Lesson 14

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Lesson 14 Capacitors Inductors
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Learning Objectives

• Define capacitance and state its symbol and unit
  of measurement.
• Predict the capacitance of a parallel plate
  capacitor.
• Analyze how a capacitor stores energy.
• Define inductance and state its symbol and unit
  of measurement.
• Predict the inductance of a coil of wire.
• Analyze how an inductor stores energy.

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CAPACITORS AND INDUCTORS

• For resistive circuits, the voltage-current
  relationships are linear and algebraic. Resistors
  can only dissipate energy they cannot store
  energy and return it to a circuit at a later
  time.
• This is not the case for capacitors and
  inductors. Capacitors and inductors are dynamic
  elements.
• The voltage-current relationships are non-linear
  and differential.
• They are dynamic because they store energy.

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Capacitor

• A capacitor is passive element designed to store
  energy in its electric field. This energy can
  then be provided to a circuit at a later time.
• Capacitors consist of two conductors (parallel
  plates) separated by an insulator (or
  dielectric).
• Capacitors accumulate electric charge.
• Conductive plates can become charged with
  opposite charges

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Capacitor

• Electrons are pulled from top plate (creating
  positive charge)
• Electrons are deposited on bottom plate (creating
  negative charge)

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Capacitor

• While charging a capacitor
• The voltage developed across the capacitor will
  increase as charge is deposited
• Current goes to zero once the voltage developed
  across the capacitor is equal to the source
  voltage

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Definition of Capacitance

• Capacitance of the capacitor is a measure of the
  capacitors ability to store charge.
• Unit is the farad (F).
• Capacitance of a capacitor (C)
• Is one farad if it stores one coulomb of charge
  when the voltage across its terminals is one volt

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Effect of Geometry

• Increased surface area means increased
  Capacitance
• Larger plate will be able to hold more charge

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Effect of Geometry

• Reduced separation distance means increased
  Capacitance
• As plates are moved closer together
• Force of attraction between opposite charges is
  greater
• Capacitance
• Inversely proportional to distance between plates

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Effect of Dielectric

• Substituting a dielectric material for the air
  gap will increase the Capacitance
• Dielectric Constant ? epsillon is calculated by
  using the relative dielectric constant and the
  absolute dielectric constant for air
• ? ?r ?0 (F/m)
• where ?0 8.854 x 10-12 F/m

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Capacitance of Parallel-Plates

• Putting the factors together, capacitance of
  parallel-plate capacitor is given bywhere ?r
  is the relative dielectric constant ?0 8.854
  x 10-12 F/m
• A is area d is the distance between plates

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Example Problem 1

• A parallel-plate capacitor with a vacuum
  dielectric has dimensions of 1 cm x 1.5 cm and
  separation of 0.1 mm. What is its capacitance?
• What would its capacitance be if the dielectric
  were mica?

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Dielectric Voltage Breakdown

• High voltage will cause an electrical discharge
  between the parallel plates
• Above a critical voltage, the force on the
  electrons is so great that they become torn from
  their orbit within the dielectric
• This damages the dielectric material, leaving
  carbonized pinholes which short the plates
  together

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Dielectric Voltage Breakdown

• The working voltage is the maximum operating
  voltage of a capacitor beyond which damage may
  occur
• This voltage can be calculated using the
  materials dielectric strength K (kV/mm)

Dielectric Strength (K) Dielectric Strength (K)
Material kV/mm
Air 3
Ceramic (high ?r) 3
Mica 40
Myler 16
Oil 15
Polystyrene 24
Rubber 18
Teflon 60
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Capacitance and Steady State DC

• In steady state DC, the rate of change of voltage
  is zero, therefore the current through a
  capacitor is zero.
• A capacitor looks like an open circuit with
  voltage vC in steady state DC.

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CAPACITORS IN SERIES AND IN PARALLEL

• Capacitors, like resistors, can be placed in
  series and in parallel.
• Increasing levels of capacitance can be obtained
  by placing capacitors in parallel, while
  decreasing levels can be obtained by placing
  capacitors in series.

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CAPACITORS IN SERIES AND IN PARALLEL
Capacitors in series are combined in the same
manner as resistor sin parallel.
Capacitors in parallel are combined in the same
manner as resistors in series.
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Power and work

• The energy (or work) stored in a capacitor under
  steady-state conditions is given by

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Inductor

• An inductor is a passive element designed to
  store energy in its magnetic field.
• Inductors consist of a coil of wire, often wound
  around a core of high magnetic permeability.

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Faradays Experiment 4 Self-induced voltage
?

• Voltage is induced across coil when i is
  changing.
• When i is steady state, the voltage across coil
  returns to zero.

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Faradays Law

• From these observations, he concludedA voltage
  is induced in a circuit whenever the flux linking
  the circuit is changing and the magnitude of the
  voltage is proportional to the rate of change of
  the flux linkages.

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EMF in an Inductor
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Counter EMF

• Induced voltage tries to counter changes in
  current so it is called counter emf or back
  voltage.
• BEMF ensures that any current changes in an
  inductor are gradual.
• An inductor RESISTS the change of current in a
  circuit
• Acts like a short circuit when current is constant

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INDUCTANCEInductor Construction

• The level of inductance is dependent on the area
  within the coil, the length of the unit, to the
  number of turns of wire in the coil and the
  permeability of the core material.

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Inductor calculations

• Induced emf in an inductor can be calculated
• L is the self-inductance of the coil. Units are
  Henry (H).
• The inductance of a coil is one henry if changing
  its current at one ampere per second inducesa
  potential difference of one volt across the coil.

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Example Problem 2

• The current in a 0.4 H inductor is changing at
  the rate of 200 A/sec. What is the voltage across
  it?

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Inductance and Steady State DC

• In steady state DC, the rate of change of current
  is zero, therefore the induced voltage across an
  inductor is also zero.
• An inductor looks like a short circuit in steady
  state dc.

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INDUCTORS IN SERIES AND IN PARALLEL

• Inductors, like resistors and capacitors, can be
  placed in series or in parallel.
• Increasing levels of inductance can be obtained
  by placing inductors in series, while decreasing
  levels can be obtained by placing inductors in
  parallel.

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INDUCTORS IN SERIES AND IN PARALLEL

• Inductors in series are combined in the same way
  as resistors in series.
• Inductors in parallel are combined in the same
  way as resistors in parallel.

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Inductor Energy Storage