ω m);
l = length of the wire (in m);
A = cross=sectional area of the wire (in m2 ).

𝑙 𝑅𝐴
Rewriting R = ρ 𝐴 , we have ρ = . The SI unit of resistivity ρ is the Ohm meter (Ωm).
𝑙

Table 17.5 lists the resistivities of some materials. In Table 17.5 Resistivities of some
general, materials that have lower resistivities are better materials at 200 C
conductors of electricity. For example, since copper has Material Resistivity/ Ωm
low resistivity, and thus a low resistance, current can Silver 1.6 × 10−8
flow through copper easily. This explains why the Copper 1.7 × 10−8
wires in electric circuits are usually made of copper. Tungsten 5.5 × 10−8
Can you suggest why silver is not used to make wires? Iron 9.8 × 10−8
Constantan 49 × 10−8
Materials with high resistivities have their advantages Nichrome 100 × 10−8
too. For example,
Graphite 3000 × 10−8
(a) Nichrome is used to make the heating coils in
Polythene About 1016
electric kettles. For a given dimension, it has a
high resistance due to its high resistivity.
This causes it to produce a lot of thermal energy when a current flows through it.
(b) Tungsten has high resistivity too, hence it is used in light bulbs. Tungsten converts
electrical energy to light and thermal energy due to its high resistance.
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Figure 17.23 Change of resistance according to the length, area and resistivity of the wire

Past paper question (Nov 2000)

The terminals of the battery are joined by a length of resistance wire. Which change on its own,
will increase the current through the battery?

A. Connecting an identical wire in series with the first one

B. Covering the wire with plastic insulation
C. Using a shorter wire of the same material and the same thickness
D. Using a thinner wire of the same material and the same length.

Ans wer: C
Explanation To increase the current, we need to lower the resistance of the connecting
wire. Since resistance of the wire is directly proportional to length and
inversely proportional to cross-sectional area, we can either reduce the
length or increase the thickness of the wire

Exam tip It will become a short circuit if the wire does not have enough resistance. The
current will be very large and it will be too dangerous.

Worked Example 17.6

In an electrical heater, 15m of nichrome wire of cross-sectional area 2.0 × 10−7 𝑚2 is used to
make the heating element.
(a) Calculate the resistance of the nichrome wire given that the resistivity of nichrome is 100
× 10−8 Ωm.
(b) If the nichrome wire is replaced by a copper wire of identical length and cross-sectional
area, what will the resistance of the copper wire be? (resistivity of copper is 1.7 ×
10−8 𝛺𝑚.
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(c) Using the answer obtained in (a) and (b), comment on the suitability o f the nichrome and
copper wires as heating elements.

Solution
(a) Given: length l of nichrome wire = 15 m
Cross-sectional area A = 2.0 × 10−7 𝑚2
Resistivity ρ of nichrome = 100 × 10−8 Ωm.
ρ𝑙
Resistance R of nichrome wire is R = 𝐴
100 × 10 −8 Ωm (15m )
= = 75 Ω
2.0 × 10 −7 𝑚 2

(b) Given: resistivity 𝜌 ′ of copper = 1.7 × 10−8 𝛺𝑚

𝜌′ 𝑙
Resistance 𝑅 ′ of copper wire is 𝑅 ′ = 𝐴
1.7 × 10 −8 Ωm (15m )
= = 1.3 Ω
2.0 × 10 −7 𝑚 2

(c) In order to produce thermal energy, heating elements should have high resistance. For
given dimensions, the nichrome wire has a higher resistance (75Ω) than the copper wire
(1.3Ω) because nichrome has a higher resistivity 100 × 10−8 Ωm than the
copper 1.7 × 10−8 Ωm . Therefore the nichrome wire is more suitable for use as a
heating element.

Past paper question (June 2000)

A 0.4m length of resistance wire with an area of cross-section 0.2𝑚𝑚2 has a resistance of 2Ω.
Which wire of the same material will also have a resistance of 2Ω ?

Wire Length Area

A. 0.2 m 0.2 𝑚𝑚2
B. 0.2 m 0.4 𝑚𝑚2
C. 0.8 m 0.1 𝑚𝑚2
D. 0.8 m 0.4 𝑚𝑚2

Ans wer: D
Explanation resistance remains unchanged if both the length of the wire and cross-
sectional area are doubled.

Exam tip There are more than one combination of the length and area to give the
same resistance. Candidates need to check the 4 options one by one to find
out the answer.