Transcript Capacitors Chapter 12

Capacitors
Chapter 12
Definition
• Capacitance – the ability of a component to
store energy by accumulating charge
• A capacitor is a circuit component designed
to store charge
• Practical applications with capacitors:
Camera flash – Charges up and then quickly
discharges
Power storage – Solar collectors charge up
capacitors so that energy can be used after
dark
Capacitor Construction
• 2 Plates
• Separated by a Dielectric
Variable Capacitors
– Interleaved-Plate Capacitors
Fixed Value Capacitors
• Polarized Electrolytic Capacitors
• Most electrolytic capacitors are
polarized
Capacitance
• Amount of charge that a capacitor can
store per unit volt applied
Q
C
or
Q  CV
V
where
C = the capacitance of the component, in
Coulombs per Volt defined as Farad (F)
[C] = [Q]/[V]=C/V = F.
Q = the total charge stored by the component
V = the voltage across the capacitor corresponding to
the value of Q
Capacitance Examples
C=
C=
C=
• Unit of Measure
– farad (F) = 1 coulomb per volt (C/V)
• Typical ranges
– Most capacitors fall in the picofarad
(pF) to microfarad (F) range
– Tolerance
• Usually fairly poor
• Variable capacitors used where
exact values required
Capacitor Value Codes
• Physically large capacitors usually have their values printed
directly on the case
• Smaller capacitors are generally labeled using a code:
– 2-digit code: the number represents the value of the
component in pF
Example: 15 = 15 pF
– 3-digit code: the code is interpreted like the first three
digits of a resistor code
Example: 473 = 47 x 103 pF = 47 nF
– The numbers 6 and 7 are not used as multiplier values
– The numbers 8 and 9 are decoded as follows: 8 = 0.01
and 9 = 0.1
Example: 158 = 0.15 pF
Physical Characteristics of
Capacitors
A
A
C 
d
d
where
C

A
d
= the capacity of the component, in farads (F)
= permittivity of the dielectric
= the area of either plate, in square meters (m2)
= the distance between the plates, in meters (m)
What are the units of  ?
Comparison to Resistance
• For resistance, R = rL/A
• For capacitance, C = A/d
• As r increases, R increases; as  increases, C increases
• As L increases, R increases; as d increases, C
decreases
• As A increases, R decreases; as A increases, C
increases
Permittivity
• Permittivity of a capacitor dielectric is
 = o x r
- Permittivity of a vacuum: o = 8.85x10-12 F/m
MULTIPLIED BY
- The relative permittivity of the material r e.g.:
Material r
air
1
paper 2.5
mica
5
glass
7.5
Team Activity 1
• If you have a capacitor with the following parameters,
what is its capacitance?
• Plate cross-sectional area = 1cm2
Dielectric material = air
distance between plates = 2cm
• What happens to the capacitance if you change the
dielectric to oil and the distance between plates to 1cm?
• For the original dielectric material and plate distance,
what would the cross-sectional area need to be to create
a 1 F capacitor?
Series Capacitors
CT 
1
1
1
1

  
C1 C2
Cn
Where
CT = the total series capacitance
Cn = the highest-numbered capacitor in the
circuit
Team Activity 2
Determine the total capacitance
Parallel Capacitors
CT  C1  C2      Cn
A1
A2
where
Cn = the highest-numbered capacitor in
the parallel circuit
Team Activity 3
Determine the total capacitance
Demonstration
• http://www.howstuffworks.com/framed.htm
?parent=capacitor.htm&url=http://micro.ma
gnet.fsu.edu/electromag/java/capacitor/
Relationship between Capacitor
Voltage and Current
• Capacitor Current
vc
i
+
dvC
iC
dt
_
where
i = the instantaneous value of capacitor current
C = the capacity, in farads
dvC
= the instantaneous rate of change in capacitor
dt
voltage
Team Activity 4
• If the voltage across a 2F capacitor is
vc (t )  5 sin( 30t )V
what is the current through the
capacitor?