Step 1: Use Ohm's law
\[
V = IR
\]
Where:
- \( V \) is the potential difference
- \( I \) is the current
- \( R \) is the resistance
Given:
- \( I = 2 \, \text{A} \)
- \( R = 10 \, \Omega \)
Substitute the values into the formula:
\[
V = 2 \times 10 = 20 \, \text{V}
\]
Answer: Therefore, the potential difference across the wire is \( 20 \, \text{V} \). So, the correct answer is option (1).