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Chapter 7: Energy Storage Elements
©2001, John Wiley & Sons, Inc.Introduction To Electric Circuits, 5th Ed
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 The voltage-controlled switch. (a) Switch symbol. (b) Typical control voltage.
Chapter 7: Energy Storage Elements
©2001, John Wiley & Sons, Inc.Introduction To Electric Circuits, 5th Ed
Figure 7.1-2 Using an integrator to measure an interval of time.
Chapter 7: Energy Storage Elements
©2001, John Wiley & Sons, Inc.Introduction To Electric Circuits, 5th Ed
Figure 7.2-1 Hans C. Oersted (1777-1851), the first person to observe the magnetic effects of an electric current. Courtesy of Burndy Library.
Chapter 7: Energy Storage Elements
©2001, John Wiley & Sons, Inc.Introduction To Electric Circuits, 5th Ed
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.
Chapter 7: Energy Storage Elements
©2001, John Wiley & Sons, Inc.Introduction To Electric Circuits, 5th Ed
Figure 7.2-3 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.
Chapter 7: Energy Storage Elements
©2001, John Wiley & Sons, Inc.Introduction To Electric Circuits, 5th Ed
Figure 7.3-1 Capacitor connected to a battery.
Chapter 7: Energy Storage Elements
©2001, John Wiley & Sons, Inc.Introduction To Electric Circuits, 5th Ed
Figure 7.3-2 Circuit symbol of a capacitor.
Chapter 7: Energy Storage Elements
©2001, John Wiley & Sons, Inc.Introduction To Electric Circuits, 5th Ed
Figure 7.3-3 Miniature metal film capacitors ranging from 1 mF to 50 mF. Courtesy of Electronic Concepts, Inc.
Chapter 7: Energy Storage Elements
©2001, John Wiley & Sons, Inc.Introduction To Electric Circuits, 5th Ed
Figure 7.3-4 Miniature hermetically sealed polycarbonate capacitors ranging from 1 μF to 50 μF. Courtesy of Electronic Concepts Inc.
Chapter 7: Energy Storage Elements
©2001, John Wiley & Sons, Inc.Introduction To Electric Circuits, 5th Ed
Figure 7.3-5 Waveform of the voltage across a capacitor for Example 7.3-1. The units are volts and seconds.
Chapter 7: Energy Storage Elements
©2001, John Wiley & Sons, Inc.Introduction To Electric Circuits, 5th Ed
Figure 7.3-6 Current for Example 7.3-1.
Chapter 7: Energy Storage Elements
©2001, John Wiley & Sons, Inc.Introduction To Electric Circuits, 5th Ed
Figure 7.3-7 Voltage waveform where the change in voltage occurs over an increment of time t.
Chapter 7: Energy Storage Elements
©2001, John Wiley & Sons, Inc.Introduction To Electric Circuits, 5th Ed
Figure 7.3-8 Current waveform for Example 7.3-2. The units are in amperes and seconds.
Chapter 7: Energy Storage Elements
©2001, John Wiley & Sons, Inc.Introduction To Electric Circuits, 5th Ed
Figure 7.3-9 Voltage waveform for Example 7.3-2.
Chapter 7: Energy Storage Elements
©2001, John Wiley & Sons, Inc.Introduction To Electric Circuits, 5th Ed
Figure E 7.3-1 (a) The voltage source voltage. (b) The circuit.
Chapter 7: Energy Storage Elements
©2001, John Wiley & Sons, Inc.Introduction To Electric Circuits, 5th Ed
Figure E 7.3-2 (a) The current source current. (b) The circuit.
Chapter 7: Energy Storage Elements
©2001, John Wiley & Sons, Inc.Introduction To Electric Circuits, 5th Ed
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.
Chapter 7: Energy Storage Elements
©2001, John Wiley & Sons, Inc.Introduction To Electric Circuits, 5th Ed
Figure 7.4-2 Circuit of Example 7.4-1 with C = 10 mF.
Chapter 7: Energy Storage Elements
©2001, John Wiley & Sons, Inc.Introduction To Electric Circuits, 5th Ed
Figure 7.4-3 The voltage across a capacitor.
Chapter 7: Energy Storage Elements
©2001, John Wiley & Sons, Inc.Introduction To Electric Circuits, 5th Ed
Figure 7.4-4 The current, power, and energy of the capacitor of Example 7.4-2.
Chapter 7: Energy Storage Elements
©2001, John Wiley & Sons, Inc.Introduction To Electric Circuits, 5th Ed
Figure E 7.4-3
Chapter 7: Energy Storage Elements
©2001, John Wiley & Sons, Inc.Introduction To Electric Circuits, 5th Ed
Figure 7.5-1 Parallel connection of N capacitors.
Chapter 7: Energy Storage Elements
©2001, John Wiley & Sons, Inc.Introduction To Electric Circuits, 5th Ed
Figure 7.5-2 Equivalent circuit for N parallel capacitors.
Chapter 7: Energy Storage Elements
©2001, John Wiley & Sons, Inc.Introduction To Electric Circuits, 5th Ed
Figure 7.5-3 Series connection of N capacitors.
