SI Unit for Electric Potential: The Volt, Its Definition, Equivalent Forms, and Worked Examples
The SI unit for electric potential is the volt (V), where 1 V = 1 J/C. The volt also measures potential difference, which is called voltage. In SI base units, 1 V = 1 kg·m²·s⁻³·A⁻¹. This guide covers the definition, 5 equivalent forms, 4 formulas, the prefixes, and 5 worked examples.
For a related explanation, see Electric Potential Energy Formula.
What Is the SI Unit for Electric Potential?
The SI unit for electric potential is the volt (V). One volt equals 1 joule of potential energy per coulomb of charge. According to NIST, the volt is the SI derived unit of electric potential difference. Examples include a 12.0 V battery, a 25.0 kV electron gun, and the 80 mV potential difference of the inner ear that Britannica reports.
What Is the Definition of the Volt?
The volt is the potential difference that gives 1 joule of energy to each coulomb of charge, so 1 V = 1 J/C. OpenStax defines electric potential as potential energy per unit charge, V = U/q. NIST also gives the equivalent definition 1 V = 1 W/A, which means 1 watt of power at a current of 1 ampere.
What Is the Dimensional Formula of the Volt?
The dimensional formula of the volt is ML²T⁻³I⁻¹, where M is mass, L is length, T is time, and I is electric current. The formula follows from 1 V = 1 kg·m²·s⁻³·A⁻¹.
What Are the Equivalent Forms of the Volt?
The volt has 5 equivalent forms: J/C, W/A, N·m/C, Ω·A, and kg·m²·s⁻³·A⁻¹. The table below lists each form with its meaning.
| Equivalent Form | Meaning | Basis |
|---|---|---|
| J/C | Energy per unit charge | OpenStax |
| W/A | Power per unit current | NIST |
| N·m/C | Work per unit charge | 1 J = 1 N·m |
| Ω·A | Resistance times current | NIST: 1 Ω = 1 V/A |
| kg·m²·s⁻³·A⁻¹ | SI base units | NIST |
The base-unit form follows from the other forms: 1 J/C = (kg·m²/s²)/(A·s) = kg·m²·s⁻³·A⁻¹.
Which Formulas Give Electric Potential in Volts?
Four formulas give electric potential or potential difference in volts. The table below lists each situation with its formula and symbol definitions.
| Situation | Formula | Symbol Definitions |
|---|---|---|
| Potential from energy | V = U/q | V = electric potential (V), U = potential energy (J), q = charge (C) |
| Potential difference from energy | ΔV = ΔU/q | ΔV = potential difference (V), ΔU = change in potential energy (J), q = charge (C) |
| Point charge | V = kq/r | k = 8.99 × 10⁹ N·m²/C², q = charge (C), r = distance from the charge (m) |
| Uniform electric field | V = Ed | E = field strength (V/m), d = distance along the field (m) |
OpenStax gives the first 3 formulas, and OpenStax College Physics gives V = Ed for the uniform field between parallel plates.
How Do the Volt and Other Electrical Units Compare?
The volt measures electric potential and potential difference, and other units measure related quantities. The table below compares 5 quantities with their symbols, SI units, and meanings.
| Quantity | Symbol | SI Unit | Meaning |
|---|---|---|---|
| Electric potential | V | volt (V) | Potential energy per unit charge at a point |
| Potential difference (voltage) | ΔV | volt (V) | Change in electric potential between 2 points |
| Electric potential energy | U | joule (J) | Energy of a charge in an electric field |
| Electric field | E | V/m, equal to N/C | Force per unit charge |
| Electric charge | q | coulomb (C) | Amount of electric charge |
According to NIST and Britannica, potential difference is also called voltage. Britannica states that electric potential is measured from a reference point, such as Earth. Britannica also describes the volt as a unit of electromotive force.
Is Voltage the Same as Electric Potential?
Voltage is another name for electric potential difference, and electric potential is measured from a reference point. Both quantities use the volt. OpenStax states that voltage is not the same as energy, because voltage is energy per unit charge.
How Is the Volt Related to the Electron-Volt?
The electron-volt (eV) is a unit of energy, and the volt (V) is a unit of electric potential. One electron-volt is the energy gained by an elementary charge through a potential difference of 1 V. The value is 1 eV = 1.602 176 634 × 10⁻¹⁹ J, which is exact in the 2022 CODATA values from NIST.
What Are the SI Prefixes for the Volt?
SI prefixes multiply the volt by powers of 10, and the prefix symbol attaches directly to the unit symbol. NIST states that a prefix symbol attaches directly to the symbol for a unit, as in km for kilometer. The same rule gives mV for millivolt and kV for kilovolt. The table below lists 4 prefixes with their symbols, factors, and examples.
| Prefix | Symbol | Factor | Example |
|---|---|---|---|
| micro | μ | 10⁻⁶ | 1 μV = 1 × 10⁻⁶ V |
| milli | m | 10⁻³ | 80 mV = 0.080 V |
| kilo | k | 10³ | 25.0 kV = 2.50 × 10⁴ V |
| mega | M | 10⁶ | 1 MV = 1 × 10⁶ V |
How Do You Calculate Electric Potential in Volts?
