A wire of resistance R is stretched till its length is double of the original wire.
Then, the resistance of the stretched wire is:-

Options

A. 2R
B. 4 R
C. 8 R
D. 16 R

Explanation

To find the resistance of a wire that is stretched until its length is doubled, we can follow these steps:

### Step 1: Understand the initial conditions
Let the original length of the wire be \( L \), the original cross-sectional area be \( A \), and the original resistance be \( R \). The resistance of the wire can be expressed using the formula:
\[ R = \frac{\rho L}{A} \]
where \( \rho \) is the resistivity of the material.

### Step 2: Determine the new length and area after stretching
When the wire is stretched to double its length, the new length \( L' \) becomes:
\[ L' = 2L \]

Since the volume of the wire remains constant during stretching, we can express the volume \( V \) as:
\[ V = A \cdot L = A' \cdot L' \]
where \( A' \) is the new cross-sectional area after stretching. Therefore, we have:
\[ A \cdot L = A' \cdot (2L) \]
From this, we can solve for the new area \( A' \):
\[ A' = \frac{A}{2} \]

### Step 3: Calculate the new resistance
Now, we can find the new resistance \( R' \) using the new length and area:
\[ R' = \frac{\rho L'}{A'} = \frac{\rho (2L)}{\frac{A}{2}} = \frac{2\rho L}{\frac{A}{2}} = \frac{2\rho L \cdot 2}{A} = \frac{4\rho L}{A} \]
Thus, we can express the new resistance in terms of the original resistance:
\[ R' = 4R \]

### Conclusion
The resistance of the stretched wire is \( 4R \).

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