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Chapter 27: Q. 39 (page 763)
For what electric field strength would the current in a diameter nichrome wire be the same as the current in a diameter aluminum wire in which the electric field strength is?
The electric field strength is.
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FIGURE P27.42 shows a wide plastic film being wrapped onto a diameter roller that turns at The plastic has a uniform surface charge density of .
a. What is the current of the moving film?
b. How long does it take the roller to accumulate a charge of ?
The two wires in FIGURE P27.62 are made of the same material. What are the current and the electron drift speed in the diameter segment of the wire?
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 biochemistry that takes place inside cells depends on various elements, such as sodium, potassium, and calcium, that are dissolved in water as ions. These ions enter cells through narrow pores in the cell membrane known as ion channels. Each ion channel, which is formed from a specialized protein molecule, is selective for one type of ion. Measurements with microelectrodes have shown that a diameter potassium ion channel carries a current of role="math" localid="1649134390247" .
a. How many potassium ions pass through if the ion channel opens for ?
b. What is the current density in the ion channel?
74. FIGURE CP27.74 shows a wire that is made of two equal diameter segments with conductivities and . When current passes through the wire, a thin layer of charge appears at the boundary between the segments.
a. Find an expression for the surface charge density on the boundary. Give your result in terms of , and the wire's cross-section area .
b. A -mm-diameter wire made of copper and iron segments carries a current. How much charge accumulates at the boundary between the segments?
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