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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脳1.0mmsquare cross-section?

Short Answer

Expert verified

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

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

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=蚁LA

Modify the expression,

=蚁4L蟺D2

Substitute the values,

R=2.4脳10-8惟m脳4脳2m蟺脳0.0002mm2

R=1.53惟

03

Final Answer (Part a) 

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

04

Given Information (Part a) 

Carbon Cross-section dimension=1.0mm脳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=蚁LA

=蚁La2

Substitute the values,

R=3.5脳10-5惟m脳20.001mm2

=3.5惟

06

Final Answer (Part a) 

Hence, the resistance of a long piece of carbon with a 1.0mm脳1.0mmis 3.5惟.

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