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?

### 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, and
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 very 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.
5. An electric power distribution cable is made of multiple strands of aluminum and steel wire as shown in the diagram below [.

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 1 dry skin 100,000
pain 5 wet skin 5,000
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?