6.1 The Inductor

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6.1 The Inductor
Is a passive element ( can not generate energy)
However the inductor is capable of storing energy
in the magnetic field which can be released
Represented graphically as a coiled wire
Symbolized by the letter L
Measured in henrys (H)
The voltage drop across the inductor the inductor
and the current in the direction of voltage drop
are related as follows
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Example 6.1
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(b) At what instant of time is the current
maximum ?
Since the maximum will occur were the derivative
of the current is zero
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(c) Find the voltage across the terminals of the
inductor ?
(d) Sketch the voltage across the terminals
of the inductor ?
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(e) Are the voltage and the current at a maximum
at the same time ?
Since the voltage across the inductor is
proportional to di/dt not i
the voltage maximum is not at the same time as
current maximum
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(f) At what instant of time does the voltage
change polarity ?
At t 0.2 s which corresponds to the moment
when di/dt is passing through zero changing sign
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(g) Is there ever an instantaneous change in
voltage across the inductor ? If so at what time ?
Yes, At t 0 s
Note that the voltage can change instantaneously
across the terminals of an inductor
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Current in an Inductor in Terms of the Voltage
Across the Inductor
Since
Multiplying both side by the differential dt
OR
Integrating both side with respect to the
differentials di and dt we have
Note we used x and t the variables of
integration, were i and t become limits on
the integrals
( x and t become dummy variables )
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Example 6.2 The voltage pulse applied to the
100mH inductor. Assume i 0 for t 0
(a) Sketch the voltage v(t) ?
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(b) Find the inductor current i(t) ?
(c) Sketch the current i(t) ?
Note the inductor current i(t) approaches a
constant vlue of 2 A as t increases.
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Power and Energy in the Inductor
Integrating both side with respect to the
differentials dw and di were w 0 if i 0
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The Inductor
The Capacitor
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Inductors in Series
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Therefore inductor combine like resistor
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5.1.1 Capacitors in Series
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5.1.1 Capacitors in Parallel
Therefore capacitor combine like conductor
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Example 5.1

• A voltage source is applied to a 5-F capacitor as
  shown.
• Sketch the capacitor current and the stored
  energy as a function of time.

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Example 5.2

• A current source is applied to a 5-F capacitor.
• Sketch the capacitor voltage as a function of
  time.

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The capacitor voltage is related to area Under
current source.
For example area at t 1 s is
Area of Triangle is (1)(10)10
V(1s)10/5 2V.
For example area at t3 s is 10105 25 hence
V(3s)25/5 5V.
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Example 5.3

• A current source is applied to a 5-H inductor as
  shown. Sketch the voltage across the inductor
  versus time.

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Example 5.4

• A voltage source is applied to a 5-H inductor
  as shown. Sketch the inductor current versus
  time.

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EE 202-01 Fall 2012(121)--Quiz 4
For the circuit shown above , if no energy
initially stored in the capacitor, find the
followings
 (b) The energy stored at the capacitor at t
1 s ?
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Solution
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 (b) The energy stored at the capacitor at t
1 s ?