Volt (V)

Also called V, Joule per coulomb

The volt is the SI unit of electric potential and potential difference, equal to one joule per coulomb. It measures energy per unit charge, so a volt is not itself a quantity of energy.

Divide an energy by a charge and a volt is what is left:

1 V=1 J/C1\ \text{V} = 1\ \text{J/C}

That comes straight from the sheet's ΔUE=qΔV\Delta U_E = q\Delta V. Move 2.02.0 C through a potential difference of 9.09.0 V and the electric potential energy changes by 1818 J. Move 1.01.0 C through the same 9.09.0 V and it changes by 9.09.0 J. The potential difference did not move; the energy did.

Which is why a 9 V battery does not hold 9 J. It maintains nine joules per coulomb across its terminals, and the energy it delivers depends entirely on how much charge goes through. Treating a voltage as a quantity of energy survives the arithmetic unnoticed, because both are scalars that add, so nothing in the working looks wrong.

A volt per metre is a newton per coulomb. The sheet prints E=ΔV/Δr\lvert \vec{E} \rvert = \lvert \Delta V / \Delta r \rvert alongside E=FE/q\vec{E} = \vec{F}_E / q, so field strength ends up with two unit expressions, and they agree: (J/C)/m=(Nm/C)/m=N/C(\text{J/C})/\text{m} = (\text{N} \cdot \text{m/C})/\text{m} = \text{N/C}. Either is acceptable in an answer.

Volts and voltage. Voltage is loose shorthand. What the equations carry is a potential difference between two points. A bare VV at a point only means something once a zero is chosen, and both electricity exam-convention boxes fix that zero at an infinite distance from an isolated point charge.

Volt is printed on the AP Physics 2 and AP Physics C: Electricity and Magnetism unit-symbol tables.

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