Energy-Storage Elements Capacitance and Inductance

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Energy-Storage ElementsCapacitance and Inductance

• ELEC 308
• Elements of Electrical Engineering
• Dr. Ron Hayne
• Images Courtesy of Allan Hambley and Prentice-Hall

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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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Fluid-Flow Analogy
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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, C
• Units are farads (F)
• Units equivalent to Coulombs per volt
• Farad 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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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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Example 3.1

• Plot the current vs. time

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Stored Energy in a Capacitor

• Remember
• For an ideal capacitor
• For an ideal, uncharged capacitor (v(t0) 0)

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Example 3.3

• Plot current, power delivered and energy stored

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Capacitances in Parallel
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Capacitances in Series
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Parallel-Plate Capacitors
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Parallel-Plate Capacitors

• If dltltW and dltltL, the capacitance is approx.
• where e is the dielectric constant of the
  material BETWEEN the plates
• For vacuum, the dielectric constant is
• For other materials, where er is the relative
  dielectric constant
• See Table 3.1 on page 135 of textbook

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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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Inductors

• Constructed by coiling a wire around some type of
  form

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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, L
• Units are henries (H)
• Units equivalent to volt-seconds per amperes
• Usually 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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Example 3.6

• Plot voltage, power, and energy

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Equivalent Inductance
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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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Electronic Photo Flash
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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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Mutual Inductance

• Flux of one coil aids the flux produced by the
  other coil

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Ideal Transformers
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Ideal Transformers
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Power Transmission Losses

• Power Line Losses
• Large Voltages and Small Currents
• Smaller Line Loss

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Power Transmission

• Step-Up and Step-Down Transformers
• 99 Efficiency (vs. 50 with no transformers)

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U.S. Power Grid
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Summary

• Capacitance
• Voltage
• Current
• Power
• Energy
• Series
• Parallel

• Inductance
• Voltage
• Current
• Power
• Energy
• Series
• Parallel
• Mutual Inductance
• Transformers