Statement 1: The potential difference is measured in volts.
Statement 2: One volt is equal to one newton per coulomb.
Which of the following is true?

The correct option is Only Statement 1 is correct.

Let us analyze each statement step-by-step to understand the underlying physics concepts:

Analysis of Statement 1:
Electric potential difference between two points is defined as the work done in moving a unit positive charge from one point to another in an electric field. The standard SI unit of potential difference is the volt (V). Therefore, Statement 1 is correct.

Analysis of Statement 2:
By definition, potential difference ($V$) is work done ($W$) per unit charge ($Q$):

$V=\frac{W}{Q}$

The SI unit of work done is the joule (J), and the SI unit of electric charge is the coulomb (C). Thus:

$1\text{volt}=1\text{joule per coulomb}=1\text{J/C}$

On the other hand, a newton per coulomb (N/C) is the SI unit of electric field intensity ($E=\frac{F}{Q}$), not electric potential difference. Therefore, Statement 2 is incorrect.

Conclusion:
Since Statement 1 is true and Statement 2 is false, the correct choice is Only Statement 1 is correct.