CapacitorsStorage of charge

Introduction

• Read Chapter 14 in ESA and then;

– Write a brief description of what a capacitor is

and what it does, make sure you mention

dielectric

– Describe the maths; capacitance, units,

capacitor formula

– Explain how capacitors behave in DC circuits

in series and parallel

Electronic Components

• Capacitors are electronic components that store charge efficiently

• They can be charged and discharged very quickly and hold their charge indefinitely

• Symbol

The structure of the capacitor

• Capacitors are made

from two parallel

metal plates

separated by an

insulator called a

dielectric

• In practice they

appear a little more

complex

Charging a Capacitor

• In a circuit the capacitor plate closest to the negative terminal of the battery or power supply is “stacked” with electrons (negative charges)

• The opposite plate becomes positively charged

• There is no movement of charge between the plates as they are insulated by the dielectric

Capacitance (symbol C)

• Capacitance is the amount of charge a capacitor can

store when connected across a potential difference of

1V (the larger the capacitance the more charge it can store)

• Units of capacitance are Farads (symbol F)

• 1 Farad = 1 coulomb per volt This is a lot of charge!!

• most capacitors are small;

µF (1 x 10-6 F)

nF (1 x 10-9 F)

pF (1 x 10-12 F)

V

QC

Where;

C=Capacitance in Farads (F)

Q=Charge in Coulombs (C)

V=Voltage in Volts(V)

Exercises

1. Calculate the capacitance of a capacitor

that stores 1.584 10-9 C at 7.2V220 μF

2. A 330μF capacitor is charged by a 9.0V

battery. How much charge will it store?2.97 10-3 C

3. A 0.1μF capacitor stores 1.5 10-7 C of

the charge. What was the voltage used to

charge it?1.5V

Capacitance (C)

Three factors determine

capacitance;

1. The area of the plates

(CA)

2. The distance separating

the plates

(C )

3. The properties of the

dielectric (εr)

so

C= constant x

d

1

d

A

• If there is air or a vacuum between the plates the

constant is;

the absolute permittivity of free space (symbol ε0)

(ε0 = 8.84 x 10-12 Fm-1)

so;

d

AC 0

Capacitor Construction Formula

Exercises

Using the absolute permittivity of free space (ε0 = 8.84 10-12 Fm-1)

1. Calculate the capacitance of a capacitor that has a plate separation of 15 microns (μm) and measures 45cm by 28cm.

74nF

2. A 1000 μF has an area of 2cm by 4.8m. What is the distance between the plates in mm?

8.48 10-7mm

3. A 0.3 μF capacitor with a plate separation of 2 microns. What is the area of the capacitor?

0.68m2

d

AC 0

• When an insulator (dielectric) is placed between

the plates the capacitance increases

• The dielectric constant (symbol εr) gives the

proportion by which the capacitance will increase so;

and therefore

Note that εr has no units as

d

AC or

airrdielecticCC

air

dielectric

r

C

C

Insulator εr

Air 1

Polystyrene 2.5

Glass 6.0

Water 80

Capacitor Construction Formula

The Role of the Dielectric

• Charge separation in a

parallel-plate capacitor

causes an internal

electric field. A

dielectric (orange)

increases the field

strength and increases

the capacitance

Examples

1. Calculate the capacitance of a capacitor with a polystyrene dielectric (εr =2.5), an area of 1.2cm by 3.2m and a plate separation of 8 microns

1.06 10-7 F

2. Calculate the plate area required for a 1000 μF, glass (εr=6.0) capacitor, with a plate separation of 2.8 micrometres.

