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EM Waves
Physics 102
Professor Lee Carkner
Lecture 24
Three AC Circuits
DVmax = 10 V, f = 1Hz, R = 10
DVrms = 0.707 DVmax = (0.707)(10) = 7.07 V
R = 10 W
Irms = DVrms/R = 0.707 A
Imax = Irms/0.707 = 1 A
Phase Shift = 0
When V = 0, I = 0
DVmax = 10 V, f = 1Hz, C = 10 F
DVrms = 0.707 DVmax = (0.707)(10) = 7.07 V
XC = 1/(2pfC) = 1/[(2)(p)(1)(10)] = 0.016 W
Irms = DVrms/XC = 441.9 A
Imax = Irms/0.707 = 625 A
Phase Shift = ¼ cycle (-p/2)
When V = 0, I = I max = 625 A
Three AC Circuits
DVmax = 10 V, f = 1Hz, L = 10 H
DVrms = 0.707 DVmax = (0.707)(10) = 7.07 V
XL = 2pfL = (2)(p)(1)(10) =62.83 W
Irms = DVrms/XL = 0.11 A
Imax = Irms/0.707 = 0.16 A
Phase Shift = ¼ cycle (+p/2)
When V = 0, I = I max = 0.16 A
For capacitor, V lags I
For inductor, V leads I
Current and Power

Z = (R2 + (XL - XC)2)½
DV = IZ
 The voltage through any one circuit element depends
only on its value of R, XC or XL however

cos f = IR/IZ = R/Z
 The phase angle is also related to the power
Pav = IrmsVrms cos f
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?
In 1887 Heinrich Hertz
experimented with an LC
oscillator

The energy is transferred
back and forth between
the inductor and
capacitor

f0 = 1/[2p(LC)½]
Hertz
and
Oscillators
Oscillators and EM Waves
Hertz found that if he set up an oscillation
in one circuit and then put another one nearby (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 = fl = 3 X 108 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/(m0e0)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 22.5-22.6
Homework Ch 22 P 13, 18, 29, 31
How would you change R, C and w to
increase the rms current through a RC
circuit?
A)
B)
C)
D)
E)
Increase all three
Increase R and C, decrease w
Decrease R, increase C and w
Decrease R and w, increase C
Decrease all three
How would you change R, L and w to
increase the rms current through a RL
circuit?
A)
B)
C)
D)
E)
Increase all three
Increase R and L, decrease w
Decrease R, increase L and w
Decrease R and w, increase L
Decrease all three
Would increasing w always increase the current
through an RLC circuit?
A)
B)
C)
D)
E)
No, since the capacitive reactance decreases
Yes, since the capacitive reactance increases
Yes, since the inductive reactance decreases
No, since the inductive reactance increases
No, continually raising w does not
continually raise I