What are the Units for V in Electric Potential and Volts?

[tony873004]

Sometimes I see V representing Electric Potential. Is this the same as electric potential energy? What are the units for V? Sometimes I see V represent volts. But this just seems weird. V is a unit of V? As an analogy, we use kg is a unit of m (mass). We never use m as a unit for m.

 

[cepheid]

V is sometimes the symbol for electric potential, which is just electric potential energy per unit charge:

$$[\textrm{potential}] = \frac{[\textrm{energy}]}{[\textrm{charge}]}$$

The unit for potential, is of, course, the joule per coulomb, also known as a volt (whose symbol is also V).

$$1 \ \textrm{V} = 1 \ \frac{\textrm{J}}{\textrm{C}}$$

So, the symbol V is being used both for the physical quantity known as potential, AND for the units in which it is measured. Note, however, that symbols for physical quantities and mathematical variables are typically italicized when typeset properly, whereas unit symbols are not, so that we might have something like:

$$V = 5 \ \textrm{V}$$

It's obvious why the UNIT symbol is a V (the unit is volt, after all, named after Volta). It's less obvious why the symbol for potential is a V. It could be because a difference in electric potential (or potential difference for short) is often referred to as a voltage. Calling voltage V is intuitive. Then again, the symbol for a physical quantity doesn't have to make intuitive sense. Why is p momentum?. Heck, sometimes we use greek letters.

 

[cepheid]

Just to confuse the matter, V is sometimes NOT used as a symbol for electric potential. Instead, it is used to denote potential energy, in which case it has units of joules (J). Although U is more commonly used to denote potential energy, I have definitely seen V used, particularly in the context of quantum mechanics. Even more confusingly, this V is referred to as a "potential" function, when a "potential energy" function is what is actually meant.

 

[D H]

Sometimes I see V representing Electric Potential. Is this the same as electric potential energy? What are the units for V? Sometimes I see V represent volts. But this just seems weird. V is a unit of V? As an analogy, we use kg is a unit of m (mass). We never use m as a unit for m.

Questions answered in order: Yes, Volts, Yes.

Alternatively, one volt is one kilogram·meter²/ampere/second³.

Add to your list the term "voltage". That would be like using "kilogramage" to mean mass expressed in kilograms. We do, however, use "tonnage" to mean mass in tons.

 

[tony873004]

Now that you mention it, I do notice italicized vs. regular in the book. Unfortunately, the book uses a font where italicized V and regular V are almost identical. And handwritten on the blackboard... forget it!

Thanks for the replies, cepheid and DH.