Calculate electric potential in volts by selecting the formula for the situation and substituting values in SI units. The calculation takes 5 steps:
- Identify the situation, such as a battery, a point charge, or a uniform field.
- Convert charges to coulombs, distances to meters, and energies to joules.
- Select the matching formula from the formula table.
- Substitute the values with their signs.
- Report the result in volts, and check that the units reduce to J/C.
What Are Worked Examples of Electric Potential in Volts?
Five worked examples apply the formulas to a battery, a point charge, a uniform field, air breakdown, and a proton. The table below lists the given values, the formula with substitution, and the result of each example.
| Example | Given | Formula and Substitution | Result |
|---|---|---|---|
| 1. Battery | U = 6.00 × 10⁴ J, q = 5,000 C | V = U/q = (6.00 × 10⁴ J)/(5,000 C) | V = 12.0 V |
| 2. Point charge | q = +2.00 nC, r = 0.100 m | V = kq/r = (8.99 × 10⁹)(2.00 × 10⁻⁹)/0.100 | V = 1.80 × 10² V |
| 3. Uniform field | E = 6.25 × 10⁵ V/m, d = 0.0400 m | V = Ed = (6.25 × 10⁵)(0.0400) | V = 2.50 × 10⁴ V = 25.0 kV |
| 4. Air breakdown | E = 3.0 × 10⁶ V/m, d = 0.025 m | V = Ed = (3.0 × 10⁶)(0.025) | V = 7.5 × 10⁴ V = 75 kV |
| 5. Proton energy | q = +1.602 × 10⁻¹⁹ C, ΔV = 3.00 × 10⁴ V | ΔU = qΔV = (1.602 × 10⁻¹⁹)(3.00 × 10⁴) | ΔU = 4.81 × 10⁻¹⁵ J = 30.0 keV |
Example 1 matches an OpenStax problem in which a 12.0 V battery moves 5,000 C and delivers 6.00 × 10⁴ J. Examples 3 and 4 use the OpenStax College Physics electron gun and dry air problems. Example 5 follows the OpenStax statement that a proton accelerated through 30 kV gains 30 keV.
The units in example 2 reduce to volts: (N·m²/C²)(C)/m = N·m/C = J/C = V.
How Do You Write the Volt and Its Symbol?
Write the unit name as "volt" in lower case and the unit symbol as "V" in upper case. NIST states that unit names start with a lower-case letter, even when the symbol begins with a capital letter. NIST also states that a symbol derived from a proper name takes a capital first letter.
Why Is the Unit of Electric Potential Called the Volt?
The volt is named after the Italian physicist Alessandro Volta. According to Britannica, the volt was named in his honor in 1881. Volta lived from 1745 to 1827 and invented the electric battery in 1800.
What Mistakes Do Students Make With the Unit of Electric Potential?
Five mistakes cause unit errors in electric potential problems:
- Writing joules (J) as the unit of electric potential
- Confusing the electron-volt (eV), a unit of energy, with the volt (V)
- Writing V instead of V/m as the unit of electric field
- Capitalizing the unit name or writing the symbol as a lower-case v
- Assuming electric potential is zero wherever the electric field is zero
A review of electricity and magnetism misconceptions cites Bagno and Eylon (1997), who found that 62% of students answered incorrectly when asked whether the potential is zero where the field is zero. The review explains that students do not distinguish potential from potential difference.
What Are People Also Asking About the SI Unit for Electric Potential?
What is the SI unit for electric potential?
The SI unit for electric potential is the volt (V).
What is the SI unit of potential difference?
The SI unit of potential difference is the volt (V).
What is 1 volt equal to?
One volt equals 1 joule per coulomb (1 V = 1 J/C).
What is the unit of electric potential in SI base units?
The unit of electric potential in SI base units is kg·m²·s⁻³·A⁻¹.
What is the SI unit of electric potential energy?
The SI unit of electric potential energy is the joule (J).
What is the SI unit of electric field?
The SI unit of electric field is the volt per meter (V/m), which equals the newton per coulomb (N/C).
Why Does the SI Unit for Electric Potential Matter in Physics?
The SI unit for electric potential matters because the volt links energy, charge, and power in electrical measurements. The volt equals 1 J/C and 1 W/A, so a potential in volts gives the energy per coulomb and the power per ampere. Consistent use of volts, joules, and coulombs gives valid results for batteries, point charges, and uniform fields.
For the official reference, consult OpenStax University Physics Electric Potential.
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