Final answer:
To calculate the resistance of the thicker wire, we can use the formula for the resistance of a wire. Given that the cross-sectional area of one wire is four times that of the other, the resistance of the thicker wire is one-fourth of the resistance of the thinner wire. By solving the equation, we find that the resistance of the thicker wire is 0.05 ohms.
Step-by-step explanation:
In this problem, we are given two wires of the same material and length but with different diameters. When connected in parallel, they have an effective resistance of 0.8 ohms.
We are also told that the cross-sectional area of one wire is four times that of the other.
To find the resistance of the thicker wire, we can use the formula for the resistance of a wire:
R = (ρ × L) / A
Where R is the resistance, ρ (rho) is the resistivity of the material, L is the length of the wire, and A is the cross-sectional area of the wire.
Since the wires have the same length and material, their lengths and resistivities cancel out in the calculation. Therefore, the resistance is directly proportional to the cross-sectional area.
If the cross-sectional area of one wire is four times that of the other, it means the resistance of the thicker wire is one-fourth of the resistance of the thinner wire.
Given that the effective resistance of the parallel combination is 0.8 ohms, we can set up the equation:
1/R1 + 1/R2 = 1/0.8
1/R2 = 1/0.8 - 1/R1
R2 = 1 / (1/0.8 - 1/R1)
Since the resistance of the thicker wire, R2, is one-fourth of the resistance of the thinner wire, R1, we can substitute R2/4 for R1:
R2 = 1 / (1/0.8 - 1/(R2/4))
By solving this equation, we find that the resistance of the thicker wire, R2, is 0.05 ohms. Therefore, the correct answer is a. 0.05 ohms.