Chapter 7: Energy Storage Elements
©2001, John Wiley & Sons, Inc.Introduction To Electric Circuits, 5th Ed
Figure 7.5-4 Equivalent circuit for N series capacitors.
Chapter 7: Energy Storage Elements
©2001, John Wiley & Sons, Inc.Introduction To Electric Circuits, 5th Ed
Figure 7.5-5 Circuit for Example 7.5-1.
Chapter 7: Energy Storage Elements
©2001, John Wiley & Sons, Inc.Introduction To Electric Circuits, 5th Ed
Figure 7.5-6 Circuit resulting from Figure 7.5-5 by replacing C2 and C3 with Cp.
Chapter 7: Energy Storage Elements
©2001, John Wiley & Sons, Inc.Introduction To Electric Circuits, 5th Ed
Figure 7.5-7 Equivalent circuit for the circuit of Example 7.5-1.
Chapter 7: Energy Storage Elements
©2001, John Wiley & Sons, Inc.Introduction To Electric Circuits, 5th Ed
Figure E 7.5-1
Chapter 7: Energy Storage Elements
©2001, John Wiley & Sons, Inc.Introduction To Electric Circuits, 5th Ed
Figure E 7.5-2
Chapter 7: Energy Storage Elements
©2001, John Wiley & Sons, Inc.Introduction To Electric Circuits, 5th Ed
Figure E 7.5-3
Chapter 7: Energy Storage Elements
©2001, John Wiley & Sons, Inc.Introduction To Electric Circuits, 5th Ed
Figure 7.6-1 Coil of wire connected to a current source.
Chapter 7: Energy Storage Elements
©2001, John Wiley & Sons, Inc.Introduction To Electric Circuits, 5th Ed
Figure 7.6-2 Coil wound as a tight helix on a core of area A.
Chapter 7: Energy Storage Elements
©2001, John Wiley & Sons, Inc.Introduction To Electric Circuits, 5th Ed
Figure 7.6-3 Model of the inductor.
Chapter 7: Energy Storage Elements
©2001, John Wiley & Sons, Inc.Introduction To Electric Circuits, 5th Ed
Figure 7.6-4 Circuit symbol for an inductor.
Chapter 7: Energy Storage Elements
©2001, John Wiley & Sons, Inc.Introduction To Electric Circuits, 5th Ed
Figure 7.6-5 Coil with a large inductance. Courtesy of MuRata Company.
Chapter 7: Energy Storage Elements
©2001, John Wiley & Sons, Inc.Introduction To Electric Circuits, 5th Ed
Figure 7.6-6Elements with inductances arranged in various forms of coils. Courtesy of Dale Electronic Inc.
Chapter 7: Energy Storage Elements
©2001, John Wiley & Sons, Inc.Introduction To Electric Circuits, 5th Ed
Figure 7.6-7 A current waveform. The current is in amperes.
Chapter 7: Energy Storage Elements
©2001, John Wiley & Sons, Inc.Introduction To Electric Circuits, 5th Ed
Figure 7.6-8 Voltage response for the current waveform of Figure 7.6-7 when L 0.1 H.
Chapter 7: Energy Storage Elements
©2001, John Wiley & Sons, Inc.Introduction To Electric Circuits, 5th Ed
Figure 7.6-9 Voltage waveform for an inductor (in volts).
Chapter 7: Energy Storage Elements
©2001, John Wiley & Sons, Inc.Introduction To Electric Circuits, 5th Ed
Figure 7.6-10 Current waveform for an inductor L 0.1 H corresponding to the voltage waveform of Figure 7.6-9.
Chapter 7: Energy Storage Elements
©2001, John Wiley & Sons, Inc.Introduction To Electric Circuits, 5th Ed
Figure 7.6-11 Voltage and current waveforms for Example 7.6-1.
Chapter 7: Energy Storage Elements
©2001, John Wiley & Sons, Inc.Introduction To Electric Circuits, 5th Ed
Figure E 7.6-1 (a) The current source current. (b) The circuit.
Chapter 7: Energy Storage Elements
©2001, John Wiley & Sons, Inc.Introduction To Electric Circuits, 5th Ed
Figure E 7.6-2 (a) The voltage source voltage. (b) The circuit.
Chapter 7: Energy Storage Elements
©2001, John Wiley & Sons, Inc.Introduction To Electric Circuits, 5th Ed
Figure 7.7-1 Voltage and current for Example 7.7-1.
Chapter 7: Energy Storage Elements
©2001, John Wiley & Sons, Inc.Introduction To Electric Circuits, 5th Ed
Figure 7.7-2 Current, voltage, power, and energy for Example 7.7-2.
Chapter 7: Energy Storage Elements
©2001, John Wiley & Sons, Inc.Introduction To Electric Circuits, 5th Ed
Figure 7.7-3 Energy stored in the inductor of Example 7.7-3.
