Energy Stored in a Capacitor
Electricity & Electronics 7:
Energy Stored in a Capacitor
AIM
In the previous unit we found that capacitors can store charge. We are now going to consider
their ability to store energy.
OBJECTIVES
On completing this unit you should be able to:
• explain why work must be done to charge a capacitor.
• state that the work done charging a capacitor is given by the area under the graph of
charge against pd
• state that the energy stored in a capacitor is given by
½ x charge x potential difference or equivalent expressions (see below).
• carry out calculations using:
o E = ½ QV
o E = ½ CV2
o E = ½ Q2 / C
• describe and explain the function of a capacitor storing energy.
Strathaven Academy
-1-
Electricity and Electronics
Energy Stored in a Capacitor
Energy Stored in a Capacitor
A charged capacitor can be used to light a bulb for a short time, therefore the capacitor must
contain a store of energy. The charging of a parallel plate capacitor is considered below.
-
Vc
+
+
E le c tr o n
c u rre n t
E le c tr o n
c u rre n t
Vs
Vs
Thereis aninitial surgeof
electrons fromthenegative
terminal of thecell ontoone
of theplates (andelectrons
out of theother platetowards
the+veterminal of thecell).
Vc = Vs
+
+
+
+
Vs
Oncesomechargeis onthe
plateit will repel morecharge
andsothecurrent decreases.
Inorder tofurther chargethe
capacitor theelectrons must
besuppliedwithenough
energytoovercomethe
potential differenceacross the
plates i.e. workis donein
chargingthecapacitor.
Eventuallythecurrent ceases
toflow. This is whenthe
p.d. across theplates of the
capacitor is equal tothe
supplyvoltage.
For a given capacitor the p.d. across the plates is directly proportional to the charge stored
Consider a capacitor being charged to a p.d. of V and holding a charge Q.
C
harge
T
heenergystoredinthecapacitorisgivenbytheareaunder
g
re
aph
th
Q
A
reaundergraph=1 QxV
2
E
nergystored =1 QxV
2
V p.d.
Ifthevoltageacrossthe
capacitorw
asconstantw
ork
done=QxV
, butsinceVis
varying, thew
orkdone=
areaundergraph.
Q = C × V and substituting for Q and V in our equation for energy gives:
Energy stored in a capacitor =
1
1
1 Q2
QV = CV 2 =
2
2
2 C
Example
A 40µF capacitor is fully charged using a 50 V supply. How much energy is stored?
Energy =
1
1
CV 2 =
× 40 × 10 6 × 2500
2
2
= 5 × 10-2 J
Strathaven Academy
-2-
Electricity and Electronics
Energy Stored in a Capacitor
Uses of a capacitor storing energy
1. Photographic flash
In photography, the flash unit of a camera has to supply the light needed in the short period of
time that the shutter is open. A large amount of light has to be emitted. This is stored as
electrical energy in a capacitor until it is needed.
K
S
power
supply
capacitor
discharge
tube
When the flash unit is switched on (switch K), the capacitor charges up from the supply and
stores energy. It can take a few seconds for it to fully charge. When the shutter button S is
pressed, the shutter is opened and the capacitor discharges through the discharge tube
releasing the stored energy as light. This usually happens within a few hundredths of a
second. Switch S automatically opens after the preset time and the capacitor charges up once
more, ready for the next photograph.
2. Memory backup
a large value capacitor (in the farad range) can store enough electrical energy to back up the
memory in a computer/digibox/DVD player for a length of time in the event of mains power
failure. In a computer, work is not lost and can be saved normally before shutting the system
down. In digiboxes and DVD players, user settings are retained. Capacitors used in this way
have an advantage over rechargeable batteries in that they can be recharged over and over
without wearing out or losing performance.
Strathaven Academy
-3-
Electricity and Electronics
Energy Stored in a Capacitor
Energy in a capacitor
13. A 100 µF capacitor is charged from a 20 V supply.
(a) How much charge is stored?
(b) How much energy is stored in the capacitor?
14. A 30 µF capacitor stores 6 × 10-3 C of charge. How much energy is stored in the
capacitor?
24. A capacitor with 60 V across its plates stores 50 mC of charge. How much energy is
stored?
25. A capacitor stores 0.36 J of energy and has a charge of 480 µC. What is the pd across its
plates?
26. Two parallel plates have a pd of 15 V across them and store 22.5 mJ of energy. What is
the charge stored?
27. A 1000 µF capacitor is charged to a pd of 6 V. How much energy is stored?
28. A 220 µF capacitor stores 40 mJ of energy. What is the pd across it?
29. If a 470 µF capacitor stores 2 J of energy, what charge must be on its plates?
30. A 16µF capacitor stores a charge of 20 mC. If it is discharged through a lamp in 100 ms,
what is the average power produced in the lamp?
31. An initially uncharged capacitor is charged using a constant current of 90 µA. After 100
seconds the pd across its plates is 12 volts.
(a) How much charge is stored on the capacitor after 100 seconds?
(b) How much energy is stored in the capacitor after 100 seconds?
(c) A second capacitor, with larger capacitance, is charged for the same time using the
same current. Explain how the pd across the capacitor and energy stored in the
capacitor compare with the first one.
32. A 3.3 F capacitor is used to back up a memory chip. It is charged to 5.5 V.
(a) Calculate how much energy is stored in the capacitor.
(b) If the power consumption of the chip is 1 mW, how long will the capacitor keep it
running? How many hours is this?
Strathaven Academy
-4-
Electricity and Electronics