Some types of spiders build webs that consist of threads made of dry silk coated

Question

Some types of spiders build webs that consist of threads made of dry silk coated with a solution of a variety of compounds. This coating leaves the threads, which are used to capture prey, hygroscopic - that is, they attract water from the atmosphere. It has been hypothesized that this aqueous coating makes the threads good electrical conductors. To test the electrical properties of coated thread, researchers placed a 5-mm length of thread between two electrical contacts. The researchers stretched the thread in 1-mm increments to more than twice its original length, and then allowed it to return to its original length, again in 1-mm increments. Some of the resistance measurements are shown in (Figure 1) .

Part A

If the conductivity of the thread results from the aqueous coating only, how does the cross-sectional area A of the coating compare when the thread is 13 mm long versus the starting length of 5 mm? Assume that the resistivity of the coating remains constant and the coating is uniform along the thread.

If the conductivity of the thread results from the aqueous coating only, how does the cross-sectional area  of the coating compare when the thread is 13  long versus the starting length of 5 ? Assume that the resistivity of the coating remains constant and the coating is uniform along the thread.

Select one of the options below:

a) A 13mm is about 1/10 A 5mm. b) A 13mm is about 1/4 A 5mm. c) A 13mm is about 2/5 A 5mm. d) A 13mm is the same as A 5mm.

Explanation / Answer

Correct option is (b)

at L1 =5 mm , R1 = 9 ohms

At L2 =13 mm , R2 = 102 ohms

R = pL/A

condcutictivity =1/p is same

here p is resisitivity

A2/A1 = (R1/R2)*(L2/L1)

A2/A1 = (9*13)/(102*5) = 0.229

A2/A1 = 1/4

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