An oceanographer is studying how the ion concentration in seawater depends on de
ID: 1433691 • Letter: A
Question
An oceanographer is studying how the ion concentration in seawater depends on depth. She makes a measurement by lowering into the water a pair of concentric metallic cylinders 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 r_a, outer radius r-b and length L much larger than rb- The scientist applies a potential difference Delta V' between the inner and outer surfaces, producing an outward radial current I. Let p represent the resistivity of the water. Find the resistance of the water between the cylinders in terms of L, p, r_a, and r_b Express the resistivity of the water in terms of the measured quantities L, r_a, r_b, Delta V, and I.Explanation / Answer
a) R = (rho/(2*pi*L))*ln(rb/ra)
b) use Ohm's law
delta_V = I*R
delta_V = I*(rho/(2*pi*L))*ln(rb/ra)
==> rho = delta_V*2*pi*L/(I*ln(rb/ra))