Alternating Current Circuits And Electromagnetic Waves Chapter 21

Introduction Alternating current circuits 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 (  v) 21.1/21.2

Resistors In An ac Circuit Current and voltage are in step with each other. (in phase)

The average value of 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 Law is 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 90 o. 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

In an inductive ac circuit, the voltage always leads the current by 90 o. ELI the ICE man 21.7

ELI the ICE man 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 90 o. –The instantaneous voltage across the capacitor lags the instantaneous current by 90 o.

The RLC Series Circuit Impedance (Z) –The total resistance (ohms) in an ac circuit –Formula: 221

Phasors –Rotating vectors which are used to represent the voltage across each component. Separated by 90 o –Phase angle  222

Phase Angle Phase angle

Schematic Symbols Review of circuit symbols –Table 21.2 (pg. 705) –Electronic Symbol Handout 23

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: cos  is called the power factor

Review Mechanical Resonance 91, 95

Resonance In A Series RLC Circuit Resonant frequency (f o ) The frequency at which X L = X C Important in tuning circuits Radios, televisions, cell phones Airport metal detectors Formula: 223

QUESTIONS 1 - 4, 6, 7 Pg. 726

Transformers What is a transformer? 218

Transformer Voltage A transformer steps up or steps down ac voltages Primary and secondary coils 218

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 N p /N s 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)

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

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

Hertz’s Apparatus

EM Resonance Hertz achieved resonance and transferred electromagnetic energy between two coils which were several meters apart. Resonant frequency (f o ) 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:

Visible Light Range of wavelengths for visible light: 400 nm to 700 nm 69

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

The Red Shift

QUESTIONS Pg. 726