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 understand the relationship between linear expansion and area expansion in materials when they are heated.

### Step-by-Step Solution:

1. **Understanding Linear Expansion**:
When a material is heated, its length increases. The change in length (ΔL) can be expressed as a percentage of the original length (L). In this case, the copper wire of length L increases by 1% when heated from temperature T1 to T2.

\[ \text{Percentage change in length} = \frac{\Delta L}{L} \times 100 = 1\% \]

2. **Relating Linear Expansion to Area Expansion**:
The area expansion (AE) is related to linear expansion (LE) by the formula:
\[ \text{Area Expansion} = 2 \times \text{Linear Expansion} \]
This means that if the linear dimensions of an object increase, the area will increase by twice that percentage.

3. **Calculating Area Expansion Percentage**:
Since the linear expansion percentage is 1%, we can calculate the area expansion percentage as follows:
\[ \text{Area Expansion Percentage} = 2 \times \text{Linear Expansion Percentage} = 2 \times 1\% = 2\% \]

4. **Conclusion**:
Therefore, when the thin copper plate with dimensions 2L x L is heated from T1 to T2, the percentage change in area is 2%.

### Final Answer:
The percentage change in area when the thin copper plate is heated from T1 to T2 is **2%**.

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