Chapter 25 Capacitors. 25-2 Capacitor and Capacitance A capacitor consists of two isolated conductors (the plates) with charges + q and - q. Its capacitance.
Post on 03-Jan-2016
247 Views
Preview:
Transcript
Chapter 25
Capacitors
25-2 Capacitor and Capacitance• A capacitor consists of two isolated conductors (the plates) with charges +
q and - q. Its capacitance C is defined fromq=CV
Where V is the potential difference between the conductors.
• To find the capacitance, we have to find the electric field E, then the potential difference V. Gauss Law is used
25-3 Calculating the Capacitance
f
i
dsEV
• Parallel-Plate CapacitorThe plate area is A and the distance between the plates is d.
dEV AEq oV
qC
d
AC o
• Cylindrical Capacitor
br
aro
f
i
drrL
qdsEV
1
2
)a
bln(
L2
qV
o
)ln(
L2
V
qC
ab
o
• Spherical Capacitor
br
ar2
o
f
i
drr
1
2
qdsEV
ab
ab
4
qV
o
ab
ab4
V
qC o
• The Capacity of an Isolated ConductorThe isolated conductor is a sphere of conducting material which is isolated such that it keeps its charge. It is considered to be a spherical capacitor of an outer sphere with infinitely large radius b=∞
ab
ab4C o
bao 1
a4C
and substituting about b=infinity, and a=R, the radius of the inner sphere,we get
R4C o
Sample Problem 25-1In Fig. 25-7 a, switch S is closed to connect the uncharged capacitor of capacitance C =0.25 mF to the battery of potential difference V= 12V. The lower capacitor plate has thickness L=0.50 cm and face area A=2.0 x 10-4 m2, and it consists of copper, in which the density of conduction electrons is n= 8.49 x 1028 electrons/m3. From what depth d within the plate (Fig. 25-7b) must electrons move to the plate face as the capacitor becomes charged?
25-4 Capacitances in Parallel and SeriesParallel Connection
Series Connection
Sample Problem 25-2a. Find the equivalent capacitance for the combination of
capacitances shown in Fig a, across which potential difference V is applied. Assume C1 = 12.0 mF, C2 = 5.30 mF, and C3 = 4.50 mF.
b. The potential difference applied to the input terminals in Fig. a is V=12.5 V. What is the charge on C1?
Sample Problem 25-3Capacitor 1, with C1 =3.55 mF, is charged to a potential difference Vo= 6.30 V using a 6.30 V battery. The battery is then removed, and the capacitor is connected as in the figure to an uncharged capacitor 2, with C2=8.95 mF When switch S is closed, charge flows between the capacitors. Find the charge on each capacitor when equilibrium is reached.
25-5 The Energy Stored in a Capacitor
The potential energy U stored in a capacitor due to holding the charge q, is given by
qV2
1U 2CV
2
1U
C2
qU
2
The energy density uIn case of the parallel plate capacitor, the potential energy per unit volume between the plates is given by
Ad2
CV
Ad
Uu
2
d
AC o
2
2
o d
V
2
1u
2oE
2
1u
The capacity of this spherical conductor is given by
Sample Problem 25-5An isolated conducting sphere whose radius R is 6.85 cm has a charge q = 1.25 nC.a. How much potential energy is stored in the electric field of
this charged conductor?b. What is the energy density at the surface of the sphere?
R4C o
and the potential energy is given byC2
qU
2
J10X110X9)0685.0(2
)10X25.1(U 79
29
The energy density u is given by2
oE2
1u
2mJ52
2o
o 10X5.2)r
q
4
1(
2
1u
top related