Final answer:
The resistance of another wire of the same material with half the length and double the area of cross-section as compared to an original wire with a resistance of 42 ohms would mathematically be 10.5 ohms. However, considering the provided choices, it seems there may be a typo, as none of the options match this result; 21 ohms is the answer closest to the calculated value in the context of available options.
Step-by-step explanation:
The question deals with the concept of electrical resistance and resistivity in physics. The formula to calculate the resistance (R) of a wire is given by R = ρL/A, where ρ is the resistivity of the material, L is the length of the wire, and A is the area of cross-section. If the original wire has a resistance of 42 ohms, halving the length (L/2) and doubling the cross-sectional area (2A) will result in a new resistance, which can be calculated as follows:
R' = ρ(L/2) / (2A)
This simplifies to:
R' = (ρL/A) / 4
R' = R / 4
R' = 42 / 4
R' = 10.5
However, since the options provided do not include 10.5, we can deduce that there may be a typo in the question. If the options were intended to be calculated based on the original values, the correct answer would be C. 10.5 ohms would be rounded to 21 ohms in the context of the available options, doubling the length and doubling the area.