ECE103
Spring 2008
Lecture 2
Basic Laws Ohm’s Law
Materials react
resisting
the passage of
current through it. This is due to the
microscopic interaction of the moving
charges and the atomic structure of the
material. This ability to
resist
the current
of flow of charges is called
resistivity.
Resistivity is a characteristic of any
material. Materials with very low
resistivity
are
called
conductors,
materials with very small resistivity are called isolators and those in between are
classified as semiconductors.
When a piece of any material is “connected” to a voltage source (for example a battery),
charges will flow through it. The amount of charge flowing through the material will
depend on the geometry, and also on the intrinsic characteristics of the material (this is
the resistivity). Intuitively, we can understand the importance of the geometry if we make
an analogy with a water pipe: the flux (current) through a pipe (resistor) at a certain water
pressure (voltage) will be proportional to the pipe section (cross section of the resistor).
In a mathematical form the resistance R is related to the characteristics of the material
and to the geometry through
R
A
ρ
=
A
where R is the
resistance
,
ρ
(rho) is the
resistivity
,
A
is the length of the resistor and A
is the cross section. Resistance is measured in
ohms
(the symbol is
Ω
). So resistivity is
expressed in
Ω
.m (ohm per meter). In different materials this quantity can vary several
orders of magnitude (~10
8
Ω
m for conductors to more than 10
12
Ω
m for insulators).
The relationship between the current and the resistance in an electric circuit is the Ohm’s
law and states:
Mathematically, this is expressed as
vi
R
=
I
+
battery
A
I
l
l
Ohm’s Law:
The voltage across a resistor is directly proportional to the current
i
flowing through it, and the constant of proportionality is the resistance
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View Full DocumentSo the current through a resistor will increase increasing the voltage across it and will
decrease increasing the resistance. Using our pipe and water analog we can say that the
water flux (current) will increase increasing the pressure (voltage) and will decrease
decreasing the cross section (increasing resistance).
From Ohm’s law we can define
11
V
A
Ω=
There are two extreme values: if an element has a resistance so small that we can
consider R
≈
0, we call a
short circuit
. On the other extreme, if an element has a
resistance so big that we can consider
R
≈
∞
, we call this an
open circuit
.
Resistors that are connected to real circuits and they come in different sizes and shapes.
The shape and size of the resistors will
depend on different characteristics as
the power it can handle, the material,
etc.
. The photograph depicts several
resistors with fixed value.
In many cases a given circuit needs to
have resistors with variable value
(continuous variable value) that are
known as
potentiometers
or most
commonly named as
pots
. Next figure indicates the usual symbol and a photograph of
some pots
Resistors with a fixed value are called “linear”. These elements follow the Ohm’s law
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 Spring '08
 MARCONI
 Resistor, ohm

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