Stud
Did you know?
In order to locate a wooden stud in
which to anchor a nail or a screw,
carpenters (and simple folks like
us) use a cool handheld device
called “stud finder”.
Have you ever wondered how
can this device detect the stud
under the drywall ?
Is it black magic or physics??
Answer by the end of this class
26. Capacitance and Dielectrics
26.1 Definition of Capacitance
26.2 Calculating Capacitance
26.5 Capacitors with Dielectrics
1
Definition of Capacitance
Capacitor (condensor) = two
conductors separated by and
insulator
V1
Capacitance of a capacitor
Q
C=
V2 − V1
V2
Capacitance of an isolated conductor
C = Q /V
Definition of Capacitance
Units:
[C ] =
[Q ] = C = F
[ ∆V ] V
(Farad)
Farad is a very large unit of capacitance
Subunits:
picofarad
(pF=10-12 F)
nanofarad
(nF=10-9 F)
microfarad
(µF=10-6 F)
How big is the Earth’s capacitance (assumed to be a
conducting sphere of radius ~6400 km)? ……..
2
Calculating Capacitance
1. Measure experimentally Q and ∆V ⇒ C=Q/ ∆V
2. Calculate theoretically ∆V for given Q ⇒ C=Q/ ∆V
C depends on: (i) the geometry of the capacitor, and
(ii) the nature of the insulator between the plates
C can be calculated analytically for capacitors with
special geometry, e.g.,
a) spherical conductor
c) parallel-plate condensor
b) spherical condensor
d) cylindrical condensor
Capacitance of a Sphere
V = ke Q / R
C = Q / C = R / ke
C = 4πε 0 R
How big is the Earth’s capacitance (assumed to be a
conducting sphere of radius ~6400 km)?
C ≈ 6400 × 103 /(9 × 109 ) ≈ 7 × 10−4 F !!!
3
Capacitance of a Spherical Condensor
 −Q Q 
+ =0
Vb = ke 
b
 b
 −Q Q 
+ 
Va = ke 
b
a

b−a
∆V = Va − Vb = ke Q
ab
Q
ab
ab
C=
=
= 4πε 0
b−a
∆V ke (b − a )
Capacitance of a Parallel-Plate Condensor
E = σ / ε0 = Q / ε0 A
∆V = Ed = Qd / ε 0 A
C = Q / ∆V = ε 0 A / d
4
Capacitance of a Cylindrical Condensor
∆V = Va − Vb = 2ke ( Q / l ) ln ( b / a )
C = Q / ∆V = l / 2ke ln ( b / a )
2πε 0
C
1
=
=
l 2ke ln ( b / a ) ln ( b / a )
Capacitors with Dielectric
dielectric
constant
C
= κ >1
C0
dielectric ⇒
• increase in capacitance
• increase in max operating voltage
• mechanical support between the plates
5
Capacitors have many applications, e.g.
computer
keyboard
buttons
tuning
device
when the capacitor
moves across a stud
in the wall, the
change in the
dielectric constant
causes a signal light
to illuminate
Types of Capacitors
tubular
high voltage
electrolytic
6