The length of a given cylindrical wire is increased by `100%`. Due to the consequent decrease in diameter the change in the resistance of the wire will be

Options

A. 2
B. 1
C. 0.5
D. 3

Explanation

To solve the problem, we need to analyze the relationship between the length, diameter, and resistance of the cylindrical wire. Let's break down the steps:

### Step 1: Understand the initial conditions
Let the initial length of the wire be \( L \) and the initial diameter be \( D \). The initial cross-sectional area \( A \) of the wire can be calculated using the formula for the area of a circle:
\[ A = \frac{\pi D^2}{4} \]

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