Phys 14
Capacitance and Dielectrics
Capacitors and Capacitance
• Any two conductors separated by
an insulator (or a vacuum) form a
capacitor.
• In circuit diagrams a capacitor is
represented by either of these
symbols:
Capacitors and Capacitance
*we can express the units of ε0 as 1 C2/N.m2 = 1 F/m
Capacitors and Capacitance
Sample Problem:
The parallel plates of a 1.0 F capacitor
are 1.0 mm apart. What is their area?
Sample Problem
The plates of a parallel-plate capacitor in vacuum are 5.00 mm apart and 2.00
m2 in area. A 10.0 kV potential difference is applied across the capacitor.
Compute (a) the capacitance; (b) the charge on each plate; and (c) the
magnitude of the electric field between the plates.
a.
b.
c.
Capacitors in Series
• Two capacitors are connected in series (one after
the other) by conducting wires between points a
and b.
• In a series connection the magnitude of
charge on all plates is the same.
• Referring to Fig. 24.8a, we can write the potential
differences between points a and c, c and b, and a
and b as:
Capacitors in Parallel
• In a parallel connection the potential
difference for all individual capacitors is the
same and is equal to Vab = V.
• The charges Q1 and Q2 are not necessarily equal,
however, since charges can reach each capacitor
independently from the source (such as a battery)
of the voltage Vab. The charges are
Sample Problem
In Figs. 24.8 and 24.9, let C1 = 6.0 μF, C2 = 3.0 μF, and Vab = 18 V. Find the
equivalent capacitance and the charge and potential difference for each capacitor
when the capacitors are connected (a) in series (see Fig. 24.8) and (b) in parallel
(see Fig. 24.9)
Fig. 24.8
a.
Fig. 24.9
b.
Sample Problem
Find the equivalent capacitance of the five-capacitor network shown in Fig. 24.10a
Energy Stored in Capacitors and Electric Field Energy
Sample Problem
(a) What is the magnitude of the electric field required to store 1.00 J of
electric potential energy in a volume of 1.00 m3 in vacuum? (b) If the
field magnitude is 10 times larger than that, how much energy is stored
per cubic meter?
Dielectrics
• Most capacitors have a nonconducting material,
or dielectric, between their conducting plates.
• A common type of capacitor uses long strips of
metal foil for the plates, separated by strips of
plastic sheet such.
• A sandwich of these materials is rolled up,
forming a unit that can provide a capacitance of
several microfarads in a compact package .
Dielectrics
• Placing a solid dielectric between the plates of
a capacitor serves three functions.
• First, it solves the mechanical problem of
maintaining two large metal sheets at a
very small separation without actual
contact.
• Second, using a dielectric increases the
maximum possible potential difference
between the capacitor plates.
• Third, the capacitance of a capacitor of
given dimensions is greater when there is
a dielectric material between the plates
than when there is vacuum.
Dielectrics
When the space between plates is completely filled by the dielectric, the ratio of C to C0
(equal to the ratio of V0 to V) is called the dielectric constant of the material, K: