chapter 7: energy storage elements ©2001, john wiley & sons, inc. introduction to electric...

Chapter 7: Energy Storage Elements

©2001, John Wiley & Sons, Inc.Introduction To Electric Circuits, 5th Ed

Chapter 7

Energy Storage Elements



Figure 7.1-1 The voltage-controlled switch. (a) Switch symbol. (b) Typical control voltage.



Figure 7.1-2 Using an integrator to measure an interval of time.



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.



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.



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.



Figure 7.3-1 Capacitor connected to a battery.



Figure 7.3-2 Circuit symbol of a capacitor.



Figure 7.3-3 Miniature metal film capacitors ranging from 1 mF to 50 mF. Courtesy of Electronic Concepts, Inc.



Figure 7.3-4 Miniature hermetically sealed polycarbonate capacitors ranging from 1 μF to 50 μF. Courtesy of Electronic Concepts Inc.



Figure 7.3-5 Waveform of the voltage across a capacitor for Example 7.3-1. The units are volts and seconds.



Figure 7.3-6 Current for Example 7.3-1.



Figure 7.3-7 Voltage waveform where the change in voltage occurs over an increment of time t.



Figure 7.3-8 Current waveform for Example 7.3-2. The units are in amperes and seconds.



Figure 7.3-9 Voltage waveform for Example 7.3-2.



Figure E 7.3-1 (a) The voltage source voltage. (b) The circuit.



Figure E 7.3-2 (a) The current source current. (b) The circuit.



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.



Figure 7.4-2 Circuit of Example 7.4-1 with C = 10 mF.



Figure 7.4-3 The voltage across a capacitor.



Figure 7.4-4 The current, power, and energy of the capacitor of Example 7.4-2.



Figure E 7.4-3



Figure 7.5-1 Parallel connection of N capacitors.



Figure 7.5-2 Equivalent circuit for N parallel capacitors.



Figure 7.5-3 Series connection of N capacitors.



Figure 7.5-4 Equivalent circuit for N series capacitors.



Figure 7.5-5 Circuit for Example 7.5-1.



Figure 7.5-6 Circuit resulting from Figure 7.5-5 by replacing C2 and C3 with Cp.



Figure 7.5-7 Equivalent circuit for the circuit of Example 7.5-1.



Figure E 7.5-1



Figure E 7.5-2



Figure E 7.5-3



Figure 7.6-1 Coil of wire connected to a current source.



Figure 7.6-2 Coil wound as a tight helix on a core of area A.



Figure 7.6-3 Model of the inductor.



Figure 7.6-4 Circuit symbol for an inductor.



Figure 7.6-5 Coil with a large inductance. Courtesy of MuRata Company.



Figure 7.6-6Elements with inductances arranged in various forms of coils. Courtesy of Dale Electronic Inc.



Figure 7.6-7 A current waveform. The current is in amperes.



Figure 7.6-8 Voltage response for the current waveform of Figure 7.6-7 when L 0.1 H.



Figure 7.6-9 Voltage waveform for an inductor (in volts).



Figure 7.6-10 Current waveform for an inductor L 0.1 H corresponding to the voltage waveform of Figure 7.6-9.



Figure 7.6-11 Voltage and current waveforms for Example 7.6-1.



Figure E 7.6-1 (a) The current source current. (b) The circuit.



Figure E 7.6-2 (a) The voltage source voltage. (b) The circuit.



Figure 7.7-1 Voltage and current for Example 7.7-1.



Figure 7.7-2 Current, voltage, power, and energy for Example 7.7-2.



Figure 7.7-3 Energy stored in the inductor of Example 7.7-3.



Figure E 7.7-2



Figure 7.8-1 Series of N inductors.



Figure 7.8-2 Equivalent inductor Ls, for N series inductors.



Figure 7.8-3 Connection of N parallel inductors.



Figure 7.8-4 Equivalent inductor Lp for the connection of N parallel inductors.



Figure 7.8-5 The circuit of Example 7.8-1. All inductances in millihenries.



Figure E 7.8-1 All inductances in millihenries.



Figure E 7.8-2 All inductances in millihenries.



Figure E 7.8-3



Figure 7.9-1 An RL circuit. R1 R2 1. The switch is open for t 0 and is closed at t 0.



Figure 7.9-2 An RC circuit. R1 R2 1. The switch is open for t 0 and opens at t 0.



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.



Figure 7.9-4 Circuit of Figure 7.9-3 for t 0.



Figure 7.9-5 Circuit for example 7.9-1. Switch 1 closes at t 0 and switch 2 opens at t 0.



Figure 7.9-6 Circuit of Figure 7.9-5 at t 0.



Figure 7.9-7 Circuit of Figure 7.9-5 at t 0 with the switch closed and the current source disconnected.



Figure 7.10-1 An integrator implemented using an operational amplifier.



Figure 7.10-2 A differentiator implemented using an operational amplifier.



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.



Figure 7.11-2 A plot of the voltage and current of a capacitor.



Figure 7.13-1 The voltage-controlled switch. (a) Switch Symbol. (b) Typical control voltage.



Figure 7.13-2 Using an integrator to measure an interval of time.



Figure 7.13-3 An integrator using an operational amplifier.



Figure 7.13-4 Using an operational amplifier integrator to measure and interval of time.

chapter 7: energy storage elements ©2001, john wiley & sons, inc. introduction to electric...

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