The Energy Storage Elements

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CHAPTER 5

• The Energy Storage Elements

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• The capacitor is a device that stores charge

The charge and the applied voltage are related by
the capacitance of the capacitor as

• Q CV

For a time varying source v(t) we have
q(t) C v(t)
The unit of capacitance is coulomb/volt or Farad
For plates if size A (m2) separated by distance
d(m) with air in between the capacitance is

• C 8.8410¹²? A/d F

Figure 5.1 A parallel-plate capacitor.
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Passive sign convention
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Capacitor Energy

• The instantaneous power delivered to the
  capacitor is

The energy stored in a capacitor at a particular
time can be found by
Assuming capacitor voltage is zero at
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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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5.1.1 Capacitors in Parallel
The terminal voltage is equal to the voltage of
each capacitors v(t) v1(t) v2(t).vn(t)
The current entering the combination is the sum
of currents of each capacitor i(t)
i1(t)i2(t)in(t)
From relation
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5.1.1 Capacitors in Series
v(t) v1(t) v2(t) . vn(t) i(t) i1(t)
i2(t) in(t)
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The Inductor

• A device that stores energy in its magnetic field

The current produces a magnetic field round the
wire
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The relation between the voltage and current of
inductor is
This relation can be inverted to yield
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The energy stored in an inductor
The instantaneous power of an inductor
Thus the energy stored in an inductor is
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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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Inductors in Series
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Inductors in Parallel
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v(t)2t 0lttlt1 V(t) -2t4
1lttlt2
iLt2/2 0lttlt1 iL -t2/22t
1lttlt2