Due Monday, April 1, In Class
Please Answer Each Question As Briefly As Possible
You May Work Together, But Write Up Your Answers Separately
Question 1: You enjoy listening to your little portable radio while jogging but it hasn't been working properly since it got wet in the rain last week. The problem is that it keeps turning itself off. The radio has an "on" button and an "off" button and it also turns itself off automatically after an hour. There is no "click" sound when you turn it on or off, so you know that the switch that controls the power is electronic. It's probably an n-channel MOSFET that's connected in series with the radio's electronics so that current from the battery must pass through both the electronics and the MOSFET before returning to the battery.
a. Why won't any power reach the electronics when the MOSFET isn't conducting current?
Answer: The circuit will be open and no electric current will flow through the electronics. With no current comes no power.
b. What must the "on" button do to make the n-channel MOSFET conduct current so that the radio will operate?
Answer: It must put positive charge onto the gate of the MOSFET (probably from the positive terminal of the battery)..
c. What must the "off" button or the automatic shutdown do to stop the n-channel MOSFET from conducting current, so that the radio will turn off?
Answer: It must remove the positive charge from the gate of the MOSFET (probably to the negative terminal of the battery).
d. Water is a poor conductor of electricity, but with patience you can send charge through it. If water is slowly turning off the radio, what is it probably doing?
Answer: It must allow positive charge to slowly leave the gate of the MOSFET (probably by letting it leak to the negative terminal of the battery).
e. You discover a small drop of water inside the "off" button, allowing positive charge to flow slowly from the gate of the n-channel MOSFET to the negative terminal of the battery. You remove the water and the radio works perfectly. Why did the drop cause trouble and why did removing the drop fix the radio?
Answer: The drop was allowing positive charge to escape from the gate of the MOSTFET and removing the drop stopped the leak.
Question 2: The Global Positioning System or GPS is a system of earth-orbiting satellites that provide position information to anyone with a GPS radio receiver. Each satellite transmits two microwaves, one at 1.57542 GHz and the other at 1.2276 GHz. These waves are modulated by carefully timed pulses so that by measuring exactly when it receives those pulses from four or more satellites, a GPS receiver can determine its position on earth to within 100 m.
a. Because each satellite carries a time-standard cesium atomic clock, its pulses are emitted at precisely known times. Since the GPS receiver knows exactly when it receives the pulses, it can tell exactly how far it is from the satellite. How?
Answer: The receiver knows the speed of light and it can determine how long the pulse took to travel to it from the satellite. By multiplying the speed of light times the travel time, the receiver can obtain the distance the wave traveled to get to it.
b. Because a GPS receiver only receives microwaves from satellites that are above the horizon, there must be at least 17 satellites in orbit at once. Why can't the receiver detect satellites that are below the horizon?
Answer: All high frequency electromagnetic waves, including microwaves, travel in straight lines. To receive the wave transmitted by the satellite, you must have a line of sight to it. The earth blocks the wave.
*c. What are the wavelengths of the two microwaves?
Answer: About 0.190 m and 0.244 m.
*d. One of the reasons for using microwaves in the GPS is that microwaves can be received by small antennas with well-defined locations. The best antenna is a quarter the length of the electromagnetic wave it emits or receives. How long should an antenna be to receive the lower frequency GPS microwave?
Answer: About 6 cm tall.
e. Geologists are using the GPS to study motions of the earth's crust that are as small as a few millimeters. To do this, they actually study the electric and magnetic fields of the microwaves. Why would two GPS receivers located a few centimeters apart detect somewhat different electric and magnetic fields if they studied the microwave from one particular satellite at precisely the same moment?
Answer: At one moment in time, the electric and magnetic fields in the microwave differ from place to place. The electric field points at right angles to the line leading back to the satellite and it alternates up and down as you move along that line. If you consider only the low frequency microwave, then the electric field point up and down and up again every 0.244 cm. Two receivers located at different positions along that line would detect these different fields.
Question 3: A cordless microphone uses a 925 MHz carrier wave to carry sound information from a performer to the audio system of a theater. The microphone uses frequency modulation to represent the sound of the performer's voice with the radio wave.
a. The tank circuits in the microphone and in the theater's receivers have been carefully tuned to the same resonant frequencies. Why is this adjustment important?
Answer: (Presumably the microphone will transmit a radio wave at the frequency at which its tank circuit is resonant.) If the tank circuit in the audio system's receiver isn't adjusted to that same frequency, very little charge will slosh back and forth in it and the reception will be poor to nonexistent.
b. The frequency of the waves emitted by the microphone include waves with frequencies slightly above and below 925 MHz. Explain.
Answer: To represent the audio signal, the transmitter deliberately shifts the frequency of its radio wave above and below 925 MHz.
c. Because the performer moves and tips the microphone during the performance, the theater uses two receivers at different locations. This ensures that the radio wave from the microphone is always strong at one of the receivers. How is it possible for the wave to be weak at one of the receivers?
