EM Waves Physics 102 Professor Lee Carkner Lecture 24

Three AC Circuits   V max = 10 V, f = 1Hz, R = 10   V rms =  V max = (0.707)(10) = 7.07 V  R = 10   I rms =  V rms /R = A  I max = I rms /0.707 = 1 A  Phase Shift = 0  When V = 0, I = 0   V max = 10 V, f = 1Hz, C = 10 F   V rms =  V max = (0.707)(10) = 7.07 V  X C = 1/(2  fC) = 1/[(2)(  )(1)(10)] =   I rms =  V rms /X C = A  I max = I rms /0.707 = 625 A  Phase Shift = ¼ cycle (-  /2)  When V = 0, I = I max = 625 A

Three AC Circuits   V max = 10 V, f = 1Hz, L = 10 H   V rms =  V max = (0.707)(10) = 7.07 V  X L = 2  fL = (2)(  )(1)(10) =62.83   I rms =  V rms /X L = 0.11 A  I max = I rms /0.707 = 0.16 A  Phase Shift = ¼ cycle (+  /2)  When V = 0, I = I max = 0.16 A

For capacitor, V lags IFor inductor, V leads I

Current and Power  Z = (R 2 + (X L - X C ) 2 ) ½  V = IZ  The voltage through any one circuit element depends only on its value of R, X C or X L however  cos  = IR/IZ = R/Z  The phase angle is also related to the power P av = I rms V rms cos 

Maxwell’s Laws  In the late 18th - early 19th centuries the relationship between electricity and magnetism was uncertain   It was known that a changing magnetic field produced an electric field   Could the two fields continuously create each other?

Hertz and Oscillators  In 1887 Heinrich Hertz experimented with an LC oscillator   The energy is transferred back and forth between the inductor and capacitor  f 0 = 1/[2  (LC) ½ ]

Oscillators and EM Waves  Hertz found that if he set up an oscillation in one circuit and then put another one near- by (with the same frequency) it would also have oscillations   First circuit transmits electromagnetic waves   Radio transmitter and receiver

  The alternating current will make one end of the rod positive, then neutral, then negative   This changing electric field generates a changing magnetic field  These fields propagate out from the rod as an EM wave

AC and EM Wave

Structure of an EM Wave   The magnetic field is at right angles to the plane of the E field   The directions of E, B and c are at right angles to each other

Radio  EM waves can be received the same way they are generated   This current can be large if the frequency of the wave matches the natural frequency of the circuit   First person to make use of radio waves for communication was Marconi  Sent first wireless message from US to England in 1903

Radio Reception

EM Waves in Nature  We are familiar with many kinds of EM waves   The major difference between them is frequency  v = f = 3 X 10 8 m/s = c c = speed of light

The Electromagnetic Spectrum

c  EM waves in a vacuum travel only at the speed of light  Why?   We can write c as: c = 1/(     ) ½   We can also write c as c = E/B

Spectrum   A plot of intensity versus wavelength is called a spectrum   Each transition produces or absorbs a single wavelength of radiation

Types of Spectra  For a dense gas (or a solid or liquid) the atoms collide so much that they blur the lines into a continuous blackbody spectrum   A low density gas excited by collisions or radiation will produce an emission spectrum   A low density gas in front of a source of continuous radiation will produce an absorption spectrum  A continuum with dark lines at specific wavelengths

Using Spectra  Each kind of atom produces light at specific wavelengths   If the atoms are moving, the lines will be Doppler shifted   We can measure this wavelength shift to find the velocity of the object

Elemental Emission Spectra

Stellar Doppler Shift

Expansion of the Universe  In the early 20th century astronomers discovered that all distant galaxies are red shifted  All galaxies are moving away from all others   In the past, everything in the universe must have been much closer together 

Next Time  Read  Homework Ch 22 P 13, 18, 29, 31

How would you change R, C and  to increase the rms current through a RC circuit? A)Increase all three B)Increase R and C, decrease  C)Decrease R, increase C and  D)Decrease R and , increase C E)Decrease all three

How would you change R, L and  to increase the rms current through a RL circuit? A)Increase all three B)Increase R and L, decrease  C)Decrease R, increase L and  D)Decrease R and , increase L E)Decrease all three

Would increasing  always increase the current through an RLC circuit? A)No, since the capacitive reactance decreases B)Yes, since the capacitive reactance increases C)Yes, since the inductive reactance decreases D)No, since the inductive reactance increases E)No, continually raising  does not continually raise I