Question

The resistivity of a conductor of 5 metre length is \(1.84 \times 10^{-6}\ \Omega\text{ m}\). What will be the resistivity of the conductor of 10 metre length and same diameter of same material provided that all other physical conditions remain same?

• A. \(3.68 \times 10^{-6}\ \Omega\text{ m}\)
• B. \(0.92 \times 10^{-6}\ \Omega\text{ m}\)
• C. \(3.68 \times 10^{-3}\ \Omega\text{ m}\)
• D. \(1.84 \times 10^{-6}\ \Omega\text{ m}\)

Hint:

Always remember that resistance (\(R\)) is an extrinsic property (depends on size/shape), while resistivity (\(\rho\)) is an intrinsic property (independent of size/shape).
If the material and temperature do not change, resistivity never changes.

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
The question asks for the resistivity of a conductor when its length is doubled from \(5\text{ m}\) to \(10\text{ m}\), keeping the material, diameter, and all other physical conditions constant.
It is critical to distinguish between electrical resistance and electrical resistivity.

Step 2: Key Formula or Approach:
The relationship between electrical resistance (\(R\)) and electrical resistivity (\(\rho\)) is given by:
\[ R = \rho \frac{l}{A} \]
where:
\(R\) is the resistance of the conductor,
\(\rho\) is the resistivity of the material,
\(l\) is the length of the conductor,
\(A\) is the cross-sectional area of the conductor.

Step 3: Detailed Explanation:

• Resistivity (\(\rho\)) is an intrinsic property of a material.

• It depends purely on the nature of the material and its temperature.

• It does not depend on the geometric dimensions of the conductor, such as its length (\(l\)) or cross-sectional area (\(A\)).

• When the length of the conductor is changed from \(5\text{ m}\) to \(10\text{ m}\), the resistance of the conductor will double, but its resistivity will remain completely unaltered because the material and temperature are kept constant.

• Since the material is the same and the physical conditions are unchanged, the resistivity remains \(1.84 \times 10^{-6}\ \Omega\text{ m}\).


Step 4: Final Answer:
Therefore, the resistivity of the conductor of \(10\text{ m}\) length remains \(1.84 \times 10^{-6}\ \Omega\text{ m}\).