If the length of a wire is doubled and its thickness (cross-sectional area) is reduced to half, what will be the effect on its electrical resistance?
Show answer & explanation
Correct answer: C
Explanation
Correct Answer
It becomes four times as much
Explanation
The electrical resistance R of a wire is determined by the formula R equals rho multiplied by length divided by area. Rho represents the resistivity of the material, length is the length of the wire, and area is the cross-sectional area. When you double the length of the wire, the resistance doubles because it is directly proportional to the length. When you reduce the thickness or cross-sectional area to half, the resistance doubles again because it is inversely proportional to the area. By combining these two effects, the total resistance increases by a factor of four compared to the original resistance.
Key Points
Resistance is directly proportional to the length of the conductor, meaning longer wires have higher resistance. Resistance is inversely proportional to the cross-sectional area, meaning thinner wires have higher resistance. Because both actions taken in this scenario work to increase resistance, the factors multiply, resulting in a total increase of four times the initial value.
Important Questions and Answers
Question: How does temperature affect the resistance of a metallic wire?
Answer: For most metals, an increase in temperature leads to an increase in electrical resistance due to the increased scattering of electrons as they move through the material.
Question: What is resistivity?
Answer: Resistivity is an intrinsic property of a material that measures how strongly it opposes the flow of electric current. It does not depend on the physical dimensions of the wire but rather on the material composition itself.