An oceanographer is studying how the ion concentration in sea water depends on depth. She does this by lowering into the water a pair of concentric metallic cylinders (Fig. P27.68) at the end of a cable and taking data to determine the resistance between these electrodes as a function of depth. The water between the two cylinders forms a cylindrical shell of inner radius ra, outer radius , and length L much larger than 7,. The scientist applies a potential difference AV between the inner and outer surfaces, producing an outward radial current L Let p represent the resistivity of the water. (a) Find the resistance of the water between the cylinders in terms of L, p. Ta, and . (b) Express the resistivity of the water in terms of the measured quantities L, ra, , AV, and I. Figure P27.68

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Chapter1: Units, Trigonometry. And Vectors
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An oceanographer is studying how the ion concentration
in sea water depends on depth. She does this by lowering
into the water a pair of concentric metallic cylinders
(Fig. P27.68) at the end of a cable and taking data to
determine the resistance between these electrodes as a
function of depth. The water between the two cylinders
forms a cylindrical shell of inner radius ra, outer radius n,
and length L much larger than . The scientist applies a
potential difference AV between the inner and outer
surfaces, producing an outward radial current I. Let p
represent the resistivity of the water. (a) Find the
resistance of the water between the cylinders in terms of L,
p, Ta, and . (b) Express the resistivity of the water in
terms of the measured quantities L, ra, V. AV, and I.
Figure P27.68
Transcribed Image Text:An oceanographer is studying how the ion concentration in sea water depends on depth. She does this by lowering into the water a pair of concentric metallic cylinders (Fig. P27.68) at the end of a cable and taking data to determine the resistance between these electrodes as a function of depth. The water between the two cylinders forms a cylindrical shell of inner radius ra, outer radius n, and length L much larger than . The scientist applies a potential difference AV between the inner and outer surfaces, producing an outward radial current I. Let p represent the resistivity of the water. (a) Find the resistance of the water between the cylinders in terms of L, p, Ta, and . (b) Express the resistivity of the water in terms of the measured quantities L, ra, V. AV, and I. Figure P27.68
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