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Chapter 7: Energy Storage Elements
Chapter 7
Energy Storage Elements
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Figure 7.1-1
Chapter 7: Energy Storage Elements
The voltage-controlled switch. (a) Switch
symbol. (b) Typical control voltage.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 7: Energy Storage Elements
Figure 7.1-2
Using an integrator to measure an interval
of time.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Figure 7.2-1
Chapter 7: Energy Storage Elements
Hans C. Oersted (1777-1851), the first person
to observe the magnetic effects of an electric
current. Courtesy of Burndy Library.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 7: Energy Storage Elements
Figure 7.2-2
Michael Faraday’s electrical discoveries were not his only
legacy; his published account of them inspired much of the
scientific work of the later nineteenth century. His
Experimental Researches in Electricity remains one of the
greatest accounts of scientific work ever written. Courtesy
of Burndy Library.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Figure 7.2-3
Chapter 7: Energy Storage Elements
Joseph Henry’s electromagnet. Direct current from the
voltaic pile (B-C) was applied to a coil wound around an
iron horseshoe core (A) to produce a powerful
electromagnet. From Joseph Henry, Galvanic Multiplier,
1831. Courtesy of Burndy Library.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 7: Energy Storage Elements
Figure 7.3-1
Capacitor connected to a battery.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 7: Energy Storage Elements
Figure 7.3-2
Circuit symbol of a capacitor.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 7: Energy Storage Elements
Figure 7.3-3
Miniature metal film capacitors ranging from 1 mF
to 50 mF. Courtesy of Electronic Concepts, Inc.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 7: Energy Storage Elements
Figure 7.3-4
Miniature hermetically sealed polycarbonate
capacitors ranging from 1 μF to 50 μF. Courtesy
of Electronic Concepts Inc.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 7: Energy Storage Elements
Figure 7.3-5
Waveform of the voltage across a capacitor for
Example 7.3-1. The units are volts and
seconds.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 7: Energy Storage Elements
Figure 7.3-6
Current for Example 7.3-1.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 7: Energy Storage Elements
Figure 7.3-7
Voltage waveform where the change in voltage
occurs over an increment of time t.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 7: Energy Storage Elements
Figure 7.3-8
Current waveform for Example 7.3-2. The units
are in amperes and seconds.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 7: Energy Storage Elements
Figure 7.3-9
Voltage waveform for Example 7.3-2.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 7: Energy Storage Elements
Figure E 7.3-1
(a) The voltage source voltage. (b) The
circuit.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 7: Energy Storage Elements
Figure E 7.3-2
(a) The current source current. (b) The
circuit.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 7: Energy Storage Elements
Figure 7.4-1
A circuit (a) where the capacitor is charged and
vc  10 V and (b) the switch is opened at t  0.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 7: Energy Storage Elements
Figure 7.4-2
Circuit of Example 7.4-1 with C = 10 mF.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 7: Energy Storage Elements
Figure 7.4-3
The voltage across a capacitor.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 7: Energy Storage Elements
Figure 7.4-4
The current,
power, and
energy of the
capacitor of
Example 7.4-2.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 7: Energy Storage Elements
Figure E 7.4-3
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 7: Energy Storage Elements
Figure 7.5-1
Parallel connection of N capacitors.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 7: Energy Storage Elements
Figure 7.5-2
Equivalent circuit for N parallel capacitors.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 7: Energy Storage Elements
Figure 7.5-3
Series connection of N capacitors.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 7: Energy Storage Elements
Figure 7.5-4
Equivalent circuit for N series capacitors.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 7: Energy Storage Elements
Figure 7.5-5
Circuit for Example 7.5-1.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 7: Energy Storage Elements
Figure 7.5-6
Circuit resulting from Figure 7.5-5 by replacing
C2 and C3 with Cp.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 7: Energy Storage Elements
Figure 7.5-7
Equivalent circuit for the circuit of Example 7.51.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 7: Energy Storage Elements
Figure E 7.5-1
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 7: Energy Storage Elements
Figure E 7.5-2
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 7: Energy Storage Elements
Figure E 7.5-3
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 7: Energy Storage Elements
Figure 7.6-1
Coil of wire connected to a current
source.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 7: Energy Storage Elements
Figure 7.6-2
Coil wound as a tight helix on a core of
area A.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 7: Energy Storage Elements
Figure 7.6-3
Model of the inductor.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 7: Energy Storage Elements
Figure 7.6-4
Circuit symbol for an inductor.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 7: Energy Storage Elements
Figure 7.6-5
Coil with a large inductance. Courtesy of
MuRata Company.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 7: Energy Storage Elements
Figure 7.6-6
Elements with inductances arranged in various
forms of coils. Courtesy of Dale Electronic Inc.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 7: Energy Storage Elements
Figure 7.6-7
A current waveform. The current is in
amperes.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 7: Energy Storage Elements
Figure 7.6-8
Voltage response for the current
waveform of Figure 7.6-7 when L  0.1 H.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 7: Energy Storage Elements
Figure 7.6-9
Voltage waveform for an inductor (in
volts).
