The Physics
Hypertextbook
Opus in profectus

# Electric Resistance

## Problems

### practice

1. A standard 60 W 120 V light bulb has a tungsten filament that is 53.3 cm long and 46 μm in diameter.
1. What is the light bulb's operating resistance?
2. Determine the cross sectional area of the filament.
3. Calculate the resistivity of tungsten using the results of part a. and b.
4. How does the resistivity calculated above compare to the value quoted in standard reference tables? Why are these two values so different?
5. How can a 53.3 cm filament fit into a light bulb that is only a few centimeters wide?
2. Write something.
3. Write something.
4. Write something completely different.

### conceptual

1. Given a wire with a resistance R, what will be the new resistance if…
1. the wire is cut in half and only one half is used to conduct electricity?
2. the wire is folded in half and both halves are used to conduct electricity?
2. A tungsten rod and an aluminum rod have the same length and resistance.
1. What is the ratio of the cross sectional area of the tungsten rod to the aluminum rod?
2. What is the ratio of the diameter of the tungsten rod to the aluminum rod?
3. Which device in your home has the highest resistance: a flood light, a reading lamp, or a night light? All three devices are plugged into standard North American 120 V outlets.
4. A strain gauge is a device that is sometimes used by building engineers to monitor the growth of cracks in brick or concrete walls. A typical electric strain gauge consists of a series of parallel wires that are affixed to a wall with opposite ends on opposite sides of the crack.

As the width of a crack increases, what happens to…
1. the length of the wires
2. the cross sectional area of the wires
3. the resistance?
5. Use the colored marking codes to determine the resistance ± the tolerance of the 24 resistors below.

### numerical

1. A power transmission cable is composed of 37 strands of aluminum wire, each 4.0 mm in diameter. The cable is 100 m long and is used to deliver 300 A of current to a commercial power user. Determine…
1. the total cross sectional area of the cable
2. the resistance of the cable
3. the power lost in the cable before it reaches the user
2. You have decided to build an 800 W, 120 V, two-slot toaster for your mother.
1. What is the resistance of your mother's new toaster?
2. How much 25 gauge (0.455 mm diameter) nichrome wire will you need to build it?
3. Approximately how many times should the wire be folded so that both sides of each slice of bread will be evenly toasted? (Assume that a typical slice of bread is a 12 cm square.)
3. Which dry pasta offers more resistance to the flow of electricity?
• spaghetti lunghi, an extra long variety of string-like pasta, 50 cm long, 1.55 mm in diameter
• capelli d'angelo: a fine hair-like pasta, 25 cm long, 0.965 mm in diameter
Assume that both pastas are made from durum semolina wheat prepared under identical conditions.
4. What is the resistance of a roll of 100 pennies? To simplify calculations, assume the pennies are made entirely of copper.
• If you use American pennies, assume they were minted before 1982. American pennies minted after 1982 have a zinc core in a copper jacket.
• If you use Canadian pennies, assume they were minted before 1996. Canadian pennies minted after 1996 have a zinc or nickel-steel core in a copper jacket. (Canadian pennies were eventually withdrawn from circulation in 2013.)
5. An electric power distribution cable is made of multiple strands of aluminum and steel wire as shown in the diagram below.

Magnify

The diameters are 2.00 mm and 1.33 mm for the aluminum and steel strands, respectively. Determine the resistance for one kilometer of this cable…

1. assuming that each strand is straight
2. assuming that each aluminum strand is wound with a 16° pitch
6. What dimensions should a 50 nm thick aluminum film have to yield a resistance of 40 Ω?
7. An electric current of 1 mA through the human body is just barely detectable. At 5 mA, the sensation becomes painful. A current above 15 mA is sufficient to cause paralysis in major voluntary muscles. At 75 mA, the current will begin to scramble the normally coordinated contractions of the heart — a condition that is fatal if it persists for more than a few seconds. This information is summarized in the table below along with some information on the arm-to-arm resistance of the human body.
Physiological effects of current
current (mA) resistance (Ω)
sensation 01 dry skin 100,000
pain 05 wet skin 005,000
paralysis 15
fibrillation 75
1. What voltage across the arms of a human with dry skin would result in a barely detectable current?
2. The voltage you calculated in part a. is now applied to a human with wet skin. What is the effect?
3. Why is it dangerous to handle electrical equipment with wet skin?
4. What minimum voltage is needed to produce sensation in wet skin?
5. How could the situation described in part d. be demonstrated? (No exotic or dangerous equipment, please.)
8. You are a cruel and unusual electrical engineer and have been given the cruel and unusual task of designing an electric chair for the purposes of executing criminals in a cruel and unusual fashion.
1. How is your victim to be attached to the chair and what special preparations would you do to ensure the chair worked most effectively?
3. What do the terms DC and AC refer to and which of these was used in electric chairs? Explain the reasoning behind this choice.
9. Cars don't have batteries to power the lights, roll down the windows, or light your cigarette. Although the battery can be used to do all these things, it's primary purpose is to start the engine. It does this by turning or cranking the crank shaft with the starter motor while at the same time supplying enough current to generate a spark across the gap of the spark plug inside each piston. Once the engine gets going, the car's generator or alternator takes on the task of powering the electrical system. Since doing this job is harder in cold weather than hot weather, battery manufacturers have agreed to a standard measure known as the cold cranking amp rating (CCA). This number measures the maximum current that a battery can deliver to the electrical system for 30 seconds at 0 °F (−17.8 °C), while maintaining a terminal voltage of 7.2 V (1.2 V per cell).
1. If a car battery delivers 450 A of current during a CCA test, what is the resistance of the load to which it is attached?
2. The electromotive force of a standard passenger car battery is 12 V (2 V per cell). The drop in terminal voltage during a CCA test is due to the resistance of the battery itself, not the load to which it is attached. Determine the value of this internal resistance.

### statistical

1. The data in the accompanying text files were collected by students making voltage-current graphs for commercially available resistors — one with a significantly higher resistance than the other. Determine the resistance of each using your favorite data analysis application.
2. A group of students performed a classic physics experiment. They connected a series of five small light bulbs to a voltmeter, an ammeter, and a variable power supply one at a time and gradually increased the voltage. They data they recorded were trimmed down to isolate the meter readings taken when the temperature of the filament was most stable. Using these data sets, and your favorite application for analyzing data sets, determine the resistance of each light bulb.
3. zero-the-meters.txt
A group of students were assigned the task of testing various off the shelf resistors. They were told to gradually increase the voltage across the resistor and measure both the voltage and the current. Unfortunately, they wired the meters in backward and forgot to zero them before taking measurements. The situation is not all that bad, however. Using a spreadsheet program or other similar data analysis software…
1. repair the voltage and current data to compensate for the students' errors
2. construct a graph from the repaired voltage and current data
3. determine the resistance of the resistor to the nearest ohm