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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