Question

When both the length and area of cross-section of a wire are doubled, then the resistance will be

• A. doubled
• B. quadrupled
• C. halved
• D. remains same

Answer 1

The Correct Option is D

Step 1: Recall the formula for the resistance of a wire.

The resistance \( R \) of a wire is given by:

\[ R = \rho \frac{L}{A}, \]

where:

• \( \rho \) is the resistivity of the material (a constant for a given material),
• \( L \) is the length of the wire, and
• \( A \) is the cross-sectional area of the wire.

 

Step 2: Analyze the effect of doubling the length and area.

If the length \( L \) is doubled, the new length becomes \( 2L \). If the cross-sectional area \( A \) is doubled, the new area becomes \( 2A \). Substituting these into the formula for resistance:

\[ R_{\text{new}} = \rho \frac{2L}{2A}. \]

Simplify the expression:

\[ R_{\text{new}} = \rho \frac{L}{A}. \]

Step 3: Compare the new resistance with the original resistance.

The new resistance \( R_{\text{new}} \) is equal to the original resistance \( R \). Thus, the resistance remains unchanged.

Final Answer: The resistance will \( \mathbf{\text{remain the same}} \), which corresponds to option \( \mathbf{(4)} \).