Transcript Resistance - Mona Shores Blogs

Chapter 17
Current and Resistance
Chapter 17 Objectives
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Describe electric current
Relate current, charge, and time
Drift speed
Resistance and resistivity
Behavior of resistors
Superconductors
Electric power
Current
• Electric current, I, is the rate at which electric
charges move through a given area.
– It would be like standing in front of Burger King and
count all the cars traveling down Henry Street over a
given time period.
• For our purposes, we will consider the traveling
of positive charges from positive fields to
negative fields.
I
+
-
Drift Speed
• The electric force due to an electric field present causes
electrons to flow.
• The electrons do not flow in a straight line, but rather in a zigzag
path.
• The nature of the path is due to the collisions of the electrons
with other atoms in the conductor.
• The electrons flow opposite of the direction of the force due to
the nature of electric charges repelling like charges.
– Remember that a negative electron flowing to the negative post of
the battery would actually repel.
• So some work is required to move that electron.
• And that work can only be done by the electric potential energy that
was stored in the voltage source.
• Since the pattern is unpredictable, we can only come up with an
average speed.
• The net speed of a charge carrier moving in an electric field is
known as drift speed.
Amperes
• The SI unit for measuring current is an
ampere, A.
• Remember current is the rate of flow of
electric charges, so the formula looks like:
Q
I=
Δt
1A=1C
1s
Resistance
• The resistance of a conductor is the ratio of voltage
across the conductor to the current flowing through the
conductor.
– Resistance can be thought of as a conducting material that
alters the flow of charge carriers through the circuit.
– Resistors can be
• light bulbs
• appliances
• a new material
• SI unit is called an ohm.
– Denoted
• R
– Symbol
• Ω
• Symbol in a circuit is:
Ohm’s Law
• Georg Simon Ohm (1787-1854) found that for many materials,
including most metals, the resistance of the material is constant
over a wide range of voltages.
– That is Ohm’s Law in theory
• During his experiments, he noticed that the relationship between
current and voltage were proportional to one another in an ohmic
material.
– An ohmic material is one in which the resistance remains constant.
• Since the resistance is constant, the relationship between voltage
and current is written in the more useful form of Ohm’s Law:
V = I R
Resistivity
• With Ohm’s discovery that the resistance is constant for a material
under any voltage, that brings about the question:
– Is the resistance the same for every material?
• The answer is that the every material has its own, unique ability to
resist charge flow.
• That ability to resist charge flow is the resistivity, , characteristic
of the material.
• The resistivity of a material is:
– proportional to its length, l.
• longer distance means more time for charge to flow
– inversely proportional to its area, A.
• two lane highway versus a four lane highway
l
R=
A
Temperature v Resistance
• In general, the resistivity of a material increases as temperature
increases.
– This is due to the atoms inside the material becoming more excited
from the increased kinetic energy.
– The extra excitement causes them to vibrate faster, which creates
more collisions with the charge carriers as they attempt to pass
through.
• Each material has a different rate at which temperature can excite
its atoms.
• Remember the specific heat capacity concept!
– Thus we must account for this difference in the form of the
temperature coefficient of resistivity, .
 = 0[1 + (T – T0)]
Since R is directly proportional to 
R = R0[1 + (T – T0)]
Superconductors
• There are some metals and other compounds whose
resistances fall to virtually zero when they are cooled.
• When cooled such that their temperature falls below the
critical temperature, Tc, the resistance of the material
becomes next to nothing.
• These materials are called superconductors.
– They include metals such as Al, Sn, Pb, Zn, Hg, In, Nb.
• Copper, silver, and gold are great conductors but do not exhibit the
properties of a superconductor.
• An interesting phenomenon of superconductors is that
once a current is established in them, the current will
persist without any applied voltage.
– This has lead to extensive research to find a superconductor
with a critical temperature in a moderate range to allow for
technology to exist in our lives that can power themselves!
Semiconductors
• Another altering phenomenon of electrical current can increase the
resistance of a material as the voltage increased.
– This increase in both resistance and voltage leads to an nonlinear
increase in the current flow in a circuit.
• These nonohmic materials are called semiconductors.
– Often called diodes.
• They act much like a gate or a valve for the current.
– Semiconductors will allow current flow in certain directions, and
greatly restrict the flow in other directions.
•
Diodes are often used in circuitry for electronic devices to send
specific coded signals, and also to prevent back flow of current that
could overload the device.
• Semiconductors behave like resistors, so use the same sign
conventions.
– However, Ohm’s Law does not directly apply to semiconductors.
• The symbol in a circuit is:
Grounded Circuit
• Quite often a circuit is grounded to ensure a complete
transfer of charge from the positive terminal.
– Most house circuits are grounded as a safety precaution so that
any excess charge goes to the ground and not back into the
circuit where it does not belong and may do damage.
• For calculation purposes, a grounded location allows us
to identify a place where PE = 0 J.
• The symbol in a circuit for a ground is:
+
-
Electrical Power
• Recall the definition of power is the rate at which work is
performed.
• P = W/t
– Thanks to the Work-Kinetic Energy Theorem:
• W = KE
– And Conservation of Energy states:
• KE = PE
– And the electrical potential energy can be found by:
• PE = qV
– So the total power used during a transfer of electrical energy is:
• P = QV/t
– And the amount of charge transferred in a unit of time is defined as the
current.
• P = (Q/t)V = IV
– By using Ohm’s Law to incorporate resistance we get
• P = I2R
– If the voltage is unknown
• P = (V)2 / R
– If the current is unknown