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. what is the ratio of the largest resistance between parallel sides, to the smallest resistance between parallel sides?

Answer 1

To find the resistance between two parallel sides of the block, we can use the formula:

R = ρ * L / A

where:
R = resistance
ρ = resistivity of copper (1.68*10^-8 Ωm)
L = length of the side
A = cross-sectional area of the side

For the largest resistance:
L = 50 cm
A = 15 cm * 20 cm = 300 cm^2

R_largest = (1.68*10^-8) * 50 / 300 = 2.8*10^-9 Ω

For the smallest resistance:
L = 15 cm
A = 20 cm * 50 cm = 1000 cm^2

R_smallest = (1.68*10^-8) * 15 / 1000 = 2.52*10^-10 Ω

Therefore, the ratio of the largest resistance to the smallest resistance is:

R_largest / R_smallest = (2.8*10^-9) / (2.52*10^-10) = 11.11