CapacitorsChapter 12

• 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 dischargesPower storage – Solar collectors charge up capacitors so that energy can be used after dark

Definition

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

CVQV

QC or

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

• 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 pFExample: 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

Capacitor Value Codes

Physical Characteristics of Capacitors

d

AC

whereC = the capacity of the component, in farads (F) = permittivity of the dielectricA = the area of either plate, in square meters (m2)d = the distance between the plates, in meters (m)

A

d

What are the units of ?

Comparison to Resistance• For resistance, R = L/A

• For capacitance, C = A/d

• As 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 1paper 2.5mica 5glass 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 = airdistance 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

n

T

CCC

C111

1

21

Where CT = the total series capacitance Cn = the highest-numbered capacitor in the

circuit

Team Activity 2Determine the total capacitance

Parallel Capacitors nT CCCC 21

where Cn = the highest-numbered capacitor in

the parallel circuit

A1 A2

Team Activity 3Determine the total capacitance

Demonstration

• http://www.howstuffworks.com/framed.htm?parent=capacitor.htm&url=http://micro.magnet.fsu.edu/electromag/java/capacitor/

Relationship between Capacitor Voltage and Current

• Capacitor Current Cdvi Cdt

where i = the instantaneous value of capacitor current C = the capacity, in farads

= the instantaneous rate of change in capacitor voltage

Cdv

dt

i + _vc

Team Activity 4

• If the voltage across a 2F capacitor is

what is the current through the capacitor?

Vttvc )30sin(5)(