The length of the resistance wire is increased by `10%`. What is the corresponding change in the resistance of wire?

Options

A. `10%`
B. `25%`
C. `21%`
D. `9%`

Explanation

To solve the problem of how the resistance of a wire changes when its length is increased by 10%, we can follow these steps:

### Step-by-Step Solution:

1. **Assume Initial Length**:
Let's assume the initial length of the wire, \( L_i \), is 100 units. This makes calculations easier when dealing with percentages.

**Hint**: Always start with a convenient value for initial conditions to simplify calculations.

2. **Calculate Final Length**:
Since the length is increased by 10%, the final length \( L_f \) can be calculated as:
\[ L_f = L_i + 10\% \text{ of } L_i = 100 + 10 = 110 \text{ units} \]

**Hint**: To find the final value after a percentage increase, add the percentage of the initial value to the initial value.

3. **Understand Resistance Relation**:
The resistance \( R \) of a wire is directly proportional to its length when other factors (like material and cross-sectional area) remain constant. Thus, we can express this relationship as:
\[ R \propto L \]

4. **Calculate Initial and Final Resistance**:
Let the initial resistance be \( R_i \). The final resistance \( R_f \) can be expressed as:
\[ \frac{R_f}{R_i} = \frac{L_f}{L_i} = \frac{110}{100} = 1.1 \]
Therefore, the final resistance can be expressed as:
\[ R_f = R_i \times 1.1 \]

**Hint**: When dealing with proportional relationships, set up a ratio to find the new value based on the change.

5. **Calculate Change in Resistance**:
The change in resistance \( \Delta R \) is given by:
\[ \Delta R = R_f - R_i = (1.1 R_i - R_i) = 0.1 R_i \]

**Hint**: The change in a quantity can be found by subtracting the initial value from the final value.

6. **Calculate Percentage Change in Resistance**:
The percentage change in resistance can be calculated using the formula:
\[ \text{Percentage Change} = \left( \frac{\Delta R}{R_i} \right) \times 100 = \left( \frac{0.1 R_i}{R_i} \right) \times 100 = 10\% \]

**Hint**: To find the percentage change, divide the change by the original value and multiply by 100.

### Final Answer:
The corresponding change in the resistance of the wire when its length is increased by 10% is **10%**.