Voltage: Definition, Equation, Units (W/ Examples)

Imagine water flowing downhill through a system of pipes. Your intuition should tell you what factors would make the water flow faster and what would make it flow slower. The higher the hill, the faster the current will be, and the more obstructions in the pipe, the slower it will flow.

This is all due to a ​potential energy difference​ ​between the top of the hill and the bottom​, because the water has gravitational potential energy at the top of the hill and none by the time it reaches the bottom.

This is a great analogy for electrical ​voltage​. In the same way, when there is an electric potential difference between two points on an electrical circuit, electric current flows from one part of the circuit to another.

Just like in the water example, the potential energy difference between the two points (created by the distribution of electric charge) is what creates the current flow. Of course, physicists have more precise definitions than this, and learning equations such as Ohm's law gives you a better understanding of voltage.

Voltage is the name given to an electric potential energy difference between two points, and it's defined as the electric potential energy per unit charge. Although ​electric potential​ is a more accurate term, the fact that the SI unit of electric potential is the volt (V) means that it's commonly referred to as voltage, particularly when people talk about the potential difference between the terminals of a battery or other parts of a circuit.

The definition can be written mathematically as:

\(V = \frac{E_{el}}{q}\)

Where ​V​ is the potential difference, ​E​_el is the electrical potential energy (in joules) and ​q​ is the charge (in coulombs). From this, you should be able to see that 1 V = 1 J/C, meaning one volt is defined as one joule per coulomb (i.e., per unit charge). Sometimes, you'll see ​E​ used as the symbol for voltage, because another term for the same quantity is "electromotive force" (EMF), but many sources use ​V​ to match everyday usage of the term.

The volt takes its name from Italian physicist Alessandro Volta, who is best known for inventing the first electric battery (called the "voltaic pile").

However, the above equation isn't the most commonly used equation for voltage, because most of the time you encounter the term it will involve an electrical circuit, and the most useful equation for this is ​Ohm's law​. This relates the voltage to the current flow in the circuit and the resistance to the flow of current from the wires and components of the circuit, and has the form:

\(V = IR\)

Where ​V​ is the potential difference in volts (V); ​I​ is the current flow, with a unit of the ampere or amp for short (A); and ​R​ is the resistance in ohms (Ω). At a glance, this equation tells you that for the same resistance, higher voltages produce higher currents (analogous to increasing the height of the hill in the introduction) and for the same voltage, current flow is reduced for higher resistances (analogous to the obstructions to the pipes in the example). If there is no voltage difference, no current will flow.

Different components of a circuit will have different ​voltage drops​ across them, and you can use Ohm's law to work out what they will be. In line with Kirchhoff's voltage law, though, ​the sum of voltage drops around any complete loop in a circuit must be equal to zero​.

The voltage across an element in an electric circuit can be measured with a voltmeter or a multimeter, with the latter containing a voltmeter but also other tools like an ammeter (to measure current). You connect the voltmeter in parallel across the element being measured to determine the voltage drop between the two points – never connect it in series!

Analog voltmeters work using a galvanometer (a device for measuring small electric currents) in series with a high-ohm resistor, with the galvanometer containing a coil of wire in a magnetic field. When a current flows through the wire, it creates a magnetic field, which interacts with the existing magnetic field to make the coil rotate, which then moves the pointer on the device to indicate the voltage.

Because the rotation of the coil is proportional to the current, and the current is in turn proportional to the voltage (by Ohm's law), the more the coil rotates, the bigger the voltage between the two points. This is more complicated if you're measuring alternating current rather than direct current, but different designs make this possible too.

You have to connect a voltmeter in parallel because two circuit elements in parallel have the same voltage across them. A voltmeter must have high resistance because this prevents it from drawing too large a current from the main circuit and thereby interfering with the result. Plus, voltmeters aren't constructed to draw large currents, so if you connect one in series, it could easily break or blow a fuse.

Learning to work with electric potential involves learning to use Ohm's law and learning to apply Kirchhoff's voltage law to determine voltage drops across different elements in a circuit. The simplest thing to do is apply Ohm's law to a whole circuit.

If a circuit is powered by a 12-V battery and has a total of 70 ohms of resistance, what is the current flowing through the circuit?

Here, you simply need to re-arrange Ohm's law to create an expression for electric current. The law states:

\(V = IR\)

All you need to do is divide both sides by ​R​ and reverse to get:

\(I=\frac{V}{R}\)

Inserting values gives:

\(\begin{aligned}
I&=\frac{1 \text{ V}}{70 \text{ Ω}} \
&= 0.1714 \text{ A}
\end{aligned}\)

So the current is 0.1714 A, or 171.4 milliamps (mA).

But now imagine that this 70 Ω of resistance is split across three different resistors in series, with values of 20 Ω, 10 Ω and 40 Ω. What is the voltage drop across each component?

Again, you can use Ohm's law to look at each component in turn, noting the overall electric current around the circuit of 0.1714 A. Using V = IR for each of the three resistors in turn:

For the first:

\(\begin{aligned}
V_1 &= 0.1714 \text{ A} × 20 \text{ Ω} \
&= 3.428 \text{ V}
\end{aligned}\)

The second:

\(\begin{aligned}
V_2 &= 0.1714 \text{ A} × 10 \text{ Ω} \
&= 1.714 \text{ V}
\end{aligned}\)

And the third:

\(\begin{aligned}
V_3 &= 0.1714 \text{ A} × 40 \text{ Ω} \
&= 6.856\text{ V}
\end{aligned}\)

According to Kirchhoff's voltage law, these three voltage drops should add up to 12 V:

\(\begin{aligned}
V_1 + V_2 + V_3 &= 3.428 \text{ V} + 1.714 \text{ V} + 6.856 \text{ V}\)
\(&= 11.998 \text{ V}
\end{aligned}\)

This equals 12 V to two decimal places, with the slight discrepancy being due to rounding errors.

In the discussion of how to measure voltage above, it was noted that voltage drops across parallel components in a circuit are the same. This is explained by ​Kirchhoff's voltage law, which states that the sum of all voltages (the positive voltage from the power source and the voltage drops from components) in a closed loop must equal zero​.

For a parallel circuit, with multiple branches, you can create such a loop including any one of the parallel branches and the battery. Regardless of the component on each branch, the voltage drop across any branch ​must​ therefore be equal to the voltage provided by the battery (ignoring the possibility of other components in series, for simplicity). This is true for all branches, and so parallel components will always have equal voltage drops across them.

Ohm's law can also be extended to relate to power (​P​), which is the rate of energy supply in joules per second (watts, ​W​), and it turns out that P = IV.

For a circuit component such as a light bulb, this shows that the power it dissipates (i.e., turns into light) depends on the voltage across it, with higher voltages leading to a higher power output. In line with the discussion of parallel components in the previous section, multiple light bulbs arranged in parallel glow brighter than the same bulbs arranged in series, because the full battery voltage drops across each light bulb when connected in parallel, while only a third of it does when they're connected in series.