Circuits Problems

The specific principles required are indicated in italics at the beginning of each problem.

1. Ohm's Law: Because of your physics background, you landed a summer job as an assistant technician for a telephone company in California. During a recent earthquake, a 1.0-mile long underground telephone line is crushed at some point. This telephone line is made up of two parallel copper wires of the same diameter and same length, which are normally not connected. At the place where the line is crushed, the two wires make contact. Your boss wants you to find this place so that the wire can be dug up and fixed. You disconnect the line from the telephone system by disconnecting both wires of the line at both ends. You then go to one end of the line and connect one terminal of a 6.0-V battery to one wire, and the other terminal of the battery to one terminal of an ammeter (which has essentially zero resistance). When the other terminal of the ammeter is connected to the other wire, the ammeter shows that the current through the wire is 1 A. You then disconnect everything and travel to the other end of the telephone line, where you repeat the process and find a current of 1/3 A.
   
   
2. Ohm's Law: You have a summer job in the University ecology lab. Your supervisor asks you to duplicate an electromagnet that she has borrowed. She tells you that this electromagnet is made by wrapping a wire many times around a piece of iron and provides you with all the parts, the same type of wire of the same diameter and an identical iron core. What you need to know is how much wire to wrap around the iron. Unfortunately, you cannot simply unwrap the wire from the borrowed magnet because that will destroy it. On the side of the electromagnet, it tells you that when a potential difference of 12 V is put across the ends of its wire, there is a current of 0.06 A through the wire. With a brilliant flash of insight, you realize that the cross-sectional area and the conductivity is the same for both the magnet's wire and the wire you have, so you can find the length with a simple experiment. You cut off a 100-foot piece of identical wire from your supply, attach it to a 1.5-V flashlight battery and measure a current of 0.10 A through that wire. Eureka! you can now find the length of the magnet's wire.
   
   
3. Electric Power: You and a friend are studying for an exam and the session goes until the early morning. At about 4 am you decide to cook some breakfast. Despite being sleepy you've got the coffee perking. Now you want to make some waffles but you realize there might be a problem. The 1000-watt waffle iron and the 600-watt coffee maker are plugged into the 110 V kitchen electrical outlets. If you plug in your 700-watt blender, will you overload the 20 A circuit breaker? The circuit breaker protects those kitchen circuit wires that have the most current from carrying too much current. You are trying to figure out how the electrical outlets are connected together in a circuit when your friend reminds you that when you disconnect the coffeepot, the waffle iron stays on. Now everything is clear.
   
   
4. Electric Power: You and a friend are studying for a final and the session goes until the early morning. About 4 AM you decide to cook some breakfast. Despite being sleepy, things are going well. The waffles are cooking and the coffee is perking. Should you make some toast now? The 1000-watt waffle iron and the 600-watt coffee maker are plugged into kitchen wall electrical outlets. You will also use a kitchen wall outlet for the toaster. The kitchen wall outlets are all part of the same 110-V circuit which has a 20-A circuit breaker (with negligible resistance) to protect the wire carrying the largest current from getting too hot. (Some homes have fuses to do the same job). You know that if you plug in too many appliances you will overload the circuit breaker. The toaster label says that its power output is 700 watts.
   
   
5. Electric Power: As a member of the safety group for the space shuttle scientific program, you have been asked to evaluate an electronics design change. In order to improve the reliability of a circuit to be used in the next shuttle flight, the experimental design team has suggested adding a second 12 V battery to the circuit. The equivalent resistances of the proposed design are shown below. You are worried about the heat generated by the device with the 20 ohm resistance since it will be located next to a sensitive low temperature experiment so you do the appropriate calculation.
   

6. Electric Power: As part of your summer job as a design engineer at an electronics company, you have been asked to inspect the circuit shown below. The resistors are rated at 0.5 Watts, which means they burn-up if more than 0.5 Watts of power passes through them. Will the 100W resistor in the circuit burn-up?

7. 29. Electric Power: While trying to find the power ratings of your appliances you find their circuit diagrams. Looking them over, your friend believes there must be a typo in the circuit diagram of your toaster. The heating element that toasts the bread is listed as having a resistance of 5 ohms. A variable resistor, which is changed by a knob on front of the toaster, has a range of from 2 to 20 ohms. Your friend feels that an element with this resistance will not toast bread properly. Based on the circuit diagram, given below, you decide to calculate the maximum power output by the heating element.