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Chapter 27: Q. 69 (page 765)
A flashlight battery is connected to a wire with a resistance of . FIGURE P27.69 shows the battery's potential difference as a function of time. What is the total charge lifted by the charge escalator?
The total charge lifted by the charge escalator is .
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The resistivity of a metal increases slightly with increased temperature. This can be expressed as , where T0 is a reference temperature, usually 20掳C, and a is the temperature coefficient of resistivity.
a. First find an expression for the current I through a wire of length L, cross-section area A, and temperature T when connected across the terminals of an ideal battery with terminal voltage 鈭哣. Then, because the change in resistance is small, use the binomial approximation to simplify your expression. Your final expression should have the temperature coefficient a in the numerator.
b. For copper, a = 3.9 * 10-3 掳C-1 . Suppose a 2.5-m-long, 0.40-mm-diameter copper wire is connected across the terminals of a 1.5 V ideal battery. What is the current in the wire at 20掳C?
c. What is the rate, in A/掳C, at which the current changes with temperature as the wire heats up?
The electron drift speed in a diameter gold wire is . How long does it take 1 mole of electrons to flow through a cross section of the wire?
You've been asked to determine whether a new material your company has made is ohmic and, if so, to measure its electrical conductivity. Taking a sample, you wire the ends of the long axis to a power supply and then measure the current for several different potential differences. Your data are as follows:
| Voltage (V) | Current (A) |
| 0.200 | 0.47 |
| 0.400 | 1.06 |
| 0.600 | 1.53 |
| 0.800 | 1.97 |
Use an appropriate graph of the data to determine whether the material is ohmic and, if so, its conductivity.
Variations in the resistivity of blood can give valuable clues about changes in various properties of the blood. Suppose a medical device attaches two electrodes into a diameter vein at positions role="math" localid="1649141775053" apart. What is the blood resistivity if a potential difference causes a current through the blood in the vein?
23. A -mm-diameter silver wire carries a current. What are (a) the electric field and (b) the electron drift speed in the wire?
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