Voltage

Units of Voltage

From the definition, we see that the unit for voltage is the joule per coulomb (\(\mathrm{JC}^{-1}\)). The derived unit of voltage is the volt, denoted as \(\mathrm V\), which is the same as a joule per coulomb. That is

\[1\,\mathrm{V}=1\,\mathrm{JC}^{-1}\]

where we see that charge relates voltage to energy. Voltage is measured by a voltmeter but a modern alternative is a digital multimeter that can be used to measure voltage, current and other electric quantities. The figure below is of a typical analog voltmeter.

A typical analog voltmeter is used to measure the voltage between two points in an electric circuit, Pxhere.

Formula for Voltage

The definition of voltage is the work done per unit charge and hence we can use this to write a basic formula for a voltage as below:

\[\text{voltage}=\dfrac{\text{work done (energy transferred)}}{\text{charge}}\]

or

\[V=\dfrac{W}{Q}\]

where the voltage (\(V\)) is measured in volts (\(\mathrm V\)), the work done (\(W\)) is measured in joules (\(\mathrm J\)) and the charge (\(Q\)) is measured in coulombs (\(\mathrm C\)). Looking at the formula above, we are reminded that work done and energy transferred are the same. The amount of energy transferred to a circuit component per unit charge that flows through it gives us the voltage measured across that circuit component. Look at the following example.

We have stated that voltage is measured over two different points in an electric circuit. This is because energy will be transferred to devices in that circuit, so the work done must be measured by an energy difference between two points on either side of those devices. This means that a voltmeter must be connected in parallel in a circuit. The figure below shows a simple circuit with a voltmeter (labelled with a V) connected in parallel to a lamp to measure the voltage across the lamp. This voltage is simply the energy transferred to the lamp per unit charge that flows through it.

A voltmeter is connected in parallel to a lamp to measure the voltage across it, Wikimedia Commons CC BY-SA 4.0.

Electromotive Force (EMF)

The law of conservation of energy states that energy can neither be created nor destroyed but simply converted from one form to another. If the provided voltage in a circuit is the energy available to be transferred per unit charge, where does this energy come from? In the case of many electric circuits, the answer to this question is a battery. A battery converts chemical potential energy to electrical energy, allowing charge to be driven around the circuit. This energy per unit charge is called the electromotive force (emf) of a circuit. Remember that energy per unit charge is simply voltage, so the emf in a circuit is the voltage across the battery when there is no current flowing.

This is why we typically think of the voltage of everyday appliances as being related to the energy usage of that appliance. In the context of electricity, it's more correct to think of voltage as the energy per unit charge across the appliance.

Types of Voltage

We have thus far considered simple circuits in which current always flows in one direction. This is called direct current (DC). There is another type of current that is more common; alternating current (AC).

DC Voltage

A circuit in which current flows in one direction is a DC circuit. A typical battery has a positive and a negative terminal and can only push charge in one direction in a circuit. Batteries, therefore, can provide the electromotive force (emf) for DC circuits. If a DC circuit has a fixed resistance, the current will remain constant. The energy transferred to the resistor will therefore remain constant and so will the work done per unit charge. For a circuit with a fixed resistance, the DC voltage is always constant; it does not change with time.

AC Voltage

The type of electricity that is supplied to homes around the world comes in the form of alternating current (AC). Alternating current can be transported long distances making it ideal for this purpose. In an AC circuit, the current flows in two directions along wires; they oscillate back and forth. The electrical energy still only flows in one direction so appliances can still be powered. Since the direction of the current is constantly changing, the amount of energy transferred to each circuit component must also be constantly changing, which means the voltage between any two points in the circuit is always changing. The AC voltage varies sinusoidally with time. The figure below shows a sketch of both AC and DC voltage vs time.

A sketch that shows the shape of a DC voltage vs time graph as well as an AC voltage vs time graph, StudySmarter Originals.

Other Equations for Voltage in Physics

We have studied the definition of voltage and seen its relation to the energy transfer in an electric circuit. We can also relate the voltage to other electrical quantities; in our case resistance and current. Ohm's Law describes this relationship as follows; the voltage across a conductor (\(V\)) at a constant temperature is directly proportional to the current (\(I\)) in the conductor. That is

\[V\propto I\]

\[V=IR\]

where the constant of proportionality, in this case, is the resistance of the conductor. There are many other expressions for the voltage in electric circuits that depend on the specific circuit. The basic understanding of voltage and the volt, however, does not change between scenarios.