1. Thermal expansion of each wire

If a wire of length $L$ has coefficient of linear expansion $\alpha$, then for a temperature rise $\Delta T$:

So for the two wires:

• First wire:

  $$\Delta L_1 = \alpha_1 L_1 \Delta T$$

• Second wire:

  $$\Delta L_2 = \alpha_2 L_2 \Delta T$$

2. Total initial length and total expansion

Since the wires are joined end-to-end, the total initial length is:

The total increase in length is the sum of the individual expansions:

Thus,

3. Define effective coefficient

Let the effective coefficient of linear expansion be $\alpha_{\text{eff}}$. Then for the combined wire:

Substitute the total expansion:

Cancel $\Delta T$:

Therefore,

4. Option matching

This matches Option D:

Hence, the correct answer is D.