A thin copper wire of length L increase in length by `1%` when heated from temperature `T_(1) "to" T_(2)` What is the percentage change in area when a thin copper plate having dimensions `2LxxL` is heated from `T_(1) "to "T_(2)` ?

Options

A. `1%`
B. `2%`
C. `3%`
D. `4%`

Explanation

To solve the problem, we need to determine the percentage change in the area of a thin copper plate when it is heated, given that a thin copper wire of length L increases in length by 1% when heated from temperature T1 to T2.

### Step-by-Step Solution:

1. **Understanding the Problem**:
- We have a copper wire of length \( L \) that increases in length by 1% when heated. This means:
\[ \Delta L = 0.01L \]
- We need to find the percentage change in area of a copper plate with dimensions \( 2L \times L \).

2. **Calculate the Original Area of the Plate**:
- The area \( A \) of the copper plate can be calculated as:
\[ A = \text{length} \times \text{width} = 2L \times L = 2L^2 \]

3. **Understanding Area Change with Length Change**:
- When the temperature increases, the length of the plate will also increase. The area of the plate is related to the square of its dimensions. Thus, if the length changes, the area will change according to the formula:
\[ A \propto L^2 \]
- This means that the change in area \( \Delta A \) can be expressed as:
\[ \frac{\Delta A}{A} = 2 \frac{\Delta L}{L} \]

4. **Substituting the Change in Length**:
- We know that \( \frac{\Delta L}{L} = 0.01 \) (1% increase in length). Therefore:
\[ \frac{\Delta A}{A} = 2 \times 0.01 = 0.02 \]

5. **Calculating the Percentage Change in Area**:
- To find the percentage change in area, we multiply by 100:
\[ \text{Percentage Change in Area} = 0.02 \times 100 = 2\% \]

### Final Answer:
The percentage change in area when the thin copper plate is heated from \( T_1 \) to \( T_2 \) is **2%**.