Notice that the formula for capacitors inserieslooks similar to the formula for resistors inparallel, and
vice versa.
Note the following points. For capacitors connectedin series:
- The equivalent capacitance will be smaller than the smallest capacitance in the series combination.
- If one capacitor in the series combination is much smaller than the others, the equivalent capacitance
will be approximately equal to the smallest capacitance. - Nequal capacitorsCconnected in series have an equivalent capacitance ofC=N.
For capacitors connectedin parallel:
- The equivalent capacitance will be bigger than the largest capacitance in the parallel combination.
- If one capacitor in the parallel combination is much larger than the others, the equivalent capacitance
will be approximately equal to the largest capacitance. - Nequal capacitorsCconnected in parallel have an equivalent capacitance ofNC.
25.3 Dielectric Materials in Capacitors
As shown by Eq. (25.5), the capacitance of a flat-plate capacitor can be increased by increasing the area of
the plates, or by decreasing the distance between them. Another way to increase the capacitance is to insert a
dielectric material between the plates; this will cause the capacitance to increase by a factor ofK:
CDK
" 0 A
d; (25.10)
whereKis called thedielectric constantof the material. Inserting a dielectric material between the plates
of a capacitor does triple duty: it increases the capacitance by a factor ofK; it serves to keep the two plates
physicallyseparated by a small fixed distance; and it keeps the the plates electrically insulated from each
other so that they don’t short out.
The combination
"DK" 0 (25.11)is called thepermittivityof the material.
25.4 Energy Stored in a Capacitor.
A capacitor can be thought of as a device that stores energy in the electric field between the plates of the
capacitor. Using the calculus, it can be shown that the potential energyUstored in the electric field of a
capacitor of capacitanceC, voltageV, and chargeQ(on each plate) is given by
UD^12 QVD^12 CV^2 D
1
2
Q^2
C
: (25.12)
Theenergy density(energy per unit volume) of a capacitor can be found by using the parallel-plate capacitor
as an example. The total potential energy stored in a parallel-plate capacitor (of plate areaAand separation