Formula of Voltage: V = W/Q, Potential Difference and V = IR

The formula of voltage is $V = \frac{W}{Q}$ : the work done in moving a charge between two points, divided by that charge. This is also the formula of potential difference, since voltage is simply the everyday name for potential difference. One volt means one joule of energy for every coulomb.

In circuits you will more often use Ohm's law, $V = IR$ , or the power form $V = \frac{P}{I}$ . All three describe the same quantity from different starting points. Class 10 introduces the energy definition, while AP Physics 1 and Class 12 lean on V = IR and Kirchhoff's loop rule.

Quick facts

Definition
$V = \frac{W}{Q}$
Ohm's law
$V = IR$
From power
$V = \frac{P}{I}$
SI unit
volt (V) = J/C
Dimensional formula
[M¹ L² T⁻³ I⁻¹]
Type
Scalar
Measured with
A voltmeter connected in parallel

Symbols in the formula of potential difference

Meaning of V = W / Q
Symbol	Quantity	SI unit
$V$	Potential difference between two points	volt, V
$W$	Work done on, or energy transferred by, the charge	joule, J
$Q$	Charge moved between the points	coulomb, C

Potential difference always compares two points. A 12 V battery means each coulomb gains 12 J going through it, and loses those 12 J in the outside circuit. The potential of a single point is measured from a chosen zero, usually the earth or the negative terminal.

Three versions of the formula of voltage

Pick the form that matches the data
You know	Use
Work and charge	$V = \frac{W}{Q}$
Current and resistance	$V = IR$
Power and current	$V = \frac{P}{I}$
Field and distance in a uniform field	$V = Ed$
Point charge Q at distance r	$V = \frac{kQ}{r}$

The last two rows belong to electrostatics. They link voltage to the electric field, which is the voltage drop per metre.

Worked examples

Example 1: energy per coulomb

A battery does 18 J of work moving 1.5 C of charge round a circuit. Find its voltage.

$V = \frac{18}{1.5} = 12\ \text{V}$

Example 2: Ohm's law with milliamperes

A current of 250 mA flows through a 48 Ω resistor. Find the voltage across it.

I = 0.250 A.

$V = IR = 0.250\times48 = 12\ \text{V}$

Example 3: a kettle

A 1500 W kettle draws 6.25 A. Find the supply voltage.

$V = \frac{P}{I} = \frac{1500}{6.25} = 240\ \text{V}$

Example 4: one electron through one volt

How much energy does an electron gain when it moves through a potential difference of 1.0 V?

$W = QV = (1.602\times10^{-19})(1.0) = 1.602\times10^{-19}\ \text{J}$

This amount is called one electron volt (eV).

Units and dimension of the volt

A volt is a joule per coulomb. Writing the joule as kg m² s⁻² and the coulomb as A s gives

$[V] = \frac{[M L^2 T^{-2}]}{[I T]} = [M L^2 T^{-3} I^{-1}]$

The dimensional formula of voltage page shows the same result reached through P = VI. Common multiples are mV (10⁻³ V) and kV (10³ V).

Voltage versus emf

The electromotive force of a cell is the energy it supplies per coulomb, measured when no current flows. Once current flows, some energy is lost inside the cell, so the terminal voltage is $V = \varepsilon - Ir$ , where r is the internal resistance. The emf formula page explains this in detail.

Voltmeters go in parallel across the part you are measuring. Ammeters go in series. Swapping them is a classic practical exam slip.

Errors to avoid

Calling voltage the charge that flows. It is energy per unit charge.
Forgetting to change mA to A, or kJ to J.
Assuming the voltage is the same across resistors in series. It is shared; the current is the same.
Mixing up potential (one point) with potential difference (two points).

Resistance and current, the other two parts of Ohm's law, are on the resistance formula and current formula pages. A chapter summary, including power and heating, lives on the electricity hub for quick revision.

Frequently asked questions

What is the formula of potential difference?

V = W / Q, the work done per unit charge in moving charge between two points. In a circuit you can also use V = IR.

What is the formula of voltage in physics with current and resistance?

V = IR, which is Ohm's law. Multiply the current in amperes by the resistance in ohms to get volts.

Voltage is measured in which SI unit?

The volt (V). One volt is one joule per coulomb.

Is voltage a scalar or a vector?

Scalar. Voltage carries a value and a sign, yet points nowhere in space.

What is 1 volt in terms of base units?

1 V = 1 kg m² s⁻³ A⁻¹, which matches the dimensional formula [M¹ L² T⁻³ I⁻¹].