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Conductors and Resistors
Chapter 14
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Material Resistivity, Ohm m
Material Resistivity, Ohm m
Ag 1.6×10-8 Ni (com) 6.8×10-8
Cu (com) 1.7×10-8 S. Steel 7.1×10-7
Au 2.4×10-8 Nichrome 1.08×10-6
Al (com) 2.9×10-8 Graphite 1 ×10-5
Brass (70-30)
6.2×10-8 SiC 1 ×10-1
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Material Resistivity, Ohm m
Material Resistivity, Ohm m
SiC 1 ×10-1 Bakelite 107 - 1011
Ge, pure 4.5 ×10-1 Window glass
>1010
Si, pure 2.3 ×103 Ai2O3 1010-1012
Mica 1011-1015
Diamond >1014
SiO2 >1016
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Imperfections solutes, vacancies, etc.dislocationsgrain boundaries
act as scattering centres and thereby decrease the mean free path and thus decrease .Of all the imperfections, dissolved impurities (solutes) are more effective than the others as scattering centres.
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Phonons: elastic waves produced by the random vibrations of
atoms
Random nature destroys the ideal periodicity and interferes with the electron motion.
Conductivity thus decreases with increasing temperature.
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Cu-3%
Ni
Cu-2%
Ni
Pur
e Cu
Fig. 14.6
T
Experiment 9
Dependence of resistivity on temperature and composition
= T + r
= resitivity
T = thermal part of the resitivity
r =residual resitivity due to impurity and imperfections
Mattheissen’s Rule : T and r
are independent of each other; i.e., T depends only on tempearture and r depends only on compositon
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Applications
Conductors: Requirements
1. Low I2R loss
(High Conductivity)
2. Fabricability
3. Cost
4. Strength
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Candidate MaterialsLong distance transmission lines - Al- ACSR: Al conductor steel reinforced
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(Cu is more expensive)
Distribution lines, Bus bars, Energy Conversion Applications
- OFHC copper
Use of Cd as solute in improving the strength
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Electrical Requirements
Contacts: 1. High switches 2. High Thermal brushes
Conductivity
relays 3. High m.p.
4. Good Oxidation
Resistance
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Candidate Materials - Cu and Ag
Cu is cheaper
Ag, which is expensive, is preferred for critical contacts.
Strength of Ag is increased by dispersed CdO
(Dispersion Strengthening)
Absorbs heat by decomposing
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Resistors:Requirements
1. Uniform resistivity
2. Stable resistance
3. Small temp. Coefficient of resistivity
4. Low thermoelectric pot. w.r.t. copper
5. Good resistance to atmospheric corrosion
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Candidates:
Manganin (87% Cu, 13% Mn)
= 20 × 10-6 K-1 low as compare to that for Cu, which is 4000 × 10-6 K-1 .
Constantan (60% Cu, 40% Ni)
Ballast Resistors are used in circuits to maintain constant current – these must have high .
71% Fe, 29% Ni alloy is used
= 4500 × 10-6 K-1
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Heating RequirementsElements:1. High m.p.
2. High resistivity3. Good Oxidation Resistance4. Good Creep Strength5. Resistance to thermal fatigue
- low elastic modulus- low therm.
expansion
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CandidatesNichrome (80% Ni, 20% Cr)Kanthal (69% Fe, 23% Cr, 6% Al, 2% Co)
SiC
MoSi2Graphite in inert atmosphereMo, Ta Poor oxidation resistance
W (filaments) – ThO2 dispersion to improve creep resistance
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Resistance Thermometers:
Requirement - High Candidate - Platinum (pure metal)
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Superconductors
Section 14.5
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1. Phenomenon
Resistivity of silver
(1
0-11 o
hm m
)
T, K
Fig. 14.7 a
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Resistivity of tin
Can be used for producing large permanent magnetic field
(1
0-11 o
hm m
)
T, K
Fig. 14.7 b
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Loss of superconductivity
0 H
c, W
b m
-2
T, K Tc
Superconductor
Normal
Fig. 14.8
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The maximum current that a superconductor carries at a given temperature below Tc is limited by the magnetic field it produces at the surface of the superconductor
J c,
A m
-2
T, KTc
Superconductor
Normal
Fig not in book
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Meissner Effect
NormalSuperconductor
Fig. 14.9
T>Tc T<Tc
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BCS Theory (Bardeen, Cooper, Schreiffer)
Three way interaction between two electrons and a phonon
Electron pair (cooper pair):
The attractive interaction energy
The repulsive energy
Attraction is disrupted at T Tc
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2. Two types I and II of superconductors
-M -M
Type I Type II
Hc
HH
Hc1 Hc2
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Type II
Great practical interest because of high Jc.
This state is determined by the microstructural conditions of the material
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Heavily cold worked & recovery annealed
Cell walls of high dislocation density
Magnetic flux lines are pinned effectively
Fine grain size Grain boundaries
Pinning action
Dispersed fine precipitate
Interparticle spacing of about 300 Å
Pinning action
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Nb-40% Ti at 4.2 K, 0.9 Hc2
Microstructure Jc, A m-2
Recrystallised 105
Cold worked and recovery annealed
107
Cold worked and precipitation hardened
108
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3. Potential Applications
• Strong Magnets (50 Tesla)
MHD power generation
• Logic and Storage functions in computers
switching times 10 ps
• Levitation
transportation
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• Transmission
No I2R loss
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Yamanashi Maglev Test Line
Magnetic Levitation (Maglev) is a system in which the vehicle runs levitated from the tracks by using electromagnetic forces between superconducting magnets on board the vehicle and coils on the ground.
December 2, 2003, maximum speed 581 km/h (manned run).
Max speed of Rajdhani Express 140 km/h
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Magnetic Resonance Imaging
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4. New Developments
Nb3Ge 23 K 1976
La-Ba-Cu-O 34 K 1986,
Bednorz and
Muller
YBa2Cu3O7-x 90 K 1988
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Recipe: Y2O3, BaCO3, CuO
compacted powder in right proportion
is heated (900 - 1100°C)
BaCO3 BaO + CO2
Annealing at 800 °C in O2 atmosphere
The super conducting properties appear to be sensitive function of the oxygen content and, therefore, of the partial pressure of oxygen during heat treatment
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YBa2Cu3O7-x
Ba
Y
Cu
O
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Engineering aspects remain ElusiveReactive and Brittle
• Unable to support any significant stress• Cannot be easily formed or joined
Superconducting properties deteriorate during heating for forming purposes
Or even in humid room
Attempts
Explosive forming 50 000 atm (100°C)
Isostatic Pressing