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Chapter 21Alternating Current Circuits and Electromagnetic Waves

1. Alternating Current2. Resistor in an AC circuit3. Capacitor in an AC circuit4. Inductor in an AC circuit5. RLC series circuit6. Resonance7. Transformer8. Electromagnetic waves9. Properties of electromagnetic waves10. Doppler effect and electromagnetic waves

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AC Circuit

� What is alternating current?

� What is an AC circuit?

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Resistor in an AC Circuit

� What is it?

� The voltage source

� The concept of phase

� Behavior of the resistor

� What is the power dissipated by the resistor?

� What is rms current?

� Why do we need it?

� What is the average power?

� What about ohm’s law?

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Example – rms Current

1. For the circuit show, calculate the maximum current and voltage, rms current and voltage and rms power.

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Capacitors in an AC Circuit

� Behavior of the capacitor

� What is the Voltage and Current relationship?

� What is capacitive reactance?

� How do I calculate it?

� How do I use ohm’s law?

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Inductors in an AC Circuit

� Behavior of the inductor

� Voltage and current relationship

� What is inductive reactance?

� How do I calculate it?

� How do I apply ohm’s law?

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Example - Inductor

1. In a purely inductive ac circuit as shown, Vmax=100V.

1. If the maximum current is 7.5A at 50 Hz, calculate the inductance L.

2. At what angular frequency ω is the maximum current 2.5 A?

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The RLC Series Circuit

� What is the current in the circuit?

� What about voltage and current relationship?

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Phasor Diagrams

� What is a phasor? diagram?

� How do I use it?

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Phasor Diagram for RLC series circuit

� What is the maximum Voltage?

� What is the phase?

� What about rmsvalues?

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Impedance of a Circuit

� What is impedance?

� How do I calculate it?

� How do I apply ohms’ law?

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Example - RLC Circuit

1. In a certain series RLC circuit, Irms=9.0A, Vrms=180V, and the current leads the voltage by 37°.1. What is the total resistance in the circuit?

2. Calculate the magnitude of the reactance of the circuit (XL-XC).

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Example - RLC Circuit

1. A coil of resistance 35 o and inductance 20.5 H is in series with a capacitor and a 200-Vrms, 100-Hz source. The rms current in the circuit is 4.0A.1. Calculate the capacitance in the circuit.

2. What is Vrms across the coil?

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Summary of Circuit Elements, Impedance and Phase Angles

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Power in an AC Circuit

� How do I calculate the average power?

� What is a power factor?

� Power losses in a capacitor and an inductor

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Resonance in an AC Circuit

� What is resonance in an AC circuit?

� When does is occur?

� How do I calculate resonance frequency?

� Example of devices that use resonance �

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Example - Resonance in an AC Circuit

1. Calculate the resonant frequency of a circuit of negligible resistnace containing an inductance of 40mH and a capacitance of 600pF.

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Transformers

� What is a transformer?

� How does it work?

� How do I use it?

� What about power?

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Example - Transformers

1. An AC adapter for telephone-answering unit uses a transformer to reduce the line voltage of 120Vrms to a voltage of 9.0 V. The rms current delivered to the answering system is 400mA.

1. If the primary (input) coil in the transformer in the adapter has 240 turns, how many turns are there on the secondary (output) coil?

2. What is the rms power delivered to the transformar? Assume an ideal transformer.

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Nikola Tesla

� 1865 – 1943

� Inventor

� Key figure in development of � AC electricity

� High-voltage transformers

� Transport of electrical power via AC transmission lines

� Beat Edison’s idea of DC transmission lines

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Why do we use AC and not DC

� What would you want to conserve?

� Why do we have high voltage transmission lines when our homes only have 120V?

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James Clerk Maxwell

� 1831 – 1879

� Electricity and magnetism were originally thought to be unrelated

� in 1865, James Clerk Maxwell provided a mathematical theory that showed a close relationship between all electric and magnetic phenomena

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More of Maxwell’s Contributions

� Electromagnetic theory of light

� Kinetic theory of gases

� Nature of Saturn’s rings

� Color vision

� Electromagnetic field interpretation

� Led to Maxwell’s Equations

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Maxwell’s Predictions

�

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Hertz’s Confirmation of Maxwell’s Predictions

� 1857 – 1894

� First to generate and detect electromagnetic waves in a laboratory setting

� Showed radio waves could be reflected, refracted and diffracted

� The unit Hz is named for him

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Hertz’s Basic Apparatus

� How does it work?

� What about resonance frequency?

� What is the source for energy transfer?

� What are electromagnetic waves?

� How do I measure the speed of the waves?

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Electromagnetic Waves Produced by an Antenna

� Acceleration of charge

� Antenna

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Charges and Fields, Summary

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Electromagnetic Waves, Summary

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Electromagnetic Waves are Transverse Waves

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Properties of EM Waves

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The EMSpectrum

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Doppler Effect and EM Waves

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The light of a moving source is blue/red shifted by

∆λ/λ0 = vr/c

λ0 = actual wavelength

emitted by the source

∆λ = Wavelength change due to Doppler effect

vr = radial velocity

Blue Shift (to higher frequencies)

Red Shift (to lower frequencies)

vr

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Example – EM Waves

1. What are the wavelength ranges in

1. AM radio band (540-1600 kHz) and

2. The FM radio band (88-108 MHz)?

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Example – EM Waves

1. A speeder tries to explain to the police that the yellow warning lights on the side of the road looked green to her because of the Doppler shift. How fast would she have been traveling if yellow light of wavelength of 580 nm had been shifted to green with a wavelength of 560 nm?