Answer: If the wave follows several paths to a receiver, usually because of reflections in the room, those waves may interfere destructively so that receiver detects little or no wave.
d. Each receiver has two antennas, oriented at right angles to one another. Why does that ensure that the receiver can detect the radio wave, regardless of how the microphone's antenna is tipped?
Answer: The polarization of the wave emitted by the microphone varies according to the angle of its antenna. If the wave's electric field points at right angle to one of the receiver's antennas, no charge will move on the antenna and there will be no reception.
e. What happens to the radio wave as the performer talks?
Answer: To represent the sound, the microphone shifts the frequency of the radio wave up and down.
Question 4: A paint is a plastic that contains dye molecules and small particles. While the dye molecules absorb certain wavelengths of light and give the paint its color, the particles are often completely clear. Nonetheless, these particles are very important to the paint's appearance.
a. The speed of light is different in the particles than it is in the plastic surrounding them. When light strikes the surface of one of these particles, why does some of it reflect?
Answer: The light experiences a change in speed (or an impedance mismatch).
b. The particles are randomly shaped and oriented. When light strikes them from one direction, they reflect light in all directions and appear white rather than shiny. Why do their surface orientations affect the way light reflects from them?
Answer: OMIT THIS QUESTION - FULL CREDIT FOR ANYONE WHO WORKED ON QUESTION 4.
c. Lead carbonate is a clear, toxic chemical that was put in paints before 1930 to make them white. The speed of light in a particle of lead carbonate isn't that much slower than in plastic. How does this fact help explain why "lead paints" weren't very good at covering dark surfaces-it took lots of layers of paint before the surfaces really looked white?
Answer: Since the speed of light didn't change much as light entered and exited from these lead carbonate particles, not much of it reflected and a considerable amount of the light made it all the way through to the surface beneath the paint.
d. Modern paints contain particles of clear, nontoxic titanium dioxide. Light travels very slowly in this material. Explain why titanium dioxide based paints look so white, even after only a single layer of paint.
Answer: Because light experiences a large change in speed in entering and exiting from the titanium dioxide particles, lots of it reflects. The light doesn't penetrate very far into the paint, so you can't see the surface beneath it.
e. Red paint usually contains a mixture of titanium dioxide particles and red dye molecules. The red dye molecules absorb any light that isn't red but they don't affect red light at all. How would the appearance of this paint change if it didn't contain any titanium dioxide particles?
Answer: The paint would appear as a red stain rather than a paint; you would see the surface below it, but through a red filter.
Question 5: While fluorescent lamps can be dimmed, it's not as easy as dimming an incandescent light bulb. Fluorescent lamps tend to turn off when they don't run at full power, so a dimmed fluorescent fixture must make sure that the discharge continues to operate, even at low power.
a. Why can only rapid-start fluorescent fixtures be dimmed?
Answer: The fixture must keep the filaments at the ends of the tubes hot because the discharge itself won't be strong enough to keep them hot itself. A preheat fixture would simply turn off if you tried to dim it.
b. While an incandescent light bulb can be dimmed by reducing the voltage drop across its filament, reducing the voltage drop across a fluorescent tube will spoil its discharge. With the voltage drop across the tube reduced, the average energy of its electrons would be substantially lower than normal and its mercury atoms would emit almost no ultraviolet light at all. Why is there a minimum energy that an electron must have in order to cause a mercury atom to emit ultraviolet light?
Answer: To emit an ultraviolet photon, a mercury atom must receive a certain specific amount of energy from the electron that hits it. That amount of energy is the energy needed to excite the atom from the ground state to the first excited state.
c. Reducing the voltage drop across the fluorescent tube would virtually stop the production of positive mercury ions in the vapor. That would make the tube's filaments last longer, but the discharge wouldn't operate. With no positively charged particles inside the tube, what would happen to the electrons as they flowed from one electrode to the other?
Answer: The electrons would begin their journey across the tube, from the negative end to the positive end, but they would repel one another as they flew and would quickly push one another to the walls of the tube.
d. Rather than reducing the voltage drop across its fluorescent tubes, a dimmed fluorescent fixture shortens the time that the discharge is on following each reversal of current in the power line. An electronic switch allows current to flow through the tube and its ballast only for part of each half cycle of the alternating current. The switch senses the voltage reversal in the power line and then waits a certain amount of time before allowing current to flow. The switch then keeps current flowing until the next reversal of the power line, when it opens and begins waiting again. The longer into each half cycle the switch waits, the dimmer the fixture becomes. This arrangement allows the ballast to store energy when the switch first allows current to flow and then to use up its stored energy by creating light before the switch stops the current flow at the next power line reversal. Why would it be a problem trying to stop the current flow through the tube and ballast abruptly in between reversals of the power line?
Answer: A ballast or inductor resists changes in current. If the switched tried to stop the current flow abruptly, the ballast would fight the switch and drive current through the circuit anyway. (The result would probably be sparks and a damaged switch.)
e. Current passing through the electronic switching system of the dimmed fluorescent fixture experiences a small voltage drop. Why does the switching system get warm?
Answer: Since current passes through the switch and experiences a voltage drop, that current must be delivering power to the switch. This power is becoming thermal energy and making the switch warm.