Transcript Topic 5.1 Electric Current and Resistance

Topic 5.1: Electric Current
~3 hours
Electric Current
• An electric current is a movement of electric charge that
can occur in solids, liquids and gases. A steady current can
be maintained when there is a drift of charge-carriers
between two points of different electric potential. The
charges responsible for the drift are:
• Solids
– electrons in metals and graphite, and holes in semiconductors
• Liquids
– positive and negative ions in molten and aqueous electrolytes
• Gases
– electrons and positive ions stripped from gaseous molecules by
large potential differences.
Electric Current
• At this point, we will define the electric current as the
rate at which charge flows past a given cross-section.
q
I
t
or
dq
I
dt
• It makes sense that for an electric current to flow, there
must be a complete circuit for it to flow through. The
unit of current from the above equation is the coulomb
per second C s-1 and this unit is called the ampere (A).
• The ampere or ‘amp’ is a rather large unit. Current is
often expressed in milliamps (mA) and microamps (μA)
or even nanoamps and picoamps.
• When a current flows in the same direction
around an electric circuit, the current is said to
be a direct current (DC). Dry cell and wet cell
batteries supply dc. When the direction of the
current changes with time it is said to be an
alternating current (AC). Household electrical
(nonelectronic) appliances are AC.
Current Conventions
• Current is a scalar quantity but it is useful to indicate the direction of flow
of current.
• Before the electron was discovered, the direction of the charge-carriers
was already defined by scientists and engineers to be from positive to
negative.
• Benjamin Franklin stated that an excess of fluid produced one kind of
electric charge which he termed “positive”, and a lack of the same fluid
produced the other type of electric charge which he called “negative”.
Franklin’s designation of (+) being an excess of electric charge and of (–)
being a deficiency of electric charge was unfortunate.
• When batteries and generators, the first source of continuous current,
were developed in the 1800s, it was assumed that electric current
represented the flow of positive charge as defined by Franklin. This is
partly the reason that electric fields are defined in terms of a positive test
charge, and the lines of electric flux being explained as going outwards
from positive charges.
• It is now known that an electric current is a flow of electrons from
negative to positive.
• Unfortunately, this convention has been kept. The
above figure shows a simple circuit diagram of a 1.5 V
dry cell connected to a resistor. When drawing and
interpreting circuit diagrams just remember that
conventional current flows from the positive to
negative terminal unless you are specifically asked for
the correct electron flow that flows from the negative
to the positive terminal.
Conservation of Charge
• Two devices connected
in series will take the
same current.
• The total current entering a junction equals
the total current leaving it.
Electric Resistance
• Electrical resistance, R, is a measure
of how easily charge flows in a material.
• The electric resistance of a conductor (for
example, a wire of a given length) is defined as
the potential difference across its ends divided
by the current flowing through it. This is also
known as Ohm’s Law.
V
R
I
Resistors
• Conductors, semiconductors and insulators
differ in their resistance to current flow. An
ohmic*material of significant resistance placed
in an electric circuit to control current or potential
difference is called a resistor.
• The units of resistance are volts per ampere (VA-1).
However, a separate SI unit called the ohm Ω is defined
as the resistance through which a current of 1 A flows
when a potential difference of 1 V is applied. Since the
term resistance refers to a small resistance, it is
common for a resistor to have kilo ohm (kΩ) and mega
ohm (MΩ) values.
* An ohmic material is one that obeys Ohm’s law.
Factors Affecting Resistance
• The resistance of a conducting wire depends
on four main factors:
• length
• cross-sectional area
• resistivity
• temperature
Resistance of a Wire
• It can be shown that when the temperature is
kept constant
R
L
A
where R is the resistance in Ω, ρ is the
resistivity specific to the material in Ω m, L is
the length of the conductor in m, and A is the
cross-sectional area of the conductor in m2.
Resistance and Temperature
• The resistance of a material increases with
temperature because of the thermal agitation of
the atoms it contains, and this impedes the
movement of electrons that make up the current.
• The increase in resistance can be shown as
Rf = R0(1 + αT)
where R0 equals the resistance at some reference
temperature say 0 °C, Rf is the resistance at some
temperature, T °C, above the reference
temperature, and α is the temperature coefficient
for the material being used.
Superconductors
• One interesting phenomenon of the
effect of temperature on resistance
is superconductivity.
• In 1911, H. Kammerlingh Onnes found
that mercury loses all its resistance abruptly at
a critical temperature of 4.1 K.
• When a material attains zero resistance at
some critical temperature, it is called a
superconductor.
Ohm’s Law Revisited
• The German physicist, Georg Simon Ohm (1787-1854),
studied the resistance of different materials systematically.
In 1826, he published his findings for many materials
including metals. He stated that: Provided the physical
conditions such as temperature are kept constant, the
resistance is constant over a wide range of applied
potential differences, and therefore the potential
difference is directly proportional to the current flowing.
• There are two relevant statements to be made here. Firstly,
Ohm’s Law is not really a law but rather an empirical
statement of how materials behave. Many materials are
non-ohmic and this law is only applicable to ohmic
conductors. Secondly, the law should not be written as
R = V / I as this statement defines resistance.
Ohm’s Law Revisited
• The formula is commonly written as:
V = IR
where V is the potential difference across the
resistor in volts V, I is the current in the resistor in
amperes A and R is the resistance in ohms Ω.
When written in this form R is understood to be
independent of V.
• As the current moves through the resistance of a
device, it loses electric potential energy. The
potential energy of a positive charge is less upon
leaving the resistor than it was upon entering. We
say that there is a potential drop across the
device.
Ohmic Materials
• A graph of current versus the potential
difference is a straight line. Devices that
obey the linear relationship of the graph
are said to be ‘ohmic devices’ or ‘ohmic
conductors’.
• There are very few devices that are ohmic
although some metals can be if there is no
temperature increase due to the heating
effect of the current. However, many useful
devices obey the law at least over a
reasonable range. Remember that a
resistor is any device with a potential
difference and is not only restricted to the
typical resistor used in the laboratory. It
could be any useful electrical device – a
filament lamp, a diode, a thermistor.
• When a device does not obey Ohm’s Law, it
is said to be non-ohmic. The filament lamp
is non-ohmic because Ohm’s Law requires
that the temperature remains constant,
and this is not the case for an operating
filament lamp.
Current vs Voltage relationships for a
few common devices
Power Dissipation in Resistors
• Electric power is the rate at which energy is
supplied to or used by a device. It is measured
in J/s or watts W.
• When a steady current is flowing through a
load such as a resistor, it dissipates energy in
it. This energy is equal to the potential energy
lost by the charge as it moves through the
potential difference that exists between the
terminals of the load.
E p
qV
P

or P  IV
t
t
Power and Ohm’s Law
• Note that because V = IR and I = V/R we have
the following relationships for power.
• If a vacuum cleaner has a power rating of 500
W, it means it is converting electrical energy to
mechanical, sound and heat energy at the rate
of 500 J s-1. A 60 W light globe converts
electrical energy to light and heat energy at
the rate of 60 J s-1.
Problems:
• Tsokos, Pages 316 and 317, Questions 1 to 20
• Giancoli, Page 516, Odd Numbered Questions
from #13 to 25 (Answers on page A-35 at the
back of the book).