-Capacitors and Capacitance

AP Physics C Mrs. Coyle



Capacitors: devices that store electric charge

Consist of two isolated conductors (plates) with

equal and opposite charges +Q and −Q; the charge on the capacitor is referred to as "Q".

Ex:Parallel Plate Capacitor

Applications of Capacitors

 Tune the frequency of radio receivers  Used as filters in power supplies  Used as energy-storing devices in electronic flashes (ex: cameras)

    

Charging a Parallel Plate

Capacitor

The battery establishes a field on the plates.

This forces the electrons from the wire to move on to the plate that will become the negative plate.

This continues until equilibrium is achieved( the plate, the wire and the terminal are all at the same potential) and the movement of the electrons ceases.

At the other plate, electrons move away from the plate, leaving it positively charged.

Finally, the potential difference across the capacitor plates is the same as that between the terminals of the battery.

Capacitor Animation  http://phet.colorado.edu/en/simulation/capacit or-lab

Capacitance:

a measure of the capacitor’s ability to store charge

C



Q



V

 Ratio of the magnitude of the charge on either conductor to the potential difference between the conductors.

 The SI unit of capacitance is the

farad

(F)   1 F = 1 Coulomb/Volt Also see the units pF (10 -12 ) or m F (10 -6 )

Factors that affect capacitance    Size (Area, distance between plates) Geometric arrangement  Plates   Cylinders Spheres Material between plates (dielectric)    Air Paper Wax

Note:  Capacitance is always positive  The capacitance of a

given capacitor is constant. If the voltage changes the charge will change not the capacitance.

Note:  The electric field is uniform in the central region, but not at the ends of the plates. It is zero elsewhere.

 If the separation between the plates is

small

compared with the length of the plates, the effect of the non-uniform field can be ignored.

Capacitance of a Parallel Plate Capacitor  

C



Q



V



Q Ed

From Gauss's Law EA=Q/

ε o C C



Q Qd

/

ε A o



ε A o d A

is the area of each plate

Q

is the charge on each plate, equal with opposite signs  The capacitance is

proportional to the area

of its plates and

inversely proportional to the distance between the plates

 A single conductor can have a capacitance.

Example: Isolated charged sphere can be thought of being surrounded by a concentric shell of infinite radius carrying a charge of the same magnitude but opposite sign.

 Capacitance of an Isolated Charged Sphere, Cont’d

C



Q



V



V



e

Assume

V

= 0 at infinity

C



Q e

 Note, the capacitance is independent of the charge and the potential difference.

C



R k e

 4

πε R

 Capacitance of a Cylindrical Capacitor From Gauss’s Law, the field between the cylinders is

E

= 2

k e

l /

r,

l Q/L V ba   b a    Q 2  o rL     Q 2  o L b a  dr r   Q 2  o L ln    

V

= -2

k e

l ln (

b

/

a

)

C



Q



V

 2

k e

ln  

Capacitance of a Spherical Capacitor  Potential difference:

k Q e

  1

b

 1

a

   Capacitance:

C



Q



V



e



ab k b



a

