Final answer:
Voltage is the energy per unit charge in space, and the relationship between potential difference and electric potential energy is direct proportionality. Thus, potential difference is directly proportional to electric potential energy, which can be mathematically expressed as ΔU = qΔV.
Step-by-step explanation:
Relationship Between Voltage and Energy
The relationship between voltage and energy is one where the voltage is defined as the energy per unit charge at some point in space. In terms of potential difference and electric potential energy, the relationship can be expressed as ΔU = qΔV, where ΔU is the change in electric potential energy and q is the charge. Therefore, the correct answer to the question is that potential difference is directly proportional to electric potential energy, which is option (c).
It is important to understand that voltages—potential differences—are always measured between two points because the voltage at a single point is not meaningful without a reference point, similar to how gravitational potential energy requires a reference level. In summary, voltage is not the same as energy, but it indicates how much energy per unit charge is available to be converted into other forms.