Chapter 25 Current, Resistance, Electromotive Force

1
Chapter 25Current, Resistance, Electromotive
Force

• Consider current and current density
• Study the intrinsic property of resistivity
• Use Ohms Law and study resistance and resistors
• Connect circuits and find emf
• Examine circuits and determine the energy and
  power in them
• Describe the conduction of metals
  microscopically, on an atomic scale

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The direction of current flow

• In the absence of an external field, electrons
  move randomly in a conductor. If a field exists
  near the conductor, its force on the electron
  imposes a drift.

-The electrons move at a random velocity and
collide with stationary ions. Velocity in the
order of 106 m/s -Drift velocity is
approximately 10-4 m/s
3
Current flowing

• Positive charges would move with the electric
  field, electrons move in opposition.
• The motion of electrons in a wire is analogous to
  water coursingthrough a river.

4
Electric Current
Electrical current (I) in amperes is defined as
the rate of electric charge flow in coulombs per
second. 1 ampere (A) of current is a rate of
charge flow of 1 coulomb/second.
1 mA (milliampere) 1 x 10-3 A (ampere)
(25-1)
1 ?A(microampere) 1 x 10-6 A (ampere)
Conventional Current Direction
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Electric Current Density
Current, Drift Velocity, and Current Density
where n charge carriers per unit volume
q charge per charge carrier in coulombs
vd average drift velocity of charge
carriers in
meters per second
amperes
current density in amperes/m2
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Resistivity
Drift Velocity
where ? mobility of conducting material Drift
Velocity is 1010 slower than Random Velocity
Definition of resistivity in ohm-meters (?-m).
where
conductivity of the material.
Resistivity of the material.
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Resistivity is intrinsic to a metal sample (like
density is)
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Resistivity and Temperature

• In metals, increasing temperature increases ion
  vibration amplitudes, increasing collisions and
  reducing current flow. This produces a positive
  temperature coefficient.
• In semiconductors, increasing temperature shakes
  loose more electrons, increasing mobility and
  increasing current flow. This produces a negative
  temperature coefficient.
• Superconductors, behave like metals until a phase
  transition temperature is reached. At lower
  temperatures R0.

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Resistance Defined
for a uniform E

Solve for V

Ohms Law
therefore
where R is the resistance of the material in ohms
(?)
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Ohms law an idealized model

• If current density J is nearly proportional to
  electric field E ratio E/J constant and
  Ohms law applies V I R
• Ohms Law is linear, but current flow through
  other devices may not be.

Linear
Nonlinear
Nonlinear
Ohms law applies
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Resistors are color-coded for assembly work
Examples Brown-Black-Red-Gold 1000 ohms
5 to -5 Yellow-Violet-Orange-Silver 47000
ohms 10 to -10
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Electromotive force and circuits

• If an electric field is produced in a conductor
  without a complete circuit, current flows for
  only a very short time.
• An external source is needed to produce a net
  electric field in a conductor. This source is an
  electromotive force, emf , ee-em-eff, (1V 1
  J/C)

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Ideal diagrams of open and complete circuits
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Symbols for circuit diagrams

• Shorthand symbols are in use for all wiring
  components

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Electromotive Force and Circuits
Electromotive Force (EMF)
Ideal Source
I
Complete path needed for current (I) to flow
Voltage rise in current direction

VR
Voltage drop in current direction

Ideal source of electrical energy
VR EMF R I
Real Source
I
a

External resistance
Internal source resistance

Vab


Real source of electrical energy
b
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A Source with an Open Circuit
Example 25-5
I 0 amps
Figure 25-16
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A source in a complete circuit
Example 25-6
Figure 25-17
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A Source with a Short Circuit
Example 25-8
I 6 A
Figure 25-19
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Potential Rises and Drops in a Circuit
Figure 25-21
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Energy and Power
Defined
Substitute for
Divide by
watts
Pure Resistance
1 watt 1 joule/sec
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Power Output of an EMF Source
I
a




Vab


b
Power output of battery
Power dissipated in R
Power dissipated in battery resistance
Power supplied by the battery
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Power Input to a Source
I
a


Vab greater then the EMF of the battery




b
Power dissipated in battery resistance
Power charging the battery
Total Power input to battery
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Power Input and Output in a Complete Circuit
Example 25-9
Figure 25-25
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Power in a Short Circuit
Example 25-11
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Theory of Metallic Conduction

• Simple, non-quantum-mechanical model
• Each atom in a metal crystal gives up one or
  more electrons that are free to move in the
  crystal.
• The electrons move at a random velocity and
  collide with stationary ions. Velocity in the
  order of 106 m/s (drift velocity is approximately
  10-4 m/s)
• The average time between collisions is the mean
  free time, t.
• As temperature increases the ions vibrate more
  and produce more collisions, reducing t.

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A microscopic look at conduction

• Consider Figure 25.27.
• Consider Figure 25.28.
• Follow Example 25.12.