A rectangular solid made of carbon has sides of lengths are

A rectangular solid made of carbon has sides of lengths are 1.0 cm, 2.0 cm, and 4.0 cm, lying along the x, y, and z axes respectively (see the figure). Assume the resistivity is = 3.0 × 10^-5 ·m.

Determine the resistance for current that passes through the solid in the following directions.
(a) the x direction


(b) the y direction


(c) the z direction

Solution

The resistance of a conductor with resistivity p, cross sectional area A and length of the conductor as l, is given by:

R = pl/A; Here, the direction of the length is measured along the direction of the current flow and the A is the area of the cross section perpendicular to the current flow. We will employ this relation and reasoning so to determing the resistance in the directions given.

a.) For x direction, the length along the X axis would be 1cm, while the cross sectional area would be 8 cm^2

That is, R = 3 x 10^-5 x 10^-2 / 8 x 10^-4 = 0.375 x 10^-3 Ohms

b.) For Y direction, the length along the Y axis would be 2 cm and A = 4x1 = 4 cm^2

That is, R = 3 x 10^-5 x 2 x 10^-2 / 4 x 10^-4 = 1.5 x 10^-3 Ohms

c.) For the z direction, the length along Z axis would be 4 cm and A = 1x2 = 2 cm^2

That is, R = 3 x 10^-5 x 4 x 10^-2 / 2 x 10^-4 = 6 x 10^-3 Ohms