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Alternating Current Circuits And Electromagnetic Waves

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Introduction

- Alternating currentcircuits play an important part in our lives.
- Electrical power production and transmission
- Communication systems
- Entertainment
- Medicine

224, 229

We will study

- Circuits containing a source of emf and one or more of the following in series:
- Resistors
- Capacitors
- Inductors

We will study

- Electromagnetic waves
- Composed of fluctuating electrical and magnetic waves
- Radio frequencies (RF)
- Radar
- Microwaves
- Infrared
- Visible light
- Ultraviolet
- X-rays
- Gamma Rays

AC Generators

- The output of an ac generator
- ac generator symbol
- Formula for instantaneous voltage (Dv)

21.1/21.2

Resistors In An ac Circuit

- Current and voltage arein stepwith each other.(in phase)

The average valueof the current over one cycle is zero.

- Power formula:

rms Current

- rms current(root mean square)
- It is the direct current that would dissipate the same amount of energy in a resistor as an ac current of that value.

Rms Voltage

- Rms voltage
- 120 V rms in our homes

Ohm’s Law In An ac Circuit

- Ohm’s Lawis valid for resistors in ac circuits.

Review

- Capacitors in a dc circuit
- Charging
- As the voltage across the capacitor increases, the current decreases.
- RC time constant

21.4

Capacitors In An ac Circuit

- In a capacitive ac circuit, the current always leads the voltage by 90o.

21.5

Capacitive Reactance

- Capacitive reactance (ohms)
- Similar to resistance in a dc circuit
- Decreases with frequency
- Opposes a change in ac voltage
- Formulas:

Inductive Reactance

- Inductive reactance (ohms)
- Similar to resistance in a dc circuit
- Increases with frequency
- Opposes a change in ac current
- Formulas:

21.6/21.7

ELItheICEman

- Three important relationships:
- The instantaneous voltage across the resistor is in phase with the instantaneous current.
- The instantaneous voltage across the inductor leads the instantaneous current by 90o.
- The instantaneous voltage across the capacitor lags the instantaneous current by 90o.

Phasors

- Phasors
- Rotating vectorswhich are used to represent the voltage across each component.
- Separated by 90o
- Phase angle (f)

222

Phase Angle

- Phase angle

Power In An ac Circuit

- No power is lost in capacitors or in pure inductors.
- A capacitor in an ac circuit does not dissipate energy.
- A pure inductor in a ac circuit does not dissipate energy.

Power Formulas:

NOTE:cosfis called the power factor

Resonance In A Series RLC Circuit

- Resonant frequency (fo)
- The frequency at which XL = XC
- Important in tuning circuits
- Radios, televisions, cell phones
- Airport metal detectors
- Formula:

223

Transformer Power

- The power input to the primary equals the power output at the secondary.

Transformer Efficiency

- Efficiencies are between 90% and 99%.

The Transformer Equation

Np/Ns is the turns ratio

The Transformer

- Applications:
- AC/DC electronic equipment
- Power distribution
- Automobile ignition systems

219, 220

Maxwell’s Theory

- Electric field lines originate on positive charges and terminate on negative charges.
- Magnetic field lines always form closed loops.
- A varying magnetic field induces an emf and hence an electric field.
- Magnetic fields are generated by moving charges (or currents).

21.18

Maxwell’s Hypothesis

- A changing electric field should produce a magnetic field.
- This could not be proven experimentally because the electric fields were too weak to detect at the time.

Maxwell’s Prediction

- Maxwell came up with the concept of electromagnetic waves and predicted that they would travel at the speed of light.

21.20

Maxwell’s Conclusion

- He concluded that light waves are electromagnetic in nature.

Hertz’s Discovery

- Hertz was the first to generate and detect electromagnetic waves in the laboratory.

21.17

EM Resonance

- Hertz achieved resonance and transferred electromagnetic energy between two coils which were several meters apart.
- Resonant frequency(fo)formula

Properties EM Radiation

- Hertz showed that electromagnetic radiation exhibited wave properties.
- Reflection
- Refraction
- Diffraction
- Interference
- Polarization

231, 232

The Speed of EM Waves

- Hertz showed that electromagnetic radiation traveled at the speed of light.

Hertz’s Contribution

- Hertz’s experiments provided the first proof of Maxwell’s theories.

Production Of EM Waves By An Antenna

- Energy stored in an LC circuit is constantly transferred between the electric and magnetic fields.
- Electromagnetic waves are generated if this happens rapidly.
- Antennas are used to produce electromagnetic waves.

177, 178

EM Waves

228

Properties Of EM Waves

- Electromagnetic waves are transverse waves.
- They travel at the speed of light.
- Light is an electromagnetic wave
- They can travel through a vacuum.

A Special Relationship

- The ratio of the electric field strength (E) to the magnetic field strength (B) equals the speed of light.

Energy and Momentum

- Electromagnetic waves carry both energy and momentum.

The Speed of EM Waves

- Important formula:

The Spectrum Of EM Waves

- Types of waves(increasing in frequency and energy)
- Radio waves
- Microwaves
- Infrared waves (heat waves)
- Visible light
- Ultraviolet light (UV)
- X-rays
- Gamma rays

21.23

Review-The Doppler Effect

- Sound waves exhibit the Doppler effect
- Trains
- Race cars

The Doppler Effect For EM Waves

- Astronomy
- The expanding universe
- Red shift
- Blue shift
- Rotation of galaxies

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