Chapter 7: Energy Storage Elements
©2001, John Wiley & Sons, Inc.Introduction To Electric Circuits, 5th Ed
Figure E 7.7-2
Chapter 7: Energy Storage Elements
©2001, John Wiley & Sons, Inc.Introduction To Electric Circuits, 5th Ed
Figure 7.8-1 Series of N inductors.
Chapter 7: Energy Storage Elements
©2001, John Wiley & Sons, Inc.Introduction To Electric Circuits, 5th Ed
Figure 7.8-2 Equivalent inductor Ls, for N series inductors.
Chapter 7: Energy Storage Elements
©2001, John Wiley & Sons, Inc.Introduction To Electric Circuits, 5th Ed
Figure 7.8-3 Connection of N parallel inductors.
Chapter 7: Energy Storage Elements
©2001, John Wiley & Sons, Inc.Introduction To Electric Circuits, 5th Ed
Figure 7.8-4 Equivalent inductor Lp for the connection of N parallel inductors.
Chapter 7: Energy Storage Elements
©2001, John Wiley & Sons, Inc.Introduction To Electric Circuits, 5th Ed
Figure 7.8-5 The circuit of Example 7.8-1. All inductances in millihenries.
Chapter 7: Energy Storage Elements
©2001, John Wiley & Sons, Inc.Introduction To Electric Circuits, 5th Ed
Figure E 7.8-1 All inductances in millihenries.
Chapter 7: Energy Storage Elements
©2001, John Wiley & Sons, Inc.Introduction To Electric Circuits, 5th Ed
Figure E 7.8-2 All inductances in millihenries.
Chapter 7: Energy Storage Elements
©2001, John Wiley & Sons, Inc.Introduction To Electric Circuits, 5th Ed
Figure E 7.8-3
Chapter 7: Energy Storage Elements
©2001, John Wiley & Sons, Inc.Introduction To Electric Circuits, 5th Ed
Figure 7.9-1 An RL circuit. R1 R2 1. The switch is open for t 0 and is closed at t 0.
Chapter 7: Energy Storage Elements
©2001, John Wiley & Sons, Inc.Introduction To Electric Circuits, 5th Ed
Figure 7.9-2 An RC circuit. R1 R2 1. The switch is open for t 0 and opens at t 0.
Chapter 7: Energy Storage Elements
©2001, John Wiley & Sons, Inc.Introduction To Electric Circuits, 5th Ed
Figure 7.9-3 Circuit with an inductor and a capacitor. The switch is closed for a long time prior to opening at t 0.
Chapter 7: Energy Storage Elements
©2001, John Wiley & Sons, Inc.Introduction To Electric Circuits, 5th Ed
Figure 7.9-4 Circuit of Figure 7.9-3 for t 0.
Chapter 7: Energy Storage Elements
©2001, John Wiley & Sons, Inc.Introduction To Electric Circuits, 5th Ed
Figure 7.9-5 Circuit for example 7.9-1. Switch 1 closes at t 0 and switch 2 opens at t 0.
Chapter 7: Energy Storage Elements
©2001, John Wiley & Sons, Inc.Introduction To Electric Circuits, 5th Ed
Figure 7.9-6 Circuit of Figure 7.9-5 at t 0.
Chapter 7: Energy Storage Elements
©2001, John Wiley & Sons, Inc.Introduction To Electric Circuits, 5th Ed
Figure 7.9-7 Circuit of Figure 7.9-5 at t 0 with the switch closed and the current source disconnected.
Chapter 7: Energy Storage Elements
©2001, John Wiley & Sons, Inc.Introduction To Electric Circuits, 5th Ed
Figure 7.10-1 An integrator implemented using an operational amplifier.
Chapter 7: Energy Storage Elements
©2001, John Wiley & Sons, Inc.Introduction To Electric Circuits, 5th Ed
Figure 7.10-2 A differentiator implemented using an operational amplifier.
Chapter 7: Energy Storage Elements
©2001, John Wiley & Sons, Inc.Introduction To Electric Circuits, 5th Ed
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.
Chapter 7: Energy Storage Elements
©2001, John Wiley & Sons, Inc.Introduction To Electric Circuits, 5th Ed
Figure 7.11-2 A plot of the voltage and current of a capacitor.
Chapter 7: Energy Storage Elements
©2001, John Wiley & Sons, Inc.Introduction To Electric Circuits, 5th Ed
Figure 7.13-1 The voltage-controlled switch. (a) Switch Symbol. (b) Typical control voltage.
Chapter 7: Energy Storage Elements
©2001, John Wiley & Sons, Inc.Introduction To Electric Circuits, 5th Ed
Figure 7.13-2 Using an integrator to measure an interval of time.
Chapter 7: Energy Storage Elements
©2001, John Wiley & Sons, Inc.Introduction To Electric Circuits, 5th Ed
Figure 7.13-3 An integrator using an operational amplifier.
Chapter 7: Energy Storage Elements
©2001, John Wiley & Sons, Inc.Introduction To Electric Circuits, 5th Ed
Figure 7.13-4 Using an operational amplifier integrator to measure and interval of time.