Post on 21-Dec-2015
PAL #25 RLC Circuits Power dissipated by RLC circuit Find , XC and XL
= 2f = 2(60) = 377 rad/s XL = L = (377)(130X10-3) = XC = 1/C = 1/(377)(7X10-6) =
Find Z to find Irms and P Z = (R2 + (XL – XC)2)½
Z = (10002 + (49.1 – 378.9)2)½ = Irms = Vrms/Z = 120/1053 = P = IV cos = IV (R/Z) = (0.114)(120)
(1000/1053) =
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 CE) 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 LE) 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
Maxwell’s Laws
James Clerk Maxwell unified the two fields in 1865
Maxwell thought that a changing electric field should produce a magnetic field Could the two fields continuously create each
other?
Hertz and Oscillators
A charged capacitor is placed in a circuit with an inductor
This oscillation occurs at the resonance frequency:
f0 = 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
Generating EM Waves
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
Structure of an EM Wave
The magnetic field is at right angles to the plane of the 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
EM Waves in Nature
Hertz’s radio waves are just one example
Frequency is related to wavelength and velocity
v = f = 3 X 108 m/s = cc = speed of light
c
Why? It is built into the universe
c = 1/()½
The value of c is due to the way in which electric and magnetic fields penetrate space
c = E/B
The Doppler Effect When you observe a moving object, the
wavelengths of light you observe change Moving away -- Moving towards --
Example: the change in a car’s sound as it moves past you
By measuring the shift of lines in a spectrum,
you can determine how fast the object is moving
Doppler Effect for Light
However, at low speeds (u<<c, where u is the relative velocity between source and detector) the equations reduce to the classical form:
f’ = f (1 ± u/c) In astronomy it is easier to measure the wavelength
rather than the frequency (through the shift of spectral lines):
c, the speed of light in vacuum, is constant (3 X 108 m/s)
Spectral Line Shifts
When we observe a spectrum of a object, we compare the observed wavelengths to standard ones Find how the wavelength has shifted ( and thus
find u For objects moving away from us the spectral
lines move to larger wavelengths
For objects moving towards us the spectral lines move to shorter wavelengths More shift, moving faster towards
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