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.

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

To determine the fraction of the current that will flow in the iron and in the water, we need to consider the resistance of each material.

1. Calculate the resistance of the water pipe:
The resistance of a cylindrical object can be calculated using the formula:
R = (ρ * L) / A
where R is the resistance, ρ (rho) is the resistivity of water, L is the length of the pipe, and A is the cross-sectional area of the pipe.

Given:
- Length of the pipe (L) is not provided.
- Resistivity of water (ρ) is given as 0.010 Ω∙m.
- Outside diameter of the pipe is 2.5 cm, which means the radius (R) is 1.25 cm or 0.0125 m (divided by 100 to convert cm to m).
- Inside diameter of the pipe is 2.0 cm, which means the inner radius (r) is 1.0 cm or 0.01 m (divided by 100 to convert cm to m).

To determine the length of the pipe, we need some additional information or assumptions. Let's assume the length of the pipe is 1 meter for illustration purposes.

With the given values, we can calculate the cross-sectional area (A) using the formula:
A = π * (R^2 - r^2)

Once we have A, we can calculate the resistance, R, of the water pipe.

2. Calculate the resistance of the iron core:
Since the diameter values provided are for the outer and inner diameters, we can assume that the iron core is a hollow cylinder. Hence, it is the difference between the cross-sectional areas of the outer and inner cylinders.
The cross-sectional area of the iron core (A_iron) can be calculated as follows:
A_iron = π * (R^2 - r^2)

Once we have A_iron, the resistance of the iron core can be determined using the resistance formula.

3. Calculate the fraction of current flowing in the iron and in the water:
The fraction of current flowing in the iron can be calculated using the ratio of the resistance of the iron core to the total resistance of the water pipe and iron core.
Similarly, the fraction of current flowing in the water can be calculated using the ratio of the resistance of the water pipe to the total resistance.

Finally, the fraction of current in each material can be determined by dividing the current in that material by the total current.

Let's go ahead and calculate each step using the values provided.