CHAPTER 17
Current
Electricity
© 2013 Marshall Cavendish International (Singapore) Private Limited
Chapter 17 Current Electricity
17.1 Electric Current
17.2 Electromotive Force and
Potential Difference
17.3 Resistance
17.4 Resistivity
17.1 Electric Current
Learning Outcomes
At the end of this section, you should be able to:
• define the term current and state its SI unit;
• differentiate between conventional current and
electron flow;
• apply the formula charge = current × time to solve
problems;
• draw electric circuit diagrams.
Electric Current
What is Electric Current?
Video on Lightning & Thunder
http://www.youtube.com/watch?v=Sp9bKDHRfsM
Good Electrical Conductors
Things that have free electrons
• Metals (copper & zinc?
• What’s the best conductor?
• How about water?
Good Insulators
Things that do not allow electrons to flow
• rubber
17.1 Electric Current
What is Electric Current?
An electric current is formed by moving charges.
Electric current is a measure of the rate of flow of electrons
through a conductor.
Q
I=
t
where I = current;
Q = charge;
t = time taken.
The SI unit of electric current is the ampere (A).
17.1 Electric Current
Electron Flow
• Electric current is actually caused by
the flow of electrons from the
negative terminal to the positive
terminal.
17.1 Electric Current
How do We Measure Electric Current?
• We make use of an ammeter
to measure current.
• The ammeter should be
connected in series to the
circuit.
17.1 Electric Current
Main Components of a Circuit
• A typical electric circuit consists of four main components.
A source of electromotive force
that drives electric charges around
the circuit.
Wires
Conductors that connect the
components together.
Dry cell
A load in which moving charges
can do a useful job.
Switch
A method of opening or closing the
circuit.
Bulb
17.1 Electric Current
Drawing Circuit Diagrams
• Electric circuits can be represented by circuit diagrams.
• Can you identify what the symbols in the circuit diagram
below represent?
ammeter
bulb
cell
connecting wires
switch
17.1 Electric Current
Drawing Circuit Diagrams
Some common components and their symbols are listed
in the tables below.
17.1 Electric Current
Interpreting Circuit Diagrams
Open circuit
A circuit in which current is unable to flow due to
breaks in the circuit.
17.1 Electric Current
Interpreting Circuit Diagrams
Short circuit
An alternative path of lower resistance is present and
hence, current flows through wire X instead of the bulb.
Chapter 17 Current Electricity
17.1 Electric Current
17.2 Electromotive Force and
Potential Difference
17.3 Resistance
17.4 Resistivity
17.2 Electromotive Force
and Potential Difference
Learning Outcomes
At the end of this section, you should be able to:
• define electromotive force (e.m.f.) and potential
difference (p.d);
• state the SI unit of e.m.f. and p.d.;
• calculate the e.m.f. when a few sources are
arranged in series.
17.2 Electromotive Force
and Potential Difference
Recall
We saw this circuit
in Section 17.1.
What is the role of the
battery in the circuit?
Why do you need a battery to
make the bulb light up?
17.2 Electromotive Force
and Potential Difference
What is Electromotive Force?
• A battery functions like a water
pump.
• A water pump does work (providing
energy) to drive the water around
the pipe.
• Likewise, a battery does work to
drive electrons around the circuit.
17.2 Electromotive Force
and Potential Difference
What is Electromotive Force?
The electromotive force (e.m.f) of an electrical energy
source is defined as the work done by a source in
driving a unit charge around a complete circuit.
W
e=
Q
where ε = e.m.f. of electrical energy source;
W = work done (amount of non-electrical energy
converted to electrical energy);
Q = amount of charge.
SI unit of e.m.f is the joule per coulomb (J C–1) or volt (V).
17.2 Electromotive Force
and Potential Difference
How do We Measure E.m.f.?
• We use a voltmeter to
measure e.m.f.
• The positive and negative
terminals of a voltmeter
should be connected to the
positive and negative
terminals respectively of
the electrical source.
