Energy-Storage Elements Capacitance and Inductance ELEC 308 Elements of Electrical Engineering Dr. Ron Hayne Images Courtesy of Allan Hambley and Prentice-Hall
Dec 18, 2015
Energy-Storage ElementsCapacitance and Inductance
ELEC 308
Elements of Electrical Engineering
Dr. Ron Hayne
Images Courtesy of Allan Hambley and Prentice-Hall
Energy-Storage Elements
Remember Resistors convert electrical energy into heat
Cannot store energy! Inductors and Capacitors can store energy and
later return it to the circuit Do NOT generate energy! Passive elements, like resistors
Capacitance is a circuit property that accounts for energy STORED in ELECTRIC fields
Inductance is a circuit property that accounts for energy STORED in MAGNETIC fields
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Inductance and Capacitance Uses
Microphones Capacitance changes with sound pressure
Linear variable differential transformer Position of moving iron core converted into voltage
Conversion from DC-AC, AC-DC, AC-AC Electrical signal filters
Combinations of inductances and capacitances in special circuits
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Capacitors
Constructed by separating two sheets of CONDUCTOR (usually metallic) by a thin layer of INSULATING material Insulating material called a DIELECTRIC
Can be air, Mylar®, polyester, polypropylene, mica, etc.
Parallel-plateCapacitor:
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Stored Charge in Terms of Voltage
In an IDEAL capacitor Stored charge, q, is proportional to the voltage
between the plates:
Constant of proportionality is the capacitance, CUnits are farads (F)Units equivalent to Coulombs per voltFarad is a VERY LARGE amount of capacitance
Usually deal with capacitances from 1 pF to 0.01 F Occasionally, use femtofarads (in computer chips)
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q Cv
Current in Terms of Voltage
Remember that current is the time rate of flow of charge
In an IDEAL capacitor The relationship between
current and voltage is
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i dq
dt
d
dtCv C
dv
dt
dt
tdvCti
)()(
Stored Energy in a Capacitor
Remember:
For an ideal capacitor:
For an ideal, uncharged capacitor (v(t0) = 0):
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p t v t i t
p t Cvdv
dt
tCvtw 2
2
1
Parallel-Plate Capacitors
If d<<W and d<<L, the capacitance is approx.
where ε is the dielectric constant of the material BETWEEN the plates
For vacuum, the dielectric constant is
For other materials, where εr is the relative dielectric constant
See Table 3.1 on page 135 of textbook
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0 8.85 10 12 F/m
r0
C A
d
WL
d
Practical Capacitors
Dimensions of 1μF parallel-plate capacitors are TOO LARGE for portable electronic devices
Plates are rolled into smaller area Small-volume capacitors require very thin dielectrics (with
HIGH dielectric constant) Dielectric materials break down when electric field intensity is
TOO HIGH (become conductors) Real capacitors have MAXIMUM VOLTAGE RATING
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Electrolytic Capacitors
One plate is metallic aluminum or tantalum Dielectric is OXIDE layer on surface of the metal Other “plate” is ELECTROLYTIC SOLUTION Metal plate is immersed in the electrolytic solution Gives high capacitance per unit volume
Requires that ONLY ONE polarity of voltage can be applied
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Voltage in Terms of Current
In an IDEAL inductor Voltage across the coil is
proportional to the time rate of change of the current
Constant of proportionality is the inductance, LUnits are henries (H)Units equivalent to volt-seconds per
amperesUsually deal with inductances from
0.001μH to 100 H
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Stored Energy in an Inductor
Remember:
For an ideal inductor:
For an ideal inductor with i(t0) = 0:
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p t v t i t
p t Li t di
dt
w t 1
2Li2 t
Practical Inductors
Cores (metallic iron forms) are made of thin sheets called laminations
Voltages are induced in the core by the changing magnetic fields Cause eddy currents to flow in the core
Dissipate energy Results in UNDESIRABLE core loss
Can reduce eddy-current core loss Laminations Ferrite (iron oxide) cores Powdered iron with insulating binder
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Mutual Inductance
Several coils wound on the same form Magnetic flux produced by one coil links the others Time-varying current flowing through one coil
induces voltages on the other coils
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Power Transmission Losses
Power Line Losses
Large Voltages and Small CurrentsSmaller Line Loss
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2rmslineloss IRP
Power Transmission
Step-Up and Step-Down Transformers 99% Efficiency (vs. 50% with no transformers)
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