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: What resistivity really means.
Resistivity is a property of the material itself, like density or melting point. It does not care how long or thick the wire is, it only depends on what the wire is made of and its temperature.
Step 2: Compare with resistance.
Resistance follows the formula \[ R = \rho \frac{l}{A} \] so when length changes from \(5\) m to \(10\) m, the resistance itself would double. But resistivity \(\rho\) is not part of that change, it is the constant in the formula, not the variable.
Step 3: Apply this to the given wire.
Since the material and temperature stay the same when the wire is stretched to \(10\) m, the resistivity cannot change even though the resistance does. So the resistivity of the \(10\) m wire is exactly the same as before.
\[ \boxed{1.84 \times 10^{-6}\ \Omega\text{ m}} \]