Physics 106 - How Things Work – Spring, 2001

Problem Set #5 – Electronics

Your best friend is determined to try out the latest hairstyle: the frozen yogurt swirl. She owns a curling iron and has asked you to style her hair for her. If you refuse, she’ll do it herself. Worried that she’ll do an even worse job than you’ll do, you agree to style her hair, but only if you can take her somewhere far away so that you can secretly undo it if she doesn’t like it. That’s fine with her, so the two of you drive off into the country. To power the curling iron, you stop at the hardware store along your way and buy one hundred 1.5-volt “D” batteries and some wire.

The curling iron is very simple. It’s designed to heat up properly when you plug it into a 120 volt AC (alternating current) outlet. It has two wires attached to its plug. One wire goes directly to the near end of the heating element and the second wire passes through a switch and a thermostat before connecting to the far end of the heating element. The heating element is a thin metal wire that is a poor conductor of electricity.

1. You connect 80 batteries in a chain and thus produce a source of 120 volt DC (direct current). You then connect one prong of the curling iron’s plug to the positive end of the battery chain and leave the other prong unconnected. Even when you turn the curling iron on, it doesn’t get hot. (a) Why not? (b) Is there any charge on the unconnected prong after you turn the curling iron on?

2. You connect the other prong of the curling iron’s plug to the negative end of the battery chain and turn it on again. Is there a right way to connect the plug? In other words, does it matter which of the curling iron’s two plug prongs you connect to the positive end of the battery chain? If so, why does it matter? If not, why doesn’t it matter?

3. With the curling iron heating properly, you begin to style your friend’s hair. There are voltage drops through the various wires inside the curling iron. Of the three conducting structures--(a) the wire connecting prong 1 to the near end of the heating element, (b) the wire connecting prong 2 through the switch and thermostat to the far end of the heating element, and (c) the heating element itself--which structure experiences the largest voltage drop? How do you know this?

4. When the curling iron is operating properly, its thermostat limits the maximum temperature of the curling cylinder. How must the thermostat alter the curling iron’s electric circuit in order to keep the cylinder’s temperature essentially constant?

It’s strange how all your post-college plans never turn out in these problem sets. It’s happened again. After auditioning at all the modeling agencies in New York and being summarily rejected because of that tattoo you got as a crazy second year student, you decide to enter the Peace Corp. You’re now living near a bug-infested swamp and trying to teach general relativity and string theory to the local school children. It would be the best experience of your life, were it not for the mosquitoes. You set out to build a bug-zapper. (Notice: no animals were harmed during the making of this problem. It’s fiction, after all.)

5. To cook a mosquito with electricity, you must transfer a large amount of power to the mosquito. That can occur when you send an electric current through the mosquito. In such a situation, which quantity determines how much power the mosquito receives: (a) the current passing through the mosquito, (b) the voltage drop experienced by the current as it passes through the mosquito, or (c) both the current and the voltage drop? Explain your choice.

6. Mosquitoes are pretty good insulators, so pushing charge through them will require high voltage. You need a source of high voltage. You find an old neon-sign transformer that will produce 12,000 volts of alternating current when connected to a source of 120 volt alternating current. Compare the number turns in this transformer’s primary and secondary coils. How do you know this answer?

7. There is no source of alternating current in your village, but you have lots of batteries. If you string together enough batteries, you can produce 120 volts of direct current. (Sounds like the first four questions, doesn’t it? Don’t answer that question! The real question is still ahead of us.) If you connect the primary coil of the neon sign transformer to the batteries and form a complete circuit, current will flow through that circuit. However, if you look for current or a voltage rise through the transformer’s secondary coil after a few seconds, there won’t be any. Why doesn’t the transformer transfer electric power from its primary circuit to its secondary circuit when it is powered by batteries?

8. You are determined to build the bug-zapper, so you hire an elderly man to open and close the primary circuit with a switch. He does this over and over again for hours on end. Each time he flips the switch, current starts or stops flowing through the circuit that includes the batteries and the transformer’s primary coil. Charge rushes through the secondary coil each time he flips the switch and high voltages appear at the two ends of that coil. Attached to those ends are two pieces of metal mesh and each time a mosquito passes between the meshes as the man flips the switch, the mosquito explodes in a satisfying puff of electric smoke. Why does a current of high-voltage charge pass through the secondary coil each time the man flips the switch in the primary circuit?