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A cylindrical conductor has a length L and radius r. If the radius is doubled wh

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Question: A cylindrical conductor has a length L and radius r. If the radius is doubled while keeping the length constant, how does the resistivity change?

Options:

  1. Doubles
  2. Halves
  3. Remains the same
  4. Increases four times

Correct Answer: Remains the same

Solution: 

Resistivity is an intrinsic property of the material and does not change with geometry.

A cylindrical conductor has a length L and radius r. If the radius is doubled wh

Practice Questions

Q1
A cylindrical conductor has a length L and radius r. If the radius is doubled while keeping the length constant, how does the resistivity change?
  1. Doubles
  2. Halves
  3. Remains the same
  4. Increases four times

Questions & Step-by-Step Solutions

A cylindrical conductor has a length L and radius r. If the radius is doubled while keeping the length constant, how does the resistivity change?
  • Step 1: Understand what resistivity is. Resistivity is a property of a material that measures how strongly it resists the flow of electric current.
  • Step 2: Recognize that resistivity depends on the material itself, not on its shape or size.
  • Step 3: Note that when the radius of the cylindrical conductor is doubled, the shape changes, but the material remains the same.
  • Step 4: Conclude that since resistivity is an intrinsic property, it does not change when the radius is altered while keeping the length constant.
  • Resistivity – Resistivity is a material property that quantifies how strongly a given material opposes the flow of electric current, and it is independent of the shape and size of the conductor.
  • Geometry of Conductors – The geometry of a conductor, such as its length and radius, affects its resistance but not its resistivity.
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