53m2

3. Calculate the dielectic constant of a 10000 μF capacitor with a 1.2μm plate separation and an area of 16.97m2

80

d

AC or

(ε0 = 8.84 x 10-12 Fm-

1)

Networks of Capacitors

• For two or more capacitors in parallel the capacitance is

• Each capacitor has the same voltagecharging it so;

...21 CCC parallel

Capacitors in Parallel

The more capacitors in parallel circuit the greater the capacitance of the circuit

Capacitors in Series

• Capacitors share the supply

voltage

• The inner plates are an

isolated circuit where the

existing charges are just

rearranged

so;

...111

21 CCCseries

The more capacitors in series the less the total

capacitance of the circuit

Examples

1. A circuit has three 330 μF capacitors in series. Calculate the total capacitance of the circuit 110 μF

2. Another circuit has three 330 μF capacitors in parallel. Calculate the total capacitance of the circuit. 990 μF

3. Briefly explain why these two circuits have a different total capacitance. The parallel capacitors are each charged separately while the series capacitors charge through one another, effectively just rearranging the charges within each capacitor (the electric field is weakened by the addition of each capacitor in series)

Energy Stored in Capacitors• The graph of voltage

against charge for a cell is

a horizontal line

– The energy provided by

the cell is equal to the

area under the line

• The graph of voltage

against charge is a straight

line through (0, 0)

– The energy stored in a

capacitor is;

QVEP

2

1

Q

V

Energy Produced by a Cell

Energy Stored by a Capacitor

Q

V

Energy Stored in Capacitors

• Energy of a capacitor can also be given by;

(because Q=CV)

or

(because )

QVEP

2

1

2CVEP

2

1

C

QE

P

2

2

1

C

QV

Energy is stored as electrical charge on the plates of a

capacitor

Exercises

1. Calculate the energy stored in a 330μF

capacitor charged by a 24V supply.0.095J

2. Calculate the capacitance of a capacitor

that stores 1.8 10-3 J of energy at 18V11 μF

3. Calculate the voltage require to store 0.1J

of energy on a 1000μF capacitor200V

2CVEP

2

1

Charging and Discharging Capacitors

1. Charging a Capacitor

• As a capacitor charges

the voltage increases to

the supply voltage(exponential growth curve)

• and the current

decreases as the plates

become “full” of charge (exponential decay curve)

Curr

ent

TimeV

olt

age Supply voltage

Time

The shape of these curves can be controlled by a resistor in series, the

higher the resistance the slower the charge

2. Discharging a Capacitor

• The voltage across the plates of the capacitor drops as the charges flow away from the plate

• The current decreases as there are fewer charges on the plates repelling each other

Cu

rren

tTime

Volt

age

Time

Charging and Discharging Capacitors

The shape of these curves can be controlled by a resistor in series, the

higher the resistance the slower the discharge

Time Constant ( )

• The time constant ( )is a measure of how

quickly a capacitor charges or discharges– This will depend on:

• The resistance (R) of the circuit (how much current

flows)

• The capacitance (C) of the capacitor (how much

charge is stored)

so:

NB; one time constant is not the total time to charge or

discharge but the time to discharge to 37.5% or to charge to

63.5% of the total

RC

Time Constant ( )

• One time constant is not the total

time to charge or discharge but the

time to discharge to 37.5% or to

charge to 63.5% of the total

• Experts; this is because of the exponential nature of the charge/discharge curves

V

tRC

63.5

%

V

tRC

37.

5%

C

1

1

C

t

C

V0.37V0.37,eas

eVVtwhen

eVVDecayFor

,

C

1

1

C

t

C

V0.63V0.37,eas

e1VVtwhen

e1VVgrowthFor

)(

)(,

Examples

1. Calculate the time constant for 330μF

capacitor in a 20 charging circuit6.6 10-3s

2. Calculate the time constant for 330μF

capacitor in a 15 discharging circuit5.0 10-3s

3. Calculate the amount of charge on each

of the capacitors in 1 and 2 after 1 time

constant when charged from 12V supply.1 = 2.5 10-3C, 2=1.5 10-3C

Exercises

• Try ESA, Activity 14A,B,C, Pg 224

• ABA, Pg 139-153