A water pipe is made of iron with an outside diameter of 2.5 cm and inside diameter of 2.0 cm. The pipe is used to ground an electric appliance. If a current of 20 A flows from the appliance into the water pipe, what fraction of this current will flow in the iron? What fraction in the water? Assume that water has a resistivity of 0.010 Ω∙ m.

Answer 1

Compare the resistance of the annular pipe with that of the water column of the same length.

Riron = (r,iron)L/[pi(ro^2 - ri^2]

Rwater = (r,water)L/[pi*ri^2]

You will need to look up the resisitivity of iron pipe. It is about 10^-7 Ohm-meters, which is 10^-5 times that of water.

The area ratio
(ro^2 - ri^2/ri^2 = (ro/ri)^^2 -1 = 0.56

R,iron/R,water = 10^-5/0.56, so water will conduct only about 2* 10^-5 of the current