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Lecture 9
Ch26. Ohm’s Law
University Physics: Waves and Electricity
Dr.-Ing. Erwin Sitompul
http://zitompul.wordpress.com
2013
Homework 7
(a) The rectangular ABCD is defined by its corner points of
A(2,0,0), B(0,3,0), C(0,3,2.5), and D(2,0,2.5). Draw a sketch
of the rectangular.
→
^
^
(b) Given an electric field of E = –2i + 6j N/C, draw the electric
field on the sketch from part (a).
(c) Determine the number of flux crossing the area of the
rectangular ABCD.
Erwin Sitompul
University Physics: Wave and Electricity
9/2
Solution of Homework 7
E  2iˆ  6ˆj N C
AABCD  7.5iˆ  5jˆ m2
• Projection of ABCD
on the xz plane
z
3
• Projection of ABCD
on the yz plane
ABCD  E  AABCD
 (2iˆ  6ˆj)  (7.5iˆ  5jˆ )
 15 N  m2 C
C
2
D
1
B
1
0
1
2
3
y
2
3
A
x
Erwin Sitompul
University Physics: Wave and Electricity
9/3
Electric Current
 Previously we have discussed electrostatics – the physics of
stationary charges.
 From this point onward, we will discuss the physics of
charges in motion –that is, electric currents.
 Electric currents involve many professions, especially
engineers.
 Electrical engineers are concerned with countless electrical
systems such as power systems, lightning systems, and
information storage systems.
Erwin Sitompul
University Physics: Wave and Electricity
9/4
Electric Current
 As we know, there are two kinds of electric charge carriers:
the positive charge carrier (hole) and the negative charge
carrier (electron).
 In a conducting material, a number of electrons are not
bounded to the atom and can freely move across the
material. This electron is called conduction electron.
 A hole is actually the empty state left by a freely moving
electron. We define a hole to have a positive charge, in
opposite to the electron.
• Current is defined as the rate of
movement of charge passing a given
reference point (or crossing a given
reference plane)
• Through convention, the direction of
hole movement is defined as the
direction of current
Erwin Sitompul
I
Q
t
University Physics: Wave and Electricity
9/5
Checkpoint
Consider positive and negative charges moving horizontally
through four different pieces of a conductor.
(a) Determine the current
(a) and (c) rightward,
direction of each piece.
(b) and (d) leftward
(b) Rank the current from
a, b and c tie, d
highest to lowest.
• Can you determine the→
direction of the fields E?
Erwin Sitompul
University Physics: Wave and Electricity
9/6
Electric Current
 Although an electric current is a stream of
moving charges, not all moving charges
constitute an electric current.
 An electric current through a given surface
exist only when there is a net flow of charge
through that surface.
I 0
 If an electric field exists, the charge carriers (conducting
electrons and holes) will move under the influence of the
field.
 Flow of carriers will stop when the electric field is zero or the
potential difference is zero.
E 0
Erwin Sitompul
E0
University Physics: Wave and Electricity
9/7
Electric Current
 The SI unit for current is the coulomb per second (C/s) or the
ampere (A).
q
i
t
1C
1A 
1s
 Current is a scalar quantity. We do not
need direction to define it.
 Yet, we know that current will flow in
the same direction as the electric field,
or from higher potential to lower
potential.
 We often represent the current
direction with an arrow near a
conductor (wire, cable, etc).
Erwin Sitompul
i0  i1  i2
University Physics: Wave and Electricity
9/8
Checkpoint
The figure below shows a portion of a circuit. What are the
magnitude and direction of the current I in the lower right-hand
wire?
5A
6A
8A
The magnitude of the current is 8 A,
flowing from left to right
Erwin Sitompul
University Physics: Wave and Electricity
9/9
Resistance and Resistivity
 One of the characteristics of a conductor is the electrical
resistance.
 We determine the resistance between any two points of a
conductor by applying a potential difference V between those
points and measuring the current i that results.
V
R
i
 The SI unit for resistance is the volt per ampere. This
combination, however, occurs so often that it is given a
special name ohm (symbol Ω).
1ohm  1   1 volt per ampere  1V A
Erwin Sitompul
University Physics: Wave and Electricity
9/10
Resistance and Resistivity
 A conductor whose function in an electric
circuit is to provide a specified resistance
is called a resistor.
 In a circuit diagram, the resistor is
represented by the symbols:
 We can rewrite the last equation to become:
V
i
R
Erwin Sitompul
For a given V,
• The greater the resistance, the smaller the current
• The smaller the resistance, the greater the current
University Physics: Wave and Electricity
9/11
Resistance and Resistivity
 The resistivity is
characteristic for each
material. It depends on
the properties of the
material and on
temperature.
 The next table lists the
resistivities of some
materials at 20°C.
Erwin Sitompul
University Physics: Wave and Electricity
9/12
Resistance and Resistivity
 The resistivity is denoted with ρ. The SI unit of resistivity is
ohm-meter (Ωm).
 We can also speak of the conductivity σ of a material. This is
simply the reciprocal of its resistivity, so:

