Question

If area of cross section of a wire increases, while temperature and length are constant, then resistance of the wire

• A. decreases
• B. depends on material
• C. increases
• D. none

Answer 1

The Correct Option is A

To solve the problem, we need to understand how the resistance of a wire is affected by changes in its cross-sectional area, while keeping its temperature and length constant.

1. Formula for Resistance:
The resistance $R$ of a wire is given by the formula:

$ R = \rho \frac{L}{A} $

Where:
$\rho$ = resistivity of the material (constant for a given material)
$L$ = length of the wire
$A$ = area of cross-section

2. Given Conditions:
- Temperature is constant
- Length is constant
- Area increases

3. Analyzing the Relationship:
From the formula, resistance $R$ is inversely proportional to area $A$:

$ R \propto \frac{1}{A} $

So, if the area increases, the resistance decreases.

Final Answer:
The resistance of the wire $ \text{decreases} $ when the area of cross-section increases.