Potential Difference

Have you ever thought about why you can hold a small battery between your fingers and feel nothing, but if you're struck by lightning you'd be lucky to survive? The answer, among other factors, is the voltage (or potential difference) of these two different sources of electricity. A typical battery may have a potential difference of 1.5 Volts, while a lightning strike can be as much as 150 million volts! This article explains what potential difference actually is, which will help you better understand why circuits behave the way they do, and why not to get struck by lightning!

Potential Difference Definition

Potential difference (also referred to as voltage) can be a confusing concept that many students have difficulty grasping at first. But don't let that dissuade you - we can use a hydraulic analogy to more easily understand what potential difference is, and how it affects the behaviour of an electrical circuit.

Let's consider a system of pumps and reservoirs like the one shown in the diagram below. When a pump raises water to an elevated reservoir, it adds energy to the system by raising the gravitational potential energy of the water (1). The gravity acting on the elevated water means the water at the bottom of the reservoir is at high pressure (2). If we open a valve allowing the water to descend through a pipe and drive a turbine, it flows at a rate dependent on the pressure of the water and the resistance of the turbine (3). Finally, by driving the turbine, the gravitational potential energy stored in the water is converted into kinetic energy, which is removed from the system (4). The water at the bottom of the pipe has no more stored energy - until we can use a pump to add potential energy back into the water and return it to the top of the system (1).

Diagram showing the hydraulic analogy of an electrical circuit. [Left] - a system of pumps and reservoirs which stores energy as gravitational potential and releases it as kinetic energy. [Right] - an electrical circuit that stores energy as potential difference in charge carriers, which is released as work when they pass through a resistor. StudySmarter Originals.

This system is a useful analogy of a simple electrical circuit consisting of a battery and resistor, like that shown in the diagram. The battery provides a potential difference to the charge carriers (1), which is analogous to the gravitational potential energy added to each particle of water. After passing through the battery, each electron is carrying electrical energy due to the potential difference provided by the battery (2). The charge carriers flow around the circuit which can be measured by the current \(I\) dependent on the potential difference \(V\) and the resistance of the circuit \(R\) (3), as defined by Ohm's law:

$$V=IR$$

or in words,

$\mathrm{Potential}\mathrm{difference}=\mathrm{current}\times \mathrm{resistance}$$$\mathrm{Potential}\;\mathrm{difference}\;=\;\mathrm{current}\;\times\;\mathrm{resistance}$$

As the charge carriers pass through the resistor their electrical energy is converted into work, using up their stored energy (4). As the charge carriers are no longer storing electrical energy, their potential difference is now zero as they flow back to the battery. When they pass through the battery again, they gain potential difference and the process repeats (1).

Hopefully this analogy helps you understand that potential difference is a measure of the amount of potential electrical energy a charge carrier holds between two points in a circuit. Potential difference is measured in the SI unit of volts \(\mathrm{V}\).

The hydraulic analogy can also be used to help understand how current, voltage, and resistance behave in series and parallel circuits.

Potential Difference Formula

As we just established, potential difference is a measure of the difference in potential energy each unit of charge contains between two points in an electrical circuit. This means that if we know a quantity of energy transferred \(E\)$E$between two points in a circuit and the amount of charge \(Q\) that flowed to transfer the energy, we can calculate the potential difference \(V\) between the points using the formula below:

$$V=\frac EQ\;$$

or in words,

$$\mathrm{Potential}\;\mathrm{difference}\;=\;\frac{\mathrm{energy}\;\mathrm{transferred}}{\mathrm{charge}\;\mathrm{flow}}$$

Potential difference unit

By studying the formula \(V=\frac EQ\), we can see that a potential difference of \(1\;\mathrm{V}\) is equal to \(1\;\mathrm{J}\) of energy per \(1\;\mathrm{C}\) of charge.

Potential difference equation and symbol

Another set of equations which deal with potential difference are those defined in Ohm's law, which describe how the current \(I\) passing through an Ohmic electrical component is determined by the potential difference \(V\) across the component and the component's electrical resistance \(R\). We referred to this law and its formula earlier in the article.

Linking potential difference to electrical power

Recalling that current is the rate at which charge flows in a circuit, measured in coulombs-per-second, we can derive an equation for the power (energy-per-second) of an electrical circuit.

If we know that a certain quantity of energy \(Q\) was transferred between two points in a circuit by a certain amount of charge \(C\), we can calculate the potential difference \(V\) of the charge between these points:

$$V=\frac EQ$$

$I=\frac{Q}{t}$$$I=\frac Qt$$

Rearranging both these equations for \(Q\), we get:

$\begin{array}{rcl}Q& =& \frac{E}{V},\\ Q& =& It.\end{array}$$$\begin{array}{rcl}Q&=&\textstyle\frac EV\\Q&=&It\end{array}$$

Finally, we can combine these equations to find an equation for power \(P\):

$\begin{array}{rcl}\frac{E}{V}& =& It\\ E& =& IVt\\ \frac{E}{t}& =& IV\\ P& =& IV\end{array}$$$\begin{array}{rcl}\textstyle\frac EV&=&It\\E&=&IVt\\\textstyle\frac Et&=&IV\\P&=&IV\end{array}$$

or in words,

$$\mathrm{Power}\;=\;\mathrm{current}\;\times\;\mathrm{potential}\;\mathrm{difference}$$

Potential difference in a battery

A battery adds electric potential to charge carriers as they pass through it. The battery can also be considered as the source of current in a circuit - As the positive terminal of the battery has a higher electric potential than the negative terminal, positive charges are repelled by the positive battery terminal and attracted to the negative terminal, setting up a current as they flow around the circuit. This attraction/repulsion is equivalent to gravity in the hydraulic example.

Batteries in a circuit transfer stored chemical energy into charge carrying electrons, raising their potential difference as they flow through it. Flickr.

• When the power source of an electric circuit transfers one Joule of energy to each coulomb of charge, we say that the power source provides one volt of potential difference.
• To measure the potential difference between the two terminals of a cell, battery or an alternative power source we use a voltmeter. Voltmeters can be used to measure the potential difference across any electric circuit component or between any two points.

Voltmeters can be used to measure the potential difference between two points in a circuit. If there is no energy being transferred between the two points the voltmeter measures between, the potential difference reading will be 0 volts. StudySmarter Originals.

Potential difference examples

Lets look at some example problems that will allow us to apply our newfound knowledge to different scenarios.

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