Asked: 2024-07-18T09:30:09+00:002024-07-18T09:30:09+00:00In: Class 10 Science

If the radius of a wire is halved, then its resistance will

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Poll Results

0%[A] be reduced to half.

0%[B] will become doubled

0%[C] will remain one fourth

100%[D] will become sixteen times ( 1 voter )

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If the radius of a wire is halved, its resistance will increase. The resistance of a wire is inversely proportional to the cross-sectional area, which is proportional to the square of the radius. Therefore, halving the radius increases the resistance by a factor determined by the inverse square relationship.

The correct answer is will become sixteen times (option D). Resistance of a wire is inversely proportional to the cross-sectional area of the wire, which is directly proportional to the square of its radius. Halving the radius of a wire decreases its cross-sectional area by a factor of four (since area is proportional to the square of the radius). As resistance is inversely proportional to the area, the resistance will increase by a factor of four squared, which is sixteen. Therefore, if the radius of a wire is halved, its resistance will increase sixteen times. This relationship is important in understanding how the physical dimensions of a conductor affect its electrical properties, such as resistance, in electrical and electronic applications.

The correct answer is will become sixteen times (option D). Resistance of a wire is inversely proportional to the cross-sectional area of the wire, which is directly proportional to the square of its radius. Halving the radius of a wire decreases its cross-sectional area by a factor of four (since area is proportional to the square of the radius). As resistance is inversely proportional to the area, the resistance will increase by a factor of four squared, which is sixteen. Therefore, if the radius of a wire is halved, its resistance will increase sixteen times. This relationship is important in understanding how the physical dimensions of a conductor affect its electrical properties, such as resistance, in electrical and electronic applications.