17.2 Electromotive Force
and Potential Difference
Arrangement of Cells
Series arrangement
When cells are arranged in series,
the resultant e.m.f. is the sum of
all the e.m.f.s of the cells.
Parallel arrangement
When cells are arranged in parallel,
the resultant e.m.f. is equal to that
of a single cell.
17.2 Electromotive Force
and Potential Difference
What is Potential Difference?
The potential difference (p.d.) across a component in
an electric circuit is the work done to drive a unit
charge through the component.
W
V=
Q
where V = p.d. across a component;
W = work done (amount of electrical energy
converted to other forms);
Q = amount of charge.
The SI unit of potential difference is the volt (V).
17.2 Electromotive Force
and Potential Difference
How do We Measure P.d.?
• We make use of a voltmeter to measure p.d.
• The voltmeter should be connected in parallel
with the component.
17.2 Electromotive Force
and Potential Difference
E.m.f. versus P.d.
Electromotive force
Associated with an
electrical energy source
(e.g. a dry cell)
Potential difference
Associated with two points
in an electric circuit
It is the work done by the
source in driving a unit
charge around a
complete circuit.
It is the work done to
drive a unit charge
through two points.
17.2 Electromotive Force
and Potential Difference
Question
What will the voltmeter reading show?
A The e.m.f. of the electrical source (the three
cells in series)
B The e.m.f. of the bulb
C The potential difference across the bulb
Chapter 17 Current Electricity
17.1 Electric Current
17.2 Electromotive Force and
Potential Difference
17.3 Resistance
17.4 Resistivity
17.3 Resistance
Learning Outcomes
At the end of this section, you should be able to:
• define the term resistance;
• apply the formula resistance =
to solve problems;
p.d.
current
• describe an experiment to determine resistance;
• state Ohm’s Law;
• understand and draw the I−V characteristic graphs for
ohmic and non-ohmic conductors;
• describe the relationship between the resistance of a
metallic conductor and its temperature.
17.3 Resistance
Recall
Earlier, we used the
water pump analogy to
help us understand
e.m.f.
obstacle
Question
Predict what will happen if a porous plate (an obstacle)
is placed in the path of the water flow.
17.3 Resistance
What is Resistance?
resistor
Resistor
added
Rate of flow of
electric charges
reduced
Current is
reduced
Ammeter
reading will
be reduced
• Resistance is the difficulty for an electric current to pass
through a material.
• It restricts the movement of free electrons in the material.
17.3 Resistance
What is Resistance?
The resistance of a component is the ratio of the
potential difference across the component to the
current flowing through the component.
V
R=
I
where R = resistance of a component;
V = p.d. across a component;
I = current flowing through component.
The SI unit of resistance is the ohm (Ω).
17.3 Resistance
Activity (Group)
Objective
Design an electric circuit that can be used to measure
the resistance of a component.
Instructions
Resistance =
p.d.
current
1. In groups, design a circuit that can be used to
determine the resistance of a bulb.
2. Using the materials given, check if your design
works.
17.3 Resistance
Circuit for Measuring Resistance
Note that:
• The ammeter is
connected in series
with the bulb.
• The voltmeter is
connected in parallel
with the bulb.
17.3 Resistance
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.
• There are two types of resistors — fixed resistors
and variable resistors (or rheostats).
17.3 Resistance
Ohm’s Law
Ohm’s Law states that the current passing through a
metallic conductor is directly proportional to the
potential difference across it, provided that physical
conditions remain constant.
I µV
where I = current;
V = potential difference.
17.3 Resistance
Ohmic and Non-ohmic Conductors
• Ohmic conductors are conductors that obey Ohm’s Law.
• Non-ohmic conductors are conductors that do not obey
Ohm’s Law.
Ohmic conductors
The I−V graph of an ohmic
conductor is a straight line
that passes through the
origin.
17.3 Resistance
Non-ohmic conductors
• They do not obey Ohm’s Law and
their resistance R can vary.
