Physics 106 - How Things Work - Spring, 1998

Problem Set 2 - Answers



Problem 1: Chapter 12, Case 4a-e (Pg. 460)
An uninterruptable power supply (UPS) allows a computer system to operate during a brief power outage. Most personal computer UPS systems use an electronic device to convert 12 V DC power from a battery into 120 V AC power for the computer. The UPS circuitry first converts the 12 V DC into 12 V AC and then uses a transformer to increase the voltage to 120 V, as required by the computer. In Europe, the final voltage is 220 V.

a. Why can’t the transformer directly convert 12 V DC into 120 V DC?

b. An electronic switching system converts the 12 V DC from the batteries into 12 V AC for the transformer. What is different about the current flowing through the two wires attached to the battery and the current flowing through the two wires attached to the transformer? c. How does power move from the 12 V AC side of the transformer to the 120 V AC side of the transformer? d. Energy is conserved. If there is an average current of about 20 A in the 12 V primary circuit of the transformer, what is the average current in the 120 V secondary circuit of that transformer? e. The length of time that the UPS can deliver power to the computer is limited by the battery’s chemical potential energy. Suppose you wish to extend that time by adding a second 12 V battery to the system. How should you connect the two batteries together so that the current arriving at the pair of batteries will still experience a 12 V rise in voltage and yet be able to extract power from both batteries? Problem 2: Chapter 13, Case 3a-d (Pg. 488)

The power supply in your stereo amplifier uses alternating current from the electric company to provide direct current to the amplifier. This supply converts electric power from one form to another through the use of transformers, diodes, capacitors, and transistors.

a. The power supply provides a relatively small voltage rise to the large current that it sends through the amplifier. The voltages provided by the electric company are too high for the amplifier and the currents are too small. How does a transformer make it possible for the power supply to provide a relatively small voltage rise to a relatively large current that flows between it and the amplifier?

b. The power supply’s transformer provides AC electric power through two wires, but the amplifier needs DC electric power through two wires. To fix this mismatch, the stereo connects these two pairs of wires with 4 diodes so that even though the currents through the two wires of the transformer reverse, the currents through the two wires of the amplifier don’t reverse. How are those 4 diodes connected between the transformer and amplifier? (Draw a picture and indicate which way current can flow through each diode.) c. While the diodes (see b) ensure that current always flows in one direction through the amplifier, the transformer can’t provide current when the current from the power company is reversing. To maintain a steady current through the amplifier, the power supply uses a large capacitor. When the transformer’s current is large, some of that current is used to transfer charge between the capacitor’s plates so that it stores separated charge. When the transformer’s current is small, this separated charge is allowed to flow through the amplifier as current. Draw a graph of the voltage difference between the two plates of the capacitor versus time. Mark the times when the amount of separated charge is increasing and when it’s decreasing. d. The transformer, diodes, and capacitor do a pretty good job of sending direct current through the amplifier, but there still tend to be periodic fluctuations in that current. To keep the current stable, the amplifier uses a regulating device. Just before the current enters the amplifier, it passes through an
n-channel MOSFET. An electronic sensor measures the current through the amplifier and determines if that current is too high or too low. It then adjusts the charge on the gate of the MOSFET to increase or decrease the MOSFET’s electric resistance and lower or raise the current through the amplifier. If the sensor detects that the current is too high, should it increase or decrease the positive charge on the MOSFET’s gate? Explain. Problem 3: Chapter 13, Case 4a-e (Pg. 488)

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. Because the radio makes no “click” sound when you press the “on” or “off” buttons and because it turns itself off automatically after an hour, you know that the switch that controls the radio’s 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?

b. What must the “on” button do to make the n-channel MOSFET conduct current so that the radio will operate? 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? 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? 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? Problem 4: Chapter 14, Case 1a-e (Pg. 519)

Microwave ovens allow for some interesting cooking and funny disasters.

a. Baked Alaska is a dessert in which a hot, baked meringue contains cold, frozen ice cream. The reverse is Frozen Florida, a dessert in which cold, frozen meringue contains boiling hot liqueur. Frozen Florida is prepared by taking a frozen meringue ball (cooked egg whites) containing liquid liqueur (a water-alcohol mixture that remains liquid at low temperature) out of the freezer and putting it in a microwave oven briefly. Why does the liqueur get hot while the meringue remains frozen?

b. If you try to cook an egg in a microwave oven, the egg may explode. Compare this result to the process of cooking popcorn in a microwave oven. c. Some prepared foods come with browning sheets that contain very thin metallic layers. These sheets become hot in a microwave oven and help to brown the surface of the food. Why does a thin metallic film become so hot? d. If you wrap a piece of food in sturdy metal screening with holes about 2 millimeters on a side, the food won’t cook in a
microwave oven. Why can’t the microwaves get through the screen’s holes the way light can? e. A microwave oven has air vents and a fan to cool the magnetron tube. One reason that the tube gets hot is that heat flows out of the electrically heated cathode at the center of the tube. But there are at least two other important ways in which the tube’s operation generates heat. What are they? Problem 5: Chapter 14, Case 4a-f (Pg. 520)

When you talk on a cellular telephone, two radio waves connect you with the telephone network. Your telephone transmits one of these waves and the other is sent to you by a stationary base unit. Base units are located a few kilometers apart and each one provides service to the telephones in its vicinity—its “cell.” A connection between a telephone and a base unit occupies one of 832 channels currently allocated to cellular communications. Each channel corresponds to radio waves of two frequencies: a lower frequency wave (in the range 825.03–849.96 MHz) that’s emitted by the telephone and a higher frequency wave (in the range 870.03–894.96 MHz) that’s emitted by the base unit. The waves of different channels are spaced 0.030 MHz (30 kHz) apart and those of your telephone and its base unit are 45 MHz apart.

a. When your telephone and its base unit are connected on Channel 1, your telephone’s wave has a frequency of 825.03 MHz and its base unit’s wave has a frequency of 870.03 MHz. What are the wavelengths of those two waves?

b. What is the proper length for the telephone’s antenna if it’s to have a natural resonance at the frequency of the radio wave it’s transmitting? c. Why will there be a problem if 900 people in a conference center all try to use their cellular telephones at once? d. A base unit’s antenna is oriented vertically because orienting it horizontally would leave people at certain angles from the base unit unable to receive its radio wave. Why? e. Because the base unit’s antenna is vertical, your telephone’s antenna should also be vertical. Why? f. If you’re in a valley or a metal building, your telephone may lose contact with the base unit. Why?