# Chapter 21 Alternating Current Circuits and Electromagnetic Waves 1. Alternating Current 2. Resistor in an AC circuit 3. Capacitor in an AC circuit 4.

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Chapter 21 Alternating Current Circuits and Electromagnetic Waves 1. Alternating Current 2. Resistor in an AC circuit 3. Capacitor in an AC circuit 4. Inductor in an AC circuit 5. RLC series circuit 6. Resonance 7. Transformer 8. Electromagnetic waves 9. Properties of electromagnetic waves 10. Doppler effect and electromagnetic waves

AC Circuit What is alternating current? What is an AC circuit?

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?

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

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?

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?

Example - Inductor 1. In a purely inductive ac circuit as shown, V max =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?

The RLC Series Circuit What is the current in the circuit? What about voltage and current relationship?

Phasor Diagrams What is a phasor? diagram? How do I use it?

Phasor Diagram for RLC series circuit What is the maximum Voltage? What is the phase? What about rms values?

Impedance of a Circuit What is impedance? How do I calculate it? How do I apply ohms’ law?

Example - RLC Circuit 1. A coil of resistance 35 Ω and inductance 20.5 H is in series with a capacitor and a 200-V rms, 100-Hz source. The rms current in the circuit is 4.0A. 1. Calculate the capacitance in the circuit. 2. What is V rms across the coil?

Summary of Circuit Elements, Impedance and Phase Angles

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

Example - RLC Circuit 1. In a certain series RLC circuit, I rms =9.0A, V rms =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 (X L -X C ).

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

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.

Transformers What is a transformer? How does it work? How do I use it? What about power?

Example - Transformers 1. An AC adapter for telephone-answering unit uses a transformer to reduce the line voltage of 120V rms 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.

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

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?

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

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

Maxwell’s Predictions

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

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?

Electromagnetic Waves Produced by an Antenna Acceleration of charge Antenna

Charges and Fields, Summary

Electromagnetic Waves, Summary

Electromagnetic Waves are Transverse Waves

Properties of EM Waves

The EM Spectrum

Doppler Effect and EM Waves The light of a moving source is blue/red shifted by  / 0 = v r /c 0 = actual wavelength emitted by the source  Wavelength change due to Doppler effect v r = radial velocity Blue Shift (to higher frequencies) Red Shift (to lower frequencies) vrvr

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)?

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?

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