Energy stored by capacitor (6.1.2)
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The potential difference across a capacitor is directly proportional to the charge it stores.
It is important to note that while a capacitor is charging, the charge stored on the plates increases linearly with the voltage across the plates; therefore, a graph of charge against voltage will be a straight line passing through the origin.
The gradient of the charge against voltage graph is equal to the capacitance of the capacitor:
The energy stored by a capacitor ( is equal to the area under the charge–voltage graph for the capacitor.
The area under the graph is a triangle, so it is given by:
For a capacitor with a voltage across its plates storing a charge we have:
It is useful to know that generally, energy is given by:
the integral of the charge with respect to the potential difference. You will not need to know this calculus for your physics exam, but it could be helpful in your understanding or for future learning.
It is important to note that the correct equation for the energy stored by a capacitor. Many students make this mistake in their exams, losing marks as a result.
Question walkthrough
Finding Energy and Capacitance from a V-Q Graph
Use the area under a voltage-charge graph to find energy stored, then find capacitance from the gradient.
The energy stored by a capacitor is given by:
Where:
- is the charge stored by the capacitor, and
- is the voltage across the capacitor.
Substituting where is the capacitance of the capacitor gives:
Substituting gives:
All three equations are equivalent and can be used to calculate the stored energy, depending on which two quantities (charge , capacitance or voltage ) are known.
Question walkthrough
Finding Voltage from Capacitor Energy
Rearrange the capacitor energy formula to find the potential difference given the stored energy and capacitance.
Capacitors are used in various devices where rapid energy release is needed because of their ability to quickly discharge stored energy. Some common applications include:
There are advantages and disadvantages to using capacitors instead of batteries in various practical applications.
