# What is the difference between the potential difference and potential energy of an electron?

What is the difference between the potential difference and potential energy of an electron?

Let's take an example the potential difference (PD) across a resistor. if there's a current flowing, the power lost is equal to the current x PD. But in reality, the electrons inside the resistor are losing this potential energy right? If so, what is the relationship between the energy level (or the quantised energy) of an electron inside the resistor and voltage drop?

• I don't see any reason that it should be different than any other case: $\Delta U = q\Delta V$ – garyp Apr 25 '16 at 19:28
• The potential varies along a resistor and the electrons lose tiny amounts of energy in stochastic scattering processes in the resistor material's lattice. – CuriousOne Apr 25 '16 at 19:30
• yes but here I am referring to the difference between the potential energy of the electrons (or energy level in quantum mechanics) and potential difference across a resistor – Tonylb1 Apr 25 '16 at 19:32
• The relation is as simple as garyp states. The current is made up of a large number of electrons. There is no difference between energy loss for one electron = electron charge x PD, and energy loss for all electrons = current x time [=total charge] x PD. Perhaps you are trying to ask something more profound, but it is not clear what it is. I think bringing quantized energy levels into the problem only obscures the issues. – sammy gerbil Apr 25 '16 at 20:43

## 2 Answers

What is the difference between the potential difference and potential energy of an electron?

If I understand your question right, these terms are describing the same thing - one is just in a "per charge" version.

• Electric potential energy $U_e$ is the potential energy associated with one spot in the circuit.

• Electric potential or just potential $V$ is this energy per charge, $V=U/q$.

• Potential difference $\Delta V$ is then just the difference in potential between two points, $\Delta V=V_{b}-V_{a}$.

Potential energy is the "repulsion" (like pressure in a water pipe) that pushes electrons through the resistor.

• I am referring here to the difference between energy levels of electrons (en.wikipedia.org/wiki/Energy_level) and the electrical potential difference in a circuit – Tonylb1 Apr 25 '16 at 20:18
• @Tonylb1 Aha. In that case I would use the term energy state or energy level instead of potential energy throughout in your question. – Steeven Apr 25 '16 at 20:21
• @Tonylb1 : In that case the two concepts are the same. The electron has a different electrical potential energy at different positions within an atom, and it has a different electrical potential energy at different positions along a wire in a circuit. – sammy gerbil Apr 26 '16 at 16:46
• But both energies (within an atom and position along a wire) are they related somehow? – Tonylb1 Apr 28 '16 at 12:57

Potential difference in a circuit is a collective effect of a large number (order of 10^23) electrons moving in conductors and resistors . It is a term within classical electrodynamics, and the value emerges from what happens at the level of particles and atoms, the quantum mechanical level.

This link shows what is going on at the microscopic level: In a conductor the electrons exist in practically continuous energy levels that make them act as free, they have a drift velocity, much smaller than the velocity of light which is the velocity of the collective effect, this shows more detail of how resistance is seen by individual electrons.

The individual electrons "see" the potential difference, i.e. the imposed electric field at the classical level and acquire their drift velocity, added to the statistical velocity of the fermi level.

Reading up on the band theory of solids will help to clarify this microscopic picture, as electrons in circuits are not tied to atoms but to the lattice as a whole.