Joseph Henry American Physicist (1797–1878) Henry became the first director of the Smithsonian Institution and first president of the Academy of Natural Science. He improved the design of the electromagnet and constructed one of the first motors. He also discovered the phenomenon of self-induction but failed to publish his findings. The unit of inductance, the henry, is named in his honor. (North Wind Picture Archives) p.1005

Fig 32-CO An airport metal detector contains a large coil of wire around the frame. This coil has a property called inductance. When a passenger carries metal through the detector, the inductance of the coil changes, and the change in inductance signals an alarm to sound. (Jack Hollingsworth/Getty Images) Fig 32-CO, p.1003

Miniature air-core and magnetic inductors (5 mm x 5 mm) Air-core inductor Magnetic-core inductor Cu Si NiZnCu ferrite 140nm Cu/40 nm Ti 20nm Au/20 nm Ti 65μm Cu Si 300 nm thick SiO2 140nm Cu/40 nm Ti 20nm Au/20 nm Ti 65μm 4” wafer 4” wafer 3 CONFIDENTIAL

Figure 32.1 After the switch is closed, the current produces a magnetic flux through the area enclosed by the loop. As the current increases toward its equilibrium value, this magnetic flux changes in time and induces an emf in the loop. Fig 32-1, p.1004

Figure 32.2 (a) A current in the coil produces a magnetic field directed to the left. (b) If the current increases, the increasing magnetic flux creates an induced emf having the polarity shown by the dashed battery. (c) The polarity of the induced emf reverses if the current decreases. Fig 32-2, p.1005

Active Figure 32. 3 A series RL circuit Active Figure 32.3 A series RL circuit. As the current increases toward its maximum value, an emf that opposes the increasing current is induced in the inductor. Fig 32-3, p.1007

Active Figure 32.17 Energy transfer in a resistanceless, nonradiating LC circuit. The capacitor has a charge Qmax at t = 0, the instant at which the switch is closed. The mechanical analog of this circuit is a block–spring system. Fig 32-17, p.1017

Active Figure 32.4 Plot of the current versus time for the RL circuit shown in Figure 32.3. The switch is open for t= 0 and then closed at t < 0, and the current increases toward its maximum value /R. The time constant is the time interval required for I to reach 63.2% of its maximum value. Fig 32-4, p.1008

Figure 32.5 Plot of dI/dt versus time for the RL circuit shown in Figure 32.3. The time rate of change of current is a maximum at t 0, which is the instant at which the switch is closed. The rate decreases exponentially with time as I increases toward its maximum value. Fig 32-5, p.1008

Active Figure 32. 6 An RL circuit Active Figure 32.6 An RL circuit. When the switch S is in position a, the battery is in the circuit. When the switch is thrown to position b, the battery is no longer part of the circuit. The switch is designed so that it is never open, which would cause the current to stop. Fig 32-6, p.1008

Active Figure 32.7 Current versus time for the right-hand loop of the circuit shown in Figure 32.6. For t < 0, the switch S is at position a. At t = 0, the switch is thrown to position b, and the current has its maximum value /R. Fig 32-7, p.1009

Fig 32-8, p.1009

Fig 32-9, p.1009

Fig 32-10, p.1010

Figure 32.11 (Example 32.3) (a) The switch in this RL circuit is open for t < 0 and then closed at t = 0. (b) A graph of the current versus time for the circuit in part (a). Fig 32-11, p.1010

Figure 32.11 (Example 32.3) (a) The switch in this RL circuit is open for t < 0 and then closed at t = 0. Fig 32-11a, p.1010

Figure 32.11 (Example 32.3) (b) A graph of the current versus time for the circuit in part (a). Fig 32-11b, p.1010

Figure 32.12 (Example 32.3) The time behavior of the potential differences across the resistor and inductor in Figure 32.11a. Fig 32-12, p.1010

Figure 32. 13 (Example 32. 5) Section of a long coaxial cable Figure 32.13 (Example 32.5) Section of a long coaxial cable. The inner and outer conductors carry equal currents in opposite directions. Fig 32-13, p.1013

Figure 32. 14 A cross-sectional view of two adjacent coils Figure 32.14 A cross-sectional view of two adjacent coils. A current in coil 1 sets up a magnetic field and some of the magnetic field lines pass through coil 2. Fig 32-14, p.1013

Figure 32.15 (Example 32.6) (a) This electric toothbrush uses the mutual induction of solenoids as part of its battery-charging system. Fig 32-15a, p.1015

