Contents
Introduction
Capacitors are very common electrical components that can be found in many modern electronic devices. Their purpose is to store electrical energy and release it rapidly.
In this post, we’re going to find out what capacitors are, how they store electrical energy, and how to calculate the amount of electrical potential energy a capacitor can store.
Let’s begin!
What is a capacitor?
A capacitor is an electrical component that stores electrical charge. The simplest type of capacitor is a parallel plate capacitor made from two parallel metal plates and a dielectric (insulating) material between them:
The dielectric material prevents charges from flowing between the plates. As a result, when the plates are connected to a power supply, a current flows around the circuit but cannot cross the dielectric material. Charge therefore accumulates on the plates, with one plate becoming positively charged and the other plate becoming negatively charged. The capacitor thereby stores charge on its plates, and a uniform electric field is established across the dielectric material between the charged plates:
The purpose of the dielectric layer
The dielectric material isn’t just any old insulator. It is a special insulator that contains polar molecules, each of which has a positive end and a negative end.
When charge accumulates on the plates, the positive ends of the molecules are attracted to the negative plate and the negative ends of the molecules are attracted to the positive plate. This causes the molecules to rotate into alignment with the uniform electric field:
The positive and negative ends (or poles) of the molecules have tiny electric fields around them. However, the fields of adjacent positive and negative poles of neighbouring molecules cancel each other out:
As a result, the only poles whose tiny electric fields remain un-cancelled are the negative poles on the far left and the positive poles on the far right:
Thus, the left side of the dielectric material has a negatively charged surface and the right side of the dielectric material has a positively charged surface. Each side of the dielectric material therefore attracts the charge already stored on the neighbouring plate, facilitating the further accumulation of charge on the plate. This increases the component’s capacity to store charge, and is the reason why a dielectric material (with polar molecules) is chosen as the insulating layer in a capacitor.
Some dielectric materials in capacitors have molecules that are not naturally polar, but can become polar when placed in an electric field. In this case, the uniform electric field between the charged plates causes the electron cloud around each molecule to be attracted slightly towards the positive plate and away from the negative plate. This induces polarity in the molecules, which are sometimes referred to as ‘induced dipoles’. Their polarity is aligned with the uniform electric field and they work just the same as polar molecules for increasing the capacitor’s ability to store charge.
Definition of capacitance
Zooming out, we can depict a whole circuit that includes a capacitor (depicted by the circuit symbol of two parallel lines). Charge flows around the circuit and accumulates on the two plates:
When the plates cannot store any additional charge, the capacitor is fully charged. At this point, one plate holds a charge of \(+Q\) and the other plate holds a charge of \(-Q\):
The magnitude of \(Q\) is directly proportional to the voltage supplied, \(V\), and also depends on the ability of the capacitor to store charge. This ability is called capacitance, \(C\).
Capacitance is defined as the amount of charge a capacitor can store on each plate per volt of potential difference placed across it:
\(C=\frac{Q}{V}\)
Thus, if we know the capacitance of a capacitor and the pd placed across it, we can easily calculate the amount of charge it stores:
\(Q=CV\)
Energy stored in a capacitor
Since like charges repel, it takes energy (provided by the power supply) to push more and more charges of the same type onto each plate during charging. This energy is then stored by the capacitor as electrical potential energy.
We can derive an expression for the amount of electrical potential energy stored.
Since \(Q=CV\), we know that a graph of the potential difference across a capacitor against the charge it stores is a straight line through the origin:
If we add a small amount of charge, \(q\), during charging, we are effectively moving the charge \(q\) around the circuit from one plate to another. The positive plate becomes more positive by \(+q\) and the negative plate becomes more negative by \(-q\). Since the pd across the plates is \(\Delta V\), we have moved the charge \(q\) through a pd of \(\Delta V\). From our knowledge of electric fields, the work required to do this is:
\(\Delta W=q\Delta V\)
However, as we add the small amount of charge, \(q\), the pd across the capacitor increases (because \(V=\frac{Q}{C}\)). Therefore, we need to use an average pd, \(\Delta V_{ave}\), to calculate the work done:
\(\Delta W=q\Delta V_{ave}\)
Work done is therefore equal to the area of the following rectangle:
This area is also equal to the area of the following trapezium, which is the area under the graph:
Based on this, we can conclude that the work done to fully charge the capacitor is the total area under the graph (where \(Q\) is the charge on each plate and \(V\) is the pd across the capacitor when it is fully charged).
This is a right-angled triangle whose area is \(\frac{1}{2}base \times height\), so the energy stored by the fully charged capacitor is:
\(W=\frac{1}{2}QV\)
Since \(C=\frac{Q}{V}\), we can also express the energy stored in the following two ways:
\(W=\frac{1}{2}CV^2=\frac{1}{2}\frac{V^2}{Q}\)
Conclusion
I hope you’ve enjoyed learning about capacitors! They’re nifty devices that store electrical potential energy and they have a special dielectric layer that helps them store more charge.
Next, you might like to learn about combinations of capacitors, including the total capacitance of capacitors in parallel and in series.
Happy studying!
