XL= 2πfL,
withf the frequency of the AC voltage source in hertz.
• Inductive reactanceXLhas units of ohms and is greatest at high frequencies.
- For capacitors, we find that when a sinusoidal voltage is applied to a capacitor, the voltage follows the current by one-fourth of a cycle, or by a
90ºphase angle.
- Since a capacitor can stop current when fully charged, it limits current and offers another form of AC resistance; Ohm’s law for a capacitor is
I= V
XC
,
whereVis the rms voltage across the capacitor.
• XCis defined to be the capacitive reactance, given by
XC=^1
2πfC
.
• XChas units of ohms and is greatest at low frequencies.
23.12 RLC Series AC Circuits
• The AC analogy to resistance is impedanceZ, the combined effect of resistors, inductors, and capacitors, defined by the AC version of Ohm’s
law:I 0 =
V 0
Z
orIrms=
Vrms
Z
,
whereI 0 is the peak current andV 0 is the peak source voltage.
• Impedance has units of ohms and is given byZ= R^2 + (XL−XC)^2.
• The resonant frequency f 0 , at whichXL=XC, is
f 0 =^1
2πLC
.
• In an AC circuit, there is a phase angleφbetween source voltageVand the currentI, which can be found from
cosφ=R
Z
,
• φ= 0ºfor a purely resistive circuit or anRLCcircuit at resonance.
- The average power delivered to anRLCcircuit is affected by the phase angle and is given by
Pave=IrmsVrmscosφ,
cosφis called the power factor, which ranges from 0 to 1.
Conceptual Questions
23.1 Induced Emf and Magnetic Flux
1.How do the multiple-loop coils and iron ring in the version of Faraday’s apparatus shown inFigure 23.3enhance the observation of induced emf?
2.When a magnet is thrust into a coil as inFigure 23.4(a), what is the direction of the force exerted by the coil on the magnet? Draw a diagram
showing the direction of the current induced in the coil and the magnetic field it produces, to justify your response. How does the magnitude of the
force depend on the resistance of the galvanometer?
3.Explain how magnetic flux can be zero when the magnetic field is not zero.
4.Is an emf induced in the coil inFigure 23.54when it is stretched? If so, state why and give the direction of the induced current.
Figure 23.54A circular coil of wire is stretched in a magnetic field.
23.2 Faraday’s Law of Induction: Lenz’s Law
5.A person who works with large magnets sometimes places her head inside a strong field. She reports feeling dizzy as she quickly turns her head.
How might this be associated with induction?
6.A particle accelerator sends high-velocity charged particles down an evacuated pipe. Explain how a coil of wire wrapped around the pipe could
detect the passage of individual particles. Sketch a graph of the voltage output of the coil as a single particle passes through it.
CHAPTER 23 | ELECTROMAGNETIC INDUCTION, AC CIRCUITS, AND ELECTRICAL TECHNOLOGIES 853