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 7: Energy Storage Elements
Figure 7.6-10
Current waveform for an inductor L  0.1 H
corresponding to the voltage waveform of
Figure 7.6-9.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 7: Energy Storage Elements
Figure 7.6-11
Voltage and current waveforms for
Example 7.6-1.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 7: Energy Storage Elements
Figure E 7.6-1
(a) The current source current. (b) The
circuit.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 7: Energy Storage Elements
Figure E 7.6-2
(a) The voltage source voltage. (b) The
circuit.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 7: Energy Storage Elements
Figure 7.7-1
Voltage and current for Example 7.7-1.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 7: Energy Storage Elements
Figure 7.7-2
Current, voltage, power, and energy for
Example 7.7-2.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 7: Energy Storage Elements
Figure 7.7-3
Energy stored in the inductor of Example
7.7-3.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 7: Energy Storage Elements
Figure E 7.7-2
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 7: Energy Storage Elements
Figure 7.8-1
Series of N inductors.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 7: Energy Storage Elements
Figure 7.8-2
Equivalent inductor Ls, for N series
inductors.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 7: Energy Storage Elements
Figure 7.8-3
Connection of N parallel inductors.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 7: Energy Storage Elements
Figure 7.8-4
Equivalent inductor Lp for the connection
of N parallel inductors.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 7: Energy Storage Elements
Figure 7.8-5
The circuit of Example 7.8-1. All
inductances in millihenries.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 7: Energy Storage Elements
Figure E 7.8-1
All inductances in millihenries.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 7: Energy Storage Elements
Figure E 7.8-2
All inductances in millihenries.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 7: Energy Storage Elements
Figure E 7.8-3
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 7: Energy Storage Elements
Figure 7.9-1
An RL circuit. R1  R2  1. The switch is open
for t  0 and is closed at t  0.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 7: Energy Storage Elements
Figure 7.9-2
An RC circuit. R1  R2  1. The switch is open
for t  0 and opens at t  0.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Figure 7.9-3
Chapter 7: Energy Storage Elements
Circuit with an inductor and a capacitor. The
switch is closed for a long time prior to opening
at t  0.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 7: Energy Storage Elements
Figure 7.9-4
Circuit of Figure 7.9-3 for t  0.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 7: Energy Storage Elements
Figure 7.9-5
Circuit for example 7.9-1. Switch 1 closes
at t  0 and switch 2 opens at t  0.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 7: Energy Storage Elements
Figure 7.9-6
Circuit of Figure 7.9-5 at t  0.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 7: Energy Storage Elements
Figure 7.9-7
Circuit of Figure 7.9-5 at t  0 with the switch
closed and the current source disconnected.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 7: Energy Storage Elements
Figure 7.10-1
An integrator implemented using an
operational amplifier.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 7: Energy Storage Elements
Figure 7.10-2
A differentiator implemented using an
operational amplifier.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 7: Energy Storage Elements
Figure 7.11-1
MATLAB input files representing (a) the capacitor
current, (b) the capacitor voltage and (c) the MATLAB
input file used to plot the capacitor current and voltage.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 7: Energy Storage Elements
Figure 7.11-2
A plot of the voltage and current of a
capacitor.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 7: Energy Storage Elements
Figure 7.13-1
The voltage-controlled switch. (a) Switch
Symbol. (b) Typical control voltage.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 7: Energy Storage Elements
Figure 7.13-2
Using an integrator to measure an interval
of time.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 7: Energy Storage Elements
Figure 7.13-3
An integrator using an operational
amplifier.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 7: Energy Storage Elements
Figure 7.13-4
Using an operational amplifier integrator
to measure and interval of time.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed