The resistance of a conductor is given by the formula R = ρ * L / A, where R is the resistance, ρ is the resistivity of the material, L is the length of the conductor, and A is the cross-sectional area of the conductor.
For the block of copper, the largest resistance will be between the parallel sides that have length 50 cm and cross-sectional area 15 cm * 20 cm = 300 cm^2. The resistance can be calculated as:
R_max = ρ * L / A = 1.68e-8 * 50 / 300 = 2.8e-9 ohms
The smallest resistance will be between the other two parallel sides that have length 20 cm and cross-sectional area 15 cm * 50 cm = 750 cm^2. The resistance can be calculated as:
R_min = ρ * L / A = 1.68e-8 * 20 / 750 = 4.48e-10 ohms
Therefore, the ratio of the largest resistance to the smallest resistance is:
R_max / R_min = (2.8e-9) / (4.48e-10) = 6.25
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 1.68e-8.
what is the ratio of the largest resistance between parallel sides, to the smallest resistance between parallel sides?
1 answer