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We have two wires A and B of same mass and same material. The diameter of the wire A is half of that B. If the resistance of wire A is 24 ohm then the resistance of wire B will be
  • a)
    12 Ohm
  • b)
    3.0 Ohm
  • c)
    1.5 Ohm
  • d)
    None of the above
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
We have two wires A and B of same mass and same material. The diameter...
Solution:

Given that the two wires A and B have the same mass and same material. The diameter of wire A is half of that of wire B. The resistance of wire A is 24 ohm.

Let the diameter of wire B be d. Then, the diameter of wire A is d/2.

We know that the resistance of a wire is directly proportional to its length and inversely proportional to its cross-sectional area.

Hence, the resistance of a wire is given by the formula:

Resistance = (resistivity x length) / cross-sectional area

Let the length and resistivity of both the wires A and B be the same.

Then, we have the formula:

Resistance of wire A / Resistance of wire B = (Cross-sectional area of wire B) / (Cross-sectional area of wire A)

Substituting the values, we get:

24 / Resistance of wire B = (pi/4) x d^2 / (pi/4) x (d/2)^2

24 / Resistance of wire B = 4

Resistance of wire B = 24 / 4

Resistance of wire B = 6 ohm

However, this is not one of the given options.

But, we know that the resistance of a wire is inversely proportional to the square of its diameter.

Hence, if the diameter of wire A is half of that of wire B, then the resistance of wire B will be 1/4th of the resistance of wire A.

Therefore, the resistance of wire B = (1/4) x 24

Resistance of wire B = 6 ohm / 4

Resistance of wire B = 1.5 ohm

Hence, the correct option is (c) 1.5 ohm.
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We have two wires A and B of same mass and same material. The diameter of the wire A is half of that B. If the resistance of wire A is 24 ohm then the resistance of wire B will bea)12 Ohmb)3.0 Ohmc)1.5 Ohmd)None of the aboveCorrect answer is option 'C'. Can you explain this answer?
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We have two wires A and B of same mass and same material. The diameter of the wire A is half of that B. If the resistance of wire A is 24 ohm then the resistance of wire B will bea)12 Ohmb)3.0 Ohmc)1.5 Ohmd)None of the aboveCorrect answer is option 'C'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about We have two wires A and B of same mass and same material. The diameter of the wire A is half of that B. If the resistance of wire A is 24 ohm then the resistance of wire B will bea)12 Ohmb)3.0 Ohmc)1.5 Ohmd)None of the aboveCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for We have two wires A and B of same mass and same material. The diameter of the wire A is half of that B. If the resistance of wire A is 24 ohm then the resistance of wire B will bea)12 Ohmb)3.0 Ohmc)1.5 Ohmd)None of the aboveCorrect answer is option 'C'. Can you explain this answer?.
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