The resistance of a wire is `10 Omega`. Its lengthis incrased by `10%` by stretching. The new resistance will now be

Options

A. `12 Omega`
B. `1.2 Omega`
C. `13 Omega`
D. `11 Omega`

Explanation

To find the new resistance of a wire after its length is increased by 10% due to stretching, we can follow these steps:

### Step 1: Understand the relationship between resistance, length, and area
The resistance \( R \) of a wire is given by the formula:
\[ R = \rho \frac{L}{A} \]
where:
- \( R \) is the resistance,
- \( \rho \) is the resistivity of the material,
- \( L \) is the length of the wire,
- \( A \) is the cross-sectional area of the wire.

### Step 2: Recognize the effect of stretching
When a wire is stretched, its volume remains constant. Therefore, if the length increases, the cross-sectional area must decrease. The relationship between the new length and area after stretching is important.

### Step 3: Calculate the new length
Given that the original length is \( L \) and it is increased by 10%, the new length \( L' \) is:
\[ L' = L + 0.1L = 1.1L \]

### Step 4: Relate resistance to the new length
Since the volume remains constant, we can express the relationship between the original and new dimensions:
\[ L \cdot A = L' \cdot A' \]
Substituting \( L' \):
\[ L \cdot A = 1.1L \cdot A' \]
From this, we can find the new area \( A' \):
\[ A' = \frac{A}{1.1} \]

### Step 5: Express the new resistance
Using the resistance formula, the new resistance \( R' \) can be expressed as:
\[ R' = \rho \frac{L'}{A'} = \rho \frac{1.1L}{A/1.1} = \rho \frac{1.1^2L}{A} = 1.1^2 \cdot \rho \frac{L}{A} = 1.1^2 \cdot R \]
Substituting the original resistance \( R = 10 \, \Omega \):
\[ R' = 1.1^2 \cdot 10 \, \Omega \]

### Step 6: Calculate \( 1.1^2 \)
Calculating \( 1.1^2 \):
\[ 1.1^2 = 1.21 \]

### Step 7: Find the new resistance
Now, substituting this value back:
\[ R' = 1.21 \cdot 10 \, \Omega = 12.1 \, \Omega \]

### Conclusion
Thus, the new resistance of the wire after it has been stretched is:
\[ \boxed{12.1 \, \Omega} \]

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