**Potential Difference**

Potential difference, also known as voltage, is a fundamental concept in the field of electricity. It is defined as the difference in electric potential energy between two points in an electric circuit. Essentially, potential difference refers to the amount of work done per unit charge in moving a charge from one point to another.

**Voltage**

Voltage, on the other hand, is a measure of the electric potential difference between two points in an electric circuit. It is commonly represented by the symbol V and is measured in volts (V). Voltage can be thought of as the driving force or energy per unit charge that pushes the electric current through a circuit.

**Relationship**

Potential difference and voltage are essentially the same thing and can be used interchangeably. They both refer to the difference in electric potential energy between two points. The terms potential difference and voltage are often used in different contexts, with potential difference being used more in physics and voltage being used more in engineering and practical applications.

**Physical Interpretation**

The physical interpretation of potential difference or voltage can be understood with the analogy of a water circuit. In a water circuit, potential difference can be compared to the difference in water pressure between two points. The higher the pressure difference, the faster the water flows. Similarly, in an electric circuit, a higher potential difference or voltage will result in a higher electric current.

**Mathematical Relationship**

The mathematical relationship between potential difference, current, and resistance is given by Ohm's Law: V = IR, where V is the potential difference, I is the current, and R is the resistance. This equation shows that the potential difference is directly proportional to the current flowing through the circuit and the resistance.

**Conclusion**

In conclusion, potential difference and voltage are interchangeable terms that refer to the difference in electric potential energy between two points in an electric circuit. They represent the driving force or energy per unit charge that pushes the electric current through the circuit. Potential difference is more commonly used in physics, while voltage is used in engineering and practical applications. Understanding the concept of potential difference or voltage is crucial in understanding the behavior and functioning of electric circuits.