PHYS 106 Spring 2003

"How Things Work" Problem Set #3

with solutions

 

ONE. Look up the specifications for your favorite computer microprocessor, and state how many transistors it contains, approximately what year it was first manufactured, and one other interesting fact of your choice--which you must explain. Good resources for this question are the Intel web site (for Pentiums, etc.), the IBM web site, and the Advanced Micro Devices web site. Be sure to state your source.

According to www.intel.com, their first microprocessor was the 4004, and contained about 2500 transistors. It debuted in 1971, and had a clock speed of about 100 kilohertz. By contrast, the Pentium 4, which was built starting in the year 2000, contains 42 million transistors, and has a clock speed of about 1.5 Gigahertz.

TWO. Case 1 on pages 323-324 of your text (Un-interruptible Power Supply). Do parts a, b, d and e. Omit part c, and substitute the following question as part c instead: "What is the ratio of the number of turns at the primary to the number of turns at the secondary? Which has more turns?"
    1. Transformers only convert AC to AC, because a changing current is needed in the primary to create the magnetic field which in turn induces an electric current in the secondary.
    2. DC current is constant in time, but AC current is changing direction and magnitude with time.
    3. The transformer takes an input of 12VAC at the primary and transforms it to 120VAC at the secondary. This requires more turns at the secondary--10 times more than at the primary.
    4. (There's a misprint in the text. It's 120-V at the secondary). Power, which is voltage times current, is conserved. 12*20 = x*120. This gives x = 2 amps.
    5. Connect the batteries in parallel. This will maintain the input at 12 volts, but make it last longer. (If you connected them in series, you'd have 24 volts instead of 12.)

THREE. Case 1 on pages 379-380 (Microwave Ovens). Do all parts a, b, c and d.
    1. The microwaves only efficiently heat substances containing water. The liqueur contains water, but the meringue doesn't.
    2. Just like with popcorn, the pressure in the interior increases dramatically as the water inside is heated and steam is produced. This can cause the egg, or corn kernel, to explode.
    3. The thin piece of metal has very high electrical resistance. The electric field of the microwaves causes an electric current to flow in the metal, which heats the metal.
    4. It all depends on the wavelength. Light has a wavelength of around .0005 mm, which can easily fit through the 2 mm holes. The 2.45 GHz microwaves have a much larger wavelength, about 12 cm, which won't fit through the holes. Thus the food won't cook.

FOUR. Case 4 on pages 380-381 (Cellular Phones). Do parts a, b, c, d, e and f. Omit parts g and h, but substitute the following question as part g instead: "According to the U.S. government allocation chart, in what category do these cell phone frequencies fall? Also, what is the category just to the left on the chart (slightly lower frequencies-blue on the chart)?" The web site is www.ntia.doc.gov/osmhome/allochrt.pdf
    1. Wavelength is (speed of light)/(frequency). Thus 825.03 MHz and 870.03 MHz have wavelengths of 36.36 cm and 34.48 cm respectively.
    2. It's transmitting the 36.36 cm wave. The antenna should be 1/4th as long, which is about 9.1 cm.
    3. Since there are only 832 channels available, some of the 900 people are going to be on the same channel, causing interference.
    4. If the transmitting antenna were horizontal, no power would be transmitted out the ends, so people located along those two directions would not be able to use their phones.
    5. If the transmitting antenna is vertical, the electric field of the waves it produces oscillates vertically (i.e. is vertically polarized). This only efficiently induces a current in an antenna that is also vertical, because the electrons in the antenna must be able to move with the electric field.
    6. If you're in a valley, the surrounding mountains may absorb or reflect the waves, so they won't reach your phone. If you're in a metal building, the electrons in the metal will be put in motion by the waves, which again will block the waves from reaching your phone.
    7. According to the chart, the cell phone frequencies are designated as "Land Mobile." The next lower category is "TV Broadcast channels 38-69."