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).
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?
1 answer