# Electric potential and voltage in a circuit

• I
As I understand it, electrical potential is the potential energy of a unit charge in some point in space. How does this idea relate to the idea of voltage in a circuit? The term electric potential seems to be used for both.

## Answers and Replies

Drakkith
Staff Emeritus
Science Advisor
Voltage is the difference in electric potential between two points, while electric potential itself is a way to define the electric potential energy of any charged particle placed in a specific field. Electric potential is the electric potential energy of a charged particle divided by the charge on that particle. Dividing by the charge gives you a way of characterizing the electric field itself, without need for a specific reference charge.

Basically, a charged particle with 2 coulombs of charge might have 10 joules of electric potential energy when placed in an electric field at point A. Dividing out the charge gives you 5 volts (joules per coulomb) of electric potential. At point B, the same charged particle might have 4 joules of electric potential energy. Dividing the charge out gives you 2 volts.

The voltage between points A and B is 5-2=3 volts. Note that volts is a unit of measurement, while voltage is not.

• FS98 and phinds
sophiecentaur
Science Advisor
Gold Member
2020 Award
The term electric potential seems to be used for both.
Potential is Potential.
Potential Difference is Volts.
Say that to yourself every day for a few weeks and you will not be confused.
Think in terms of gravitational potential. Climb up a step ladder 1.5m and jump off. You fell between a Gravitational Potential Difference of 1.5m and it hurt your feet. Now get in a 747 and do the same thing at 10,000m. Your Gravitational Potential is much higher but the Potential Difference and pain is the same.

Voltage is the difference in electric potential between two points, while electric potential itself is a way to define the electric potential energy of any charged particle placed in a specific field. Electric potential is the electric potential energy of a charged particle divided by the charge on that particle. Dividing by the charge gives you a way of characterizing the electric field itself, without need for a specific reference charge.

Basically, a charged particle with 2 coulombs of charge might have 10 joules of electric potential energy when placed in an electric field at point A. Dividing out the charge gives you 5 volts (joules per coulomb) of electric potential. At point B, the same charged particle might have 4 joules of electric potential energy. Dividing the charge out gives you 2 volts.

The voltage between points A and B is 5-2=3 volts. Note that volts is a unit of measurement, while voltage is not.
Isn’t electrical potential already relative? I thought we just generally use infinity as the point we’re comparing to. If that is the case, how is voltage a difference while electrical potential is not?

Drakkith
Staff Emeritus
Science Advisor
Isn’t electrical potential already relative? I thought we just generally use infinity as the point we’re comparing to. If that is the case, how is voltage a difference while electrical potential is not?

I'm not going to get into whether or not electric potential is relative. I only meant to point out what the difference between voltage and electric potential are. Perhaps I should have avoided italicizing anything.

Whether or not electric potential is relative, voltage is the difference in electric potential between two points. It represents the amount of energy, per unit of charge, required to move a charged particle between those two points. Electric potential is a measure of the amount of energy required to move a charge from infinity to its current location. However, note that infinity is not a point, though we commonly treat it as if it is. If I were to choose a point 5 gazillion lightyears away as my infinity, I would actually be finding the voltage between that point and the current location of my particle. The reason is because that point, even though it's 5 gazillion lightyears away, still has electric potential.

• FS98
sophiecentaur
Science Advisor
Gold Member
2020 Award
Isn’t electrical potential already relative? I thought we just generally use infinity as the point we’re comparing to. If that is the case, how is voltage a difference while electrical potential is not?
The "Potential" is defined relative to infinity. There is no confusion when you quote Potential (appropriately) but there is no experiment on Earth where a voltmeter can be connected to Infinity so the reference always has to be specified. Hence PD.
The system is so well established that there is not much point in questioning it or arguing against it.

• FS98
anorlunda
Staff Emeritus
A strictly practical view is to note that a voltmeter that we use to measure voltage always has two wire leads.

• sophiecentaur