Transcript Capacitance and Capacitors

Capacitance and Capacitors
• Recall heat capacity (c)
– The amount of heat energy (J) absorbed
(released) by a material of known mass
(m) when changing temperature (T) with
no phase change
Q
c
mT
Electrical capacitance
• Defined as the amount of charge per
volt that an object can hold
Q
C
V
• Anything can be a capacitor
• The capacitance is defined as Q/V, but
it is also solely dependent on the
geometry of the capacitor. There
should be an equation for the
capacitance that is based only on the
physical dimensions of the capacitor.
• The capacitance is measured in farads
(F) after Michael Faraday
Example 1:
A charged sphere of radius R
• If the charge on the sphere is Q, the
potential at the surface is V = kQ/R
• The capacitance is then
R
C   40R
k
Example 2:
Parallel plate capacitor
• When the plates are charged, one plate
has charge +Q, and the other -Q, so we
say that the charge on the capacitor is Q.
• For parallel plates, V = Ed and E = 0,
where  = Q/A is the charge density on the
plates, so
0
C
A
d
Figure 20-15
The Effect of a Dielectric on the Electric Field of a Capacitor
Dielectric
• Adding a material to the space between
the plates changes the capacitance of
the capacitor
C  C0
Table 20-1
Dielectric Constants
Substance
Dielectric constant, 
Water
80.4
Neoprene rubber
6.7
Pyrex glass
5.6
Mica
5.4
Paper
3.7
Mylar
3.1
Teflon
2.1
Air
1.00059
Vacuum
1
Figure 20-16
Capacitance and the Computer Keyboard
Capacitors in series
•Adding capacitors in
series,
•Vtot = V1 + V2, so
1
1
1
 

Ctot C1 C2
The charge on each capacitor must be the same when
they are connected in series… Why?
Energy in capacitors
1
1
2
UC  QV  CV
2
2
W = qVave
Capacitors in parallel
Adding capacitors in
parallel,
Vtot = V1 = V2, so
Ctot  C1  C2 
Sample problem
Charging capacitors in RC
circuits
• When switch is first closed, uncharged
capacitor acts like a wire, with no
voltage drop across it (t = 0)
• After a long time, once the capacitor is
fully charged, it acts like an open switch
(t  infinity)
• When switch is first closed on a charged
capacitor, it acts like a battery