Missing part in the text of the question. Found the rest on internet:
"determine the resistance for current that passes through the solid in (a) the x direction (b) the y direction and (c) the z direction"
Solution
The relationship between resistance and resitivity is given by
[tex]R= \frac{\rho L}{A} [/tex]
where R is the resistance
[tex]\rho [/tex] is the resistivity of the material (for carbon, as in this problem, [tex]\rho=3 \cdot 10^{-5} \Omega m[/tex])
L is the length of the conductor
A is its cross-sectional area.
We can solve the 3 parts of the problem by using the same formula, but every time L and A will be different (because they will depend on the direction of the current)
(a) the current is in the x-direction, so the length of the conductor is
[tex]L=1.0 cm=0.01 m[/tex]
while the cross sectional area is
[tex]A=(2.0 cm)(4.0 cm)=8.0 cm^2 = 8.0 \cdot 10^{-4}m^2[/tex]
So the resistance in this case is
[tex]R= \frac{\rho L}{A} = \frac{(3 \cdot 10^{-5}\Omega m)(0.01 m)}{8.0 \cdot 10^{-4} m^2} = 3.8 \cdot 10^{-4}\Omega[/tex]
(b) the current is in the y-direction, so the length of the conductor is
[tex]L=2.0 cm=0.02 m[/tex]
while the cross sectional area is
[tex]A=(1.0 cm)(4.0 cm)=4.0 cm^2 = 4.0 \cdot 10^{-4}m^2[/tex]
So the resistance in this case is
[tex]R= \frac{\rho L}{A} = \frac{(3 \cdot 10^{-5}\Omega m)(0.02 m)}{4.0 \cdot 10^{-4} m^2} = 1.5 \cdot 10^{-3}\Omega[/tex]
(c) the current is in the z-direction, so the length of the conductor is
[tex]L=4.0 cm=0.04 m[/tex]
while the cross sectional area is
[tex]A=(1.0 cm)(2.0 cm)=2.0 cm^2 = 2.0 \cdot 10^{-4}m^2[/tex]
So the resistance in this case is
[tex]R= \frac{\rho L}{A} = \frac{(3 \cdot 10^{-5}\Omega m)(0.04 m)}{2.0 \cdot 10^{-4} m^2} = 6.0 \cdot 10^{-3}\Omega[/tex]