• Their I−V graphs are not straight
lines, which means the ratio V/I is
not a constant.
Chapter 17 Current Electricity
17.1 Electric Current
17.2 Electromotive Force and
Potential Difference
17.3 Resistance
17.4 Resistivity
17.4 Resistivity
Learning Outcome
At the end of this section, you should be able to:
• apply the relationship of the proportionality of
resistance to the length and cross-sectional area
of a wire to solve problems.
17.4 Resistivity
Recall
Ohm’s Law states that the current passing through a
metallic conductor is directly proportional to the potential
difference across it, provided that physical conditions
remain constant.
Other than temperature, what
physical conditions affect the
resistance of a component?
17.4 Resistivity
Other than temperature, the resistance R of a
conductor also depends on
1. its length l;
2. its cross-sectional area A;
3. the material it is made of (i.e. resistivity ρ).
conductor
R=
l
A
rl
A
17.4 Resistivity
Resistivity
Rewriting R =
r l , we can obtain the formula for resistivity.
A
RA
r=
l
where ρ = resistivity of conductor;
R = resistance of conductor;
A = cross-sectional area of conductor;
l = length of conductor.
The SI unit of resistivity is the ohm metre (Ω m).
17.4 Resistivity
Resistivity
• Different materials have
different resistivities.
• Resistivity is a property of
the material and it is
independent of the
dimensions of the
material.
• The lower the resistivity of
a material, the better it is
at conducting electricity.
17.4 Resistivity
Worked Example
A length of resistance wire 50 cm long is connected in
series with an ammeter and a 3 V battery. The ammeter
reading is 0.15 A.
(a) Determine the resistance of the wire.
(b) The length of the wire is doubled and its cross-sectional
area halved. Determine the new resistance and hence
ammeter reading.
(c) Given that the diameter of the 50 cm long wire is 5 mm,
determine its resistivity.
17.4 Resistivity
Solution
(a) R = V ÷ I
= 3 ÷ 0.15
= 20 Ω
(b)
l
Rµ
A
kl1
20 =
- - - -(1)
A1
k 2l1
- - - (2)
1 A
2 1
20 1
(1) ¸ (2) :
=
R2 4
R2 =
(c)
RA
l
20 ´ p ´ 0.00252
=
0.5
= 7.85 ´ 10 -4 Wm
r=
R2 = 80W
I=
3
= 0.0375A
80
Chapter 17 Current Electricity
Electric current I
(SI unit: A)
I=
Resistance R
(SI unit: Ω)
related to
defined as
rate of flow of
Q
t
where
where
t = time
(continued on next slide)
Charge Q
(SI unit: C)
related to
Electromotive force ε
(SI unit: V)
Potential difference V
(SI unit: V)
where
ε=
W
Q
where
W = work done by source
to drive a unit charge
around the circuit
where
V=
W
Q
where
W = work done to drive a
unit charge through
a component
Chapter 17 Current Electricity
Electric current I
(SI unit: A)
related to
(continued from
previous slide)
Resistance R
(SI unit: Ω)
where
ρ=
R=
V
I
where
V = potential difference
I = current
if constant
URL
related to
resistivity ρ
RA
l
where
l = length
A = cross-sectional area
if not constant
Obeys Ohm’s Law
IαV
Does not obey
Ohm’s Law
Ohmic conductors
Non-ohmic conductors
Chapter 17 Current Electricity
The URLs are valid as at 15 October 2012.
Acknowledgements
(slides 1−47) plasma globe © Stuartkey | Dreamstime.com
(slides 6, 15) battery © Vladwitty | Dreamstime.com
(slides 6, 15) bulb © Monsieurpix | Dreamstime.com
(slide 7) ammeter © Arsty | Dreamstime.com
(slide 18) voltmeter © Arsty | Dreamstime.com
(slide 22) circuit © Marshall Cavendish International (Singapore)
Private Limited
(slide 33) fixed resistors © Sergpet | Dreamstime.com
(slide 33) rheostat © Arsty | Dreamstime.com