Consider a block of copper that is a rectangular prism (a box) with sides 15 cm by 20 cm by 50 cm. The resistivity of copper is 1.68 * 10^-8 ohmM.
If you consider the resistances between the three sets of parallel faces, which has the middle value?
The resistance between the 15 x 20 cm faces.
The resistance between the 15 x 50 cm faces.
The resistance between the 20 x 50 cm faces.
To calculate the resistance between parallel faces of a rectangular prism, we can use the formula:
R = (ρ * L) / A
where R is the resistance, ρ is the resistivity of the material (1.68 * 10^-8 ohmM for copper), L is the length between the faces, and A is the cross-sectional area.
The resistance between the 15 x 20 cm faces can be calculated as follows:
L = 15 cm
A = (20 cm) * (50 cm) = 1000 cm^2
R1 = (1.68 * 10^-8 ohmM * 15 cm) / 1000 cm^2
R1 = 2.52 * 10^-10 ohm
The resistance between the 15 x 50 cm faces can be calculated as follows:
L = 15 cm
A = (15 cm) * (20 cm) = 300 cm^2
R2 = (1.68 * 10^-8 ohmM * 15 cm) / 300 cm^2
R2 = 8.4 * 10^-10 ohm
The resistance between the 20 x 50 cm faces can be calculated as follows:
L = 20 cm
A = (15 cm) * (20 cm) = 300 cm^2
R3 = (1.68 * 10^-8 ohmM * 20 cm) / 300 cm^2
R3 = 1.12 * 10^-8 ohm
Comparing the values, we can see that the resistance between the 20 x 50 cm faces has the middle value.