1

 The SI unit of conductivity is (Ωm)–1. Sometimes the unit
mhos per meter is used.
1
mhos
(  m) 
 
m m
m
1
Erwin Sitompul
University Physics: Wave and Electricity
9/13
Calculating Resistance from Resistivity
 Distinction:
Resistance is a property of an object.
Resistivity is a property of a material
 Let A be the cross-sectional area of the wire of length L, and
let a potential difference V exist between its ends.
 The resistance of the wire is given by:
L
R
A
Erwin Sitompul
University Physics: Wave and Electricity
9/14
Checkpoint
The figure here shows three cylindrical copper conductors
along with their face areas and lengths.
Rank them according to the current through them, greatest
first, when the same potential difference V is placed across
their lengths.
(a) and (c) tie,
then (b)
L
Ra  
A
1.5 L
Rb  
A2
L
 3
A
L2
Rc  
A2
L

A
For the same potential difference V,
• The resistance >>, the current <<
• The resistance <<, the current >>
Erwin Sitompul
R
University Physics: Wave and Electricity
L
A
9/15
Variation with Temperature
 The values of resistivity varies
with temperature.
 The next figure shows the
variation of this property for
copper over temperature.
 The relation between
temperature and resistivity for
copper –and for metal in
general– is fairly linear.
 For such linear relations, the following empirical
approximation is good enough for most engineering
purposes:
  0 1   (T  T0 )
Erwin Sitompul
• T0 = 20°C = 293 K
(room temperature)
• α is the temperature
coefficient, (°C)–1,
(see table)
University Physics: Wave and Electricity
9/16
Color-Coding of Resistor Identification
1 0 4 ±10%
R  10 104   10%
 100 k  10%
±5%
1 26
R  62 101   5%
 620   5%
3 3 9 0 ±1%
R  339 100   1%
 339   1%
Erwin Sitompul
University Physics: Wave and Electricity
9/17
Homework 8
A rectangular block of iron has dimensions 1.2 cm  1.2 cm 
15 cm. The temperature of the surrounding air is 20 °C. A
potential difference is to be applied to the block between
parallel sides.
(a) What is the resistance of the block if the two parallel sides
are the square ends (with dimensions 1.2 cm  1.2 cm)?
(b) The temperature of the iron block increases up to 35 °C due
to the flowing current. What is the resistance of the block
now?
Erwin Sitompul
University Physics: Wave and Electricity
9/18
Homework 8A
1. A rectangular block of copper has dimensions 1.2 cm  1.2 cm  15 cm.
The temperature of the surrounding air is 25 °C. A current of 2.2 mA flows
through the block between parallel sides.
(a) What is the resistance of the block if the two parallel sides are the two
rectangular sides (with dimensions 1.2 cm  15 cm)?
(b) The temperature of the copper block increases up to 27°C due to the
flowing current. What is the potential difference between the parallel
sides?
2. A composite wire of unknown material has a resistance of 8.0 Ω. It is then
molded and reformed so that its new length is four times its original
length. Find the resistance of the wire now, if it may be assumed that the
density and resistivity of the composite are unchanged.
Erwin Sitompul
University Physics: Wave and Electricity
9/19