Chapter 25, Problem 25.80PP

BIO SPIDERWEB CONDUCTIVITY. 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 the table:

*Based on F. Vollrath and D. Edmonds. “Consequences of electrical conductivity in an orb spider’s capture web.” Natunvissenschaften (100:12. December 2013, pp. 1163-69).

25.80 If the conductivity of the thread results from the aqueous coaling 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 coaling remains constant and the coating is uniform along the thread. A_13mm is about (a) $\frac{1}{10}$ A_{5 mm}; (b) $\frac{1}{4}$ A_{5 mm}; (c) $\frac{2}{5}$ A_{5 mm};  (d) the same as A_{5 mm}.