Question

A cylindrical conductor of length L and uniform area of cross-section A has resistance R. Another conductor of length $2L$ and resistance $R$ of the same material has an area of cross-section:

• A. A/2
• B. 3A/2
• C. 2A
• D. 3A

Answer 1

The correct option is C 2A

Hint: Recall the relation between resistance and resistivity of a conductor.

Step 1: Evaluation of resistance of the first conductor in terms of resistivity.

We know that,
$R=\rho \frac{L}{A}$

$\rho$ is the resistivity of the cylindrical conductor.

Step 2: Evaluation of resistance of the second conductor in terms of resistivity.

We know that,
$R^{\prime }=\rho \frac{2L}{A^{\prime }}$

$A^{\prime }$ is the unknown cross section of the second conductor.
Step 3: Comparing the two expressions

Since $R^{\prime }=R$ (Given)

or, $\rho \frac{L}{A}=\rho \frac{2L}{A^{\prime }}$

$A^{\prime }=2A$

Final Step : The second conductor of length $2L$ and resistance $R$ has an area of $2A$