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 Ωm.
If you consider the resistances between the three sets of parallel faces, which has the middle value?
To find the resistance between two opposite faces of the block of copper, we can use the formula:
R = ρ * l / A,
where R is the resistance, ρ is the resistivity of copper, l is the length of the block along the direction of current flow, and A is the cross-sectional area of the block perpendicular to the direction of current flow.
Let's calculate the resistances between the three sets of parallel faces:
1. Resistance between the faces with sides 15 cm and 20 cm:
R1 = ρ * 50 cm / (15 cm * 20 cm) = 1.68*10^-8 * 0.5 m / (0.15 m * 0.2 m) = 0.0014 Ω.
2. Resistance between the faces with sides 15 cm and 50 cm:
R2 = ρ * 20 cm / (15 cm * 50 cm) = 1.68*10^-8 * 0.2 m / (0.15 m * 0.5 m) = 0.000224 Ω.
3. Resistance between the faces with sides 20 cm and 50 cm:
R3 = ρ * 15 cm / (20 cm * 50 cm) = 1.68*10^-8 * 0.15 m / (0.2 m * 0.5 m) = 0.000168 Ω.
Comparing the three resistances, we see that the middle value is 0.000224 Ω (the resistance between the faces with sides 15 cm and 50 cm).