Question
25.80 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 $13 \mathrm{~mm}$ long versus the starting length of $5 \mathrm{~mm} ?$ Assume that the resistivity of the coating remains constant and the coat- (b) $\frac{1}{4} A_{5 \mathrm{~mm}}$ ing is uniform along the thread. $A_{13 \mathrm{~mm}}$ is about (a) $\frac{1}{10} A_{5 \mathrm{~mm}}$ (c) $\frac{2}{5} A_{5 \mathrm{~mm}} ;$ (d) the same as $A_{5 \mathrm{~mm}}$.
Step 1
Step 1: The resistance of a conductor is given by the formula $R = \rho \frac{L}{A}$, where $\rho$ is the resistivity, $L$ is the length, and $A$ is the cross-sectional area. Show more…
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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 $13 \mathrm{~mm}$ long versus the starting length of $5 \mathrm{~mm}$ ? Assume that the resistivity of the coating remains constant and the coat- (a) $\frac{1}{10} A_{5} \mathrm{~mm}$; ing is uniform along the thread. $A_{13} \mathrm{~mm}$ is about (b) $\frac{1}{4} A_{5 \mathrm{~mm}}$ (c) $\frac{2}{5} A_{5} \mathrm{~mm} ;$ (d) the same as $A_{5} \mathrm{~mm}$.
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. $A_{13}$ mm 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.
What is the best explanation for the behavior exhibited in the data? (a) Longer threads can carry more current than shorter threads do and so make better electrical conductors. (b) The thread stops being a conductor when it is stretched to $13 \mathrm{~mm}$, due to breaks that occur in the thin coating. (c) As the thread is stretched, the coating thins and its resistance increases; as the thread is relaxed, the coating returns nearly to its original state. (d) The resistance of the thread increases with distance from the end of the thread.
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