Question

if the potential difference between the ends of a wire of fixed resistance is doubled by how much does the electric power increase

Answer 1

Power is directly proportional to Potential difference and the Current as by formula P = V × I.
Then, if potential difference is doubled then power will be also gets doubled.

Answer 2

We know that Power is directly proportional to potential difference.

So if potential difference is doubled then electric power will also be doubled.