Peoples Physics Concepts

http://www.ck12.org Chapter 15. Electric Circuits: Capacitors

15.2 Capacitor Energy

• Describe how energy is stored in a capacitor and calculate said energy.

Students learn how energy is stored in a capacitor and how to calculate said energy.

Key Equations

The electric potential energy,UC, stored in the capacitor is given by

UC=

1

2

CV^2

Guidance

Suppose we have two parallel metal plates set a distancedfrom one another. We place a positive charge on one of
the plates and a negative charge on the other. In this configuration, there will be a uniform electric field between the
plates pointing from, and normal to, the plate carrying the positive charge. The magnitude of this field is given by

E=

V

d

where V is the potential difference (voltage) between the two plates.

The amount of charge,Q, held by each plate is given by

Q=CV

where againVis the voltage difference between the plates andCis the capacitance of the plate configuration.

Capacitance can be thought of as the capacity a device has for storing charge. In the parallel plate case the

capacitance is given by

C=

ε 0 A
d
whereAis the area of the plates,dis the distance between the plates, andε 0 is the permittivity of free space whose
value is 8. 84 × 10 −^12 C/V·m.
The electric field between the capacitor plates stores energy.
Where does this energy come from? Recall, that in our preliminary discussion of electric forces we assert that "like
charges repel one another". To build our initial configuration we had to place an excess of positive and negative
charges, respectively, on each of the metal plates. Forcing these charges together on the plate had to overcome the
mutual repulsion that the charges experience; this takes work. The energy used in moving the charges onto the
plates gets stored in the field between the plates. It is in this way that the capacitor can be thought of as an energy
storage device. This property will become more important when we study capacitors in the context of electric
circuits in the next several Concepts.
Note: Many home-electronic circuits include capacitors; for this reason, it can be dangerous to mess around with
old electronic components, as the capacitors may be charged even if the unit is unplugged. For example, old
computer monitors (not flat screens) and TVs have capacitors that hold dangerous amounts of charge hours after the
power is turned off.