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 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 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 Hans C. Oersted ( ), 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 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 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, Courtesy of Burndy Library.

Chapter 7: Energy Storage Elements ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Figure Capacitor connected to a battery.

Chapter 7: Energy Storage Elements ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Figure Circuit symbol of a capacitor.

Chapter 7: Energy Storage Elements ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Figure 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 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 Waveform of the voltage across a capacitor for Example The units are volts and seconds.

Chapter 7: Energy Storage Elements ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Figure Current for Example

Chapter 7: Energy Storage Elements ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Figure 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 Current waveform for Example The units are in amperes and seconds.

Chapter 7: Energy Storage Elements ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Figure Voltage waveform for Example

Chapter 7: Energy Storage Elements ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Figure E (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 (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 A circuit (a) where the capacitor is charged and v c  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 Circuit of Example with C = 10 mF.

Chapter 7: Energy Storage Elements ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Figure The voltage across a capacitor.

Chapter 7: Energy Storage Elements ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Figure The current, power, and energy of the capacitor of Example

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 Parallel connection of N capacitors.

Chapter 7: Energy Storage Elements ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Figure Equivalent circuit for N parallel capacitors.

Chapter 7: Energy Storage Elements ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Figure Series connection of N capacitors.

Chapter 7: Energy Storage Elements ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Figure Equivalent circuit for N series capacitors.

Chapter 7: Energy Storage Elements ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Figure Circuit for Example

Chapter 7: Energy Storage Elements ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Figure Circuit resulting from Figure by replacing C 2 and C 3 with C p.

Chapter 7: Energy Storage Elements ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Figure Equivalent circuit for the circuit of Example

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 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 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 Model of the inductor.

Chapter 7: Energy Storage Elements ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Figure Circuit symbol for an inductor.

Chapter 7: Energy Storage Elements ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Figure 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 Elements 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 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 Voltage response for the current waveform of Figure when L  0.1 H.

Chapter 7: Energy Storage Elements ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Figure Voltage waveform for an inductor (in volts).

Chapter 7: Energy Storage Elements ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Figure Current waveform for an inductor L  0.1 H corresponding to the voltage waveform of Figure

Chapter 7: Energy Storage Elements ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Figure Voltage and current waveforms for Example

Chapter 7: Energy Storage Elements ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Figure E (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 (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 Voltage and current for Example

Chapter 7: Energy Storage Elements ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Figure Current, voltage, power, and energy for Example

Chapter 7: Energy Storage Elements ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Figure Energy stored in the inductor of Example

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 Series of N inductors.

Chapter 7: Energy Storage Elements ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Figure Equivalent inductor L s, for N series inductors.

Chapter 7: Energy Storage Elements ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Figure Connection of N parallel inductors.

Chapter 7: Energy Storage Elements ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Figure Equivalent inductor L p for the connection of N parallel inductors.

Chapter 7: Energy Storage Elements ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Figure The circuit of Example All inductances in millihenries.

Chapter 7: Energy Storage Elements ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Figure E All inductances in millihenries.

Chapter 7: Energy Storage Elements ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Figure E 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 An RL circuit. R 1  R 2  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 An RC circuit. R 1  R 2  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 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 Circuit of Figure for t  0.

Chapter 7: Energy Storage Elements ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Figure Circuit for example 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 Circuit of Figure at t  0 .

Chapter 7: Energy Storage Elements ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Figure Circuit of Figure 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 An integrator implemented using an operational amplifier.

Chapter 7: Energy Storage Elements ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Figure A differentiator implemented using an operational amplifier.

Chapter 7: Energy Storage Elements ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Figure 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 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 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 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 An integrator using an operational amplifier.

Chapter 7: Energy Storage Elements ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Figure Using an operational amplifier integrator to measure and interval of time.