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Chapter 27: Q. 27 (page 762)

What is the resistance of

a. 2.0m-long gold wire that is 0.20mmin diameter?

b. A 10cmlong piece of carbon with a 1.0mm×1.0mmsquare cross-section?

Short Answer

Expert verified

a. The resistance of a 2.0mlong gold wire that is 0.20mmin diameter is1.53Ω.

b. The resistance of a long piece of carbon with a 1.0mm×1.0mmsquare cross-section is3.5Ω.

Step by step solution

01

Given Information (Part a) 

Gold wire length=2.0m

Diameter=0.20mm

02

Explanation (Part a)

The resistance in the first case, since the cross-section area is a circle, will be given by

R=ρLA

Modify the expression,

=ρ4LπD2

Substitute the values,

R=2.4×10-8Ωm×4×2mπ×0.0002mm2

R=1.53Ω

03

Final Answer (Part a) 

Hence, the resistance of a 2.0mlong gold wire that is 0.20mmin diameter is 1.53Ω.

04

Given Information (Part a) 

Carbon Cross-section dimension=1.0mm×1.0mm

05

Explanation (Part b)

The resistance in the second case, since the cross-section area is a square, will be given by

R=ρLA

=ρLa2

Substitute the values,

R=3.5×10-5Ωm×20.001mm2

=3.5Ω

06

Final Answer (Part a) 

Hence, the resistance of a long piece of carbon with a 1.0mm×1.0mmis 3.5Ω.

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Most popular questions from this chapter

2. Consider a lightbulb circuit such as the one in FIGURE Q27.1.

a. From the simple observations and measurements you can make on this circuit, can you distinguish a current composed of positive charge carriers from a current composed of negative charge carriers? If so, describe how you can tell which it is. If not, why not?

b. One model of current is the motion of discrete charged particles. Another model is that current is the flow of a continuous charged fluid. Do simple observations and measurements on this circuit provide evidence in favor of either one of these models? If so, describe how. If not, why not?

Al the wires in FIGURE Q27.6 are made of the same material and have the same diameter. Rank in order, from largest to smallest, the currents Iato Id. Explain.

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a. How many potassium ions pass through if the ion channel opens for 1.0ms?

b. What is the current density in the ion channel?

23. A 0.50-mm-diameter silver wire carries a 20mAcurrent. What are (a) the electric field and (b) the electron drift speed in the wire?

The electron drift speed in a 1.0mmdiameter gold wire is 5.0×10-5m/s. How long does it take 1 mole of electrons to flow through a cross section of the wire?
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