Understanding the difference between potential energy, electric potential, and voltage is important, and it’s easy to mix them up. 

Potential energy

Potential energy is stored energy measured in joules (J). Picture a ball at the top of a hill. The higher it is, the more gravitational potential energy it has. Many systems tend to move toward lower potential energy.

In electrostatics, potential energy comes from interactions between charges. For two point charges, the potential energy is

U = k q1 q2 / r, where U is in joules, k ≈ 8.99×10⁹ N·m²/C², q1 and q2 are the charges, and r is the distance between them. 

Like charges (both positive or both negative) have positive U. That means you must do work to push them together. Opposite charges have negative U, which means they release energy as they move together.

You will also see potential energy written as U = qV. That version describes the potential energy of a small “test” charge q placed in the electric potential V created by other charges. So while “two charges” are needed to have interaction energy, we often talk about the energy of one test charge in the field made by the others.

Electric potential

Electric potential V tells you the potential energy per unit charge at a point. Units are joules per coulomb, which is a volt (V). For a single point charge:

V = k q / r

Here V has the sign of the source charge q. Electric potential is defined relative to a reference where V = 0. In many problems with isolated charges, that reference is infinitely far away. In circuits, we often choose one node as “ground” and call its potential 0 V.

If a point in space has V = 10 V and you place a 5 C charge there, its potential energy is

U = qV = (5 C)(10 J/C) = 50 J.

Voltage (potential difference)

Voltage is a difference in electric potential between two points:

ΔV = Vfinal − Vinitial.

It tells you how much the energy per charge changes when moving from one point to another. Energy change is

ΔU = q ΔV.

Example: move a 1 C charge across a 5 V drop. The energy change is

ΔU = (1 C)(5 J/C) = 5 J.

Sign matters. If ΔV is negative (a drop in potential), a positive charge loses potential energy; a negative charge gains it.

What about electrons? Electric fields point from higher potential to lower potential. Positive charges accelerate “downhill” in potential. Electrons have negative charge, so they feel a force opposite the field and accelerate toward higher potential.

For example, an electron (q = −1.6×10⁻¹⁹ C) moves through a 5 V increase in potential. The change in potential energy is

ΔU = q ΔV = (−1.6×10⁻¹⁹ C)(+5 J/C) = −8.0×10⁻¹⁹ J.

Negative ΔU means the electron’s potential energy decreases; that energy shows up as kinetic energy, so the electron speeds up.

Why do voltages around a circuit loop add to zero?

Imagine that you’re hiking a loop trail that starts and ends at the same spot. Every uphill is a “+” change in altitude, every downhill is a “−” change. When you get back to the starting point, your total altitude change has to be 0, since you’ve arrived back to the same location as before. Batteries are the uphills that lift charge to a higher electric potential. Resistors are the downhills where that potential is “spent” as thermal energy. Add the ups and downs around one full lap and they cancel. If they didn’t, you’d finish the loop somehow higher or lower than the starting point while standing at the starting point, which makes no sense.