Figure 32.15 (Example 32.6) (b) A coil of NH turns wrapped around the center of a solenoid of NB turns. Fig 32-15b, p.1015

Figure 32. 16 A simple LC circuit Figure 32.16 A simple LC circuit. The capacitor has an initial charge Qmax, and the switch is open for t < 0 and then closed at t = 0. Fig 32-16, p.1015

Active Figure 32.17 Energy transfer in a resistanceless, nonradiating LC circuit. The capacitor has a charge Qmax at t = 0, the instant at which the switch is closed. The mechanical analog of this circuit is a block–spring system. Fig 32-17a, p.1017

Active Figure 32.17 Energy transfer in a resistanceless, nonradiating LC circuit. The capacitor has a charge Qmax at t = 0, the instant at which the switch is closed. The mechanical analog of this circuit is a block–spring system. Fig 32-17b, p.1017

Active Figure 32.17 Energy transfer in a resistanceless, nonradiating LC circuit. The capacitor has a charge Qmax at t = 0, the instant at which the switch is closed. The mechanical analog of this circuit is a block–spring system. Fig 32-17c, p.1017

Active Figure 32.17 Energy transfer in a resistanceless, nonradiating LC circuit. The capacitor has a charge Qmax at t = 0, the instant at which the switch is closed. The mechanical analog of this circuit is a block–spring system. Fig 32-17d, p.1017

Active Figure 32.17 Energy transfer in a resistanceless, nonradiating LC circuit. The capacitor has a charge Qmax at t = 0, the instant at which the switch is closed. The mechanical analog of this circuit is a block–spring system. Fig 32-17e, p.1017

Active Figure 32.18 Graphs of charge versus time and current versus time for a resistanceless, nonradiating LC circuit. Note that Q and I are 90° out of phase with each other. Fig 32-18, p.1018

Figure 32.19 Plots of UC versus t and UL versus t for a resistanceless, nonradiating LC circuit. The sum of the two curves is a constant and equal to the total energy stored in the circuit. Fig 32-19, p.1019

Figure 32.20 (Example 32.7) First the capacitor is fully charged with the switch S1 open and S2 closed. Then, S2 is opened and S1 is closed. Fig 32-20, p.1019

Active Figure 32. 21 A series RLC circuit Active Figure 32.21 A series RLC circuit. Switch S1 is closed and the capacitor is charged. S1 is then opened and, at t = 0, switch S2 is closed. Fig 32-21, p.1020

Figure 32.22 A block–spring system moving in a viscous medium with damped harmonic motion is analogous to an RLC circuit. Fig 32-22, p.1020

Table 32-1, p.1021

Active Figure 32. 23 (a) Charge versus time for a damped RLC circuit Active Figure 32.23 (a) Charge versus time for a damped RLC circuit. The charge decays in this way when R . The Q-versus-t curve represents a plot of Equation 32.31. Fig 32-23a, p.1022

Active Figure 32.23 (b) Oscilloscope pattern showing the decay in the oscillations of an RLC circuit. Fig 32-23b, p.1022

Figure 32.24 Plot of Q versus t for an overdamped RLC circuit, which occurs for values of R > 4L/C Fig 32-24, p.1022

Fig Q32-5, p.1024

Fig Q32-7, p.1024

Fig P32-12, p.1025

Fig P32-17, p.1026

Fig P32-23, p.1026

Fig P32-25, p.1026

Fig P32-26, p.1026

Fig P32-27, p.1026

Fig P32-45, p.1027

Fig P32-48, p.1028

Fig P32-52, p.1028

Fig P32-64, p.1029

Fig P32-68, p.1029

Fig P32-69, p.1029

Fig P32-71, p.1030

Fig P32-72, p.1030

Fig P32-73, p.1030

Fig P32-75, p.1030

Fig P32-78, p.1031

Fig P32-79, p.1031

Fig P32-79a, p.1031

Fig P32-79b, p.1031

Fig P32-79c, p.1031

Figure 32.2 (a) A current in the coil produces a magnetic field directed to the left. Fig 32-2a, p.1005

Figure 32.2 (b) If the current increases, the increasing magnetic flux creates an induced emf having the polarity shown by the dashed battery. Fig 32-2b, p.1005

Figure 32.2 (c) The polarity of the induced emf reverses if the current decreases. Fig 32-2c, p.1005