chapter 25 current, resistance, electromotive force consider current and current density study the...
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Chapter 25Current, Resistance, Electromotive Force
• Consider current and current density
• Study the intrinsic property of resistivity
• Use Ohm’s 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
1
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
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 coursing
through a river.
Chapter 25 4
Electric Current
Conventional Current Direction
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.
dt
dQI (25-1)
1 mA (milliampere) = 1 x 10-3 A (ampere)
1 A(microampere) = 1 x 10-6 A (ampere)
Chapter 25 5
Electric Current Density
AdtnqvdtnAvqdQ dd )(
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
Current, Drift Velocity, and Current Density
A
IJ = current density in amperes/m2
InqAvdt
dQd dnqAv
dt
dQI amperes
Chapter 25 6
Resistivity
Evd
where = mobility of conducting material
Drift Velocity is 1010 slower than Random Velocity
1 1 E
nq J
nqwhere conductivity of the material.
EEnqvnqJ d
Definition of resistivity in ohm-meters (-m).
Drift Velocity
E
J
Resistivity of the material.
Resistivity is intrinsic to a metal sample (like density is)
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 R=0.
9
Resistance DefinedEEJ
1
EJ1
A
IJ
L
VE
L
V
A
I
1
( )I L
V L I RIA A
Ohm’s Law
where R is the resistance of the material in ohms ()
for a uniform E
+
–
V RItherefore
Solve for V
Ohm’s law an idealized model• If current density J is nearly proportional to electric field E
ratio E/J = constant and Ohm’s law applies V = I R
• Ohm’s Law is linear, but current flow through other devices may not be.
Linear Nonlinear Nonlinear
VR
I1
R
Slope1
RIV Ohm’s law applies
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%
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)
Ideal diagrams of “open” and “complete” circuits
Symbols for circuit diagrams– Shorthand symbols are in use for all wiring components
15
Electromotive Force and Circuits
Electromotive Force (EMF)
EMF R
Ideal source of electrical energy
I
+
–
+VR
–
Ideal Source
Complete path needed forcurrent (I) to flow
Voltage rise in current direction
Voltage drop in current direction
Real Source
EMF
rs
R
+
–
a
b
Vab
+
–
I
Real source of electrical energy
Internal source resistance
VR = EMF = R I
R
EMF
R
VI R
External resistance
IRIrEMFV sab
Chapter 25 16
A Source with an Open Circuit
Example 25-5
VrVIrEMFVab 12012
Figure 25-16
I = 0 amps
17
A source in a complete circuitExample 25-6
Figure 25-17
IRIrVab
)( rRIIrIR
ArR
I 224
12
VIrVab 8)2(212 VIRVV baab 8)4(2''
Chapter 25 18
A Source with a Short CircuitExample 25-8
Figure 25-19
0)0( IIRIrVab 0 Ir
AV
rI 6
2
12
Ir
0abV
I = 6 A
19
Potential Rises and Drops in a Circuit
Figure 25-21
20
Energy and Power
dt
dQI
IdtdQ
dQ
dWV abab
dQVdW abab
IdtVdW abab
IVdt
dWP ab
ab watts
1 watt = 1 joule/sec
Pure Resistance
dt
dWP ab
Substitute for IdtdQ
Defined
Divide by dt
Chapter 25 21
Power Output of an EMF Source
EMF
rs
R
I
+
––
+
Vab
a
b
IRIrEMFV sab
RIrIIEMFIIrEMFIVP ssabab22)()(
Power dissipated in battery resistancePower supplied by the battery
Power dissipated in R
RIrIIEMF s22)(
+ –
Power output of battery
22
Power Input to a SourceI
sab IrEMFV
ssabab rIIEMFIIrEMFIVP 2)()(
Power dissipated in battery resistancePower charging the battery
sab rIIEMFIV 2)(
a
b
Total Power input to battery
Vab greater then the EMF of the battery+
–
+–+
–
23
Power Input and Output in a Complete CircuitExample 25-9
Figure 25-25
24
Power in a Short Circuit
Example 25-11
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, τ.
• As temperature increases the ions vibrate more and produce more collisions, reducing τ.
Chapter 25 25
A microscopic look at conduction
– Consider Figure 25.27.– Consider Figure 25.28.– Follow Example 25.12.