Chapter 18 Capacitance

CAMBRIDGE A – LEVEL

PHYSICS

CAPACITANCECAPACITANCE

LEARNING OUTCOMES

NUMBER LEARNING OUTCOMES

i W h a t a r e c a p a c i t o r s ?

ii H o w c a p a c i t o r s w o r k ?

iii H o w d o m e a s u r e t h e v a l u e o f a c a p a c i t o r ?

iv H o w d o w e c a l c u l a t e e q u i v a l e n t c a p a c i t a n c e s f o r

c a p a c i t o r s c o n n e c t e d i n s e r i e s a n d / o r i n p a r a l l e l ?

v H o w d o w e c a l c u l a t e t h e e n e r g y s t o r e d i n a

c a p a c i t o r ?

W H AT A R E C A PAC I TO R S ?

• Capacitors are electronic devices that are• Capacitors are electronic devices that aremade up of two conductors separated fromeach other by a dielectric.

• The image below shows certain types ofcapacitors seen in electronic devices.

Diagram 24.7, page 793, Sear’s and

Zemansky’s University Physics, Young and

Freedman, 13th edition, Pearson Education,

San Francisco, 2012.


• Capacitors are electronic devices• Capacitors are electronic devicesthat are capable of:a. storing electric charge, and thus can

store electric energy,b. blocking flow of direct current, but

enabling alternating current, andc. Can be used as filters in radio/TV

receivers• Capacitors are used in the flash of

cameras, radio and television receiversand air bag sensors.


• Two parallel conducting plates can be• Two parallel conducting plates can beused to built a capacitor.

• Symbol for parallel plate capacitors incircuit diagrams:

H O W C A PA C I T O R S F U N C T I O N


��

• Whenever a potential difference, V is applied across a

capacitor, electrons flow from the negative terminal to

plate Y due to the potential difference between the

negative terminal of the battery and the plate Y.

• Electrons also flow from plate X to positive terminal.

• The potential difference across the capacitor increases.

• When potential difference, V across capacitor is equals topotential difference supplied, the charges stop flowing.

• The plate X will acquire a net positive charge of ��while plate Y will acquire a net negative charge of��.


• Since the conducting plates are separated by a

dielectric (an insulator), the charges cannot flow

across.

• Thus, the charges that are stored at the plates store

electric potential energy in them.

• Note that even though the positive plate and

negative plates carry charges of �� and ��

respectively, the charge stored in the capacitor

is Q.

H O W D O W E M E A S U R E

C A PA C I TA N C E ?



• The capacitance of a capacitor is• The capacitance of a capacitor isdefined as the amount of chargestored in the capacitor, (in C) tothe per unit of potential difference,

(in V) across the capacitor, or�

�

• The units of capacitance is the Farad(F).





• 1 Farad is the value of the• 1 Farad is the value of thecapacitance of a capacitor if it stores1 Coulomb of charge when apotential difference of 1 Volt isapplied across it.

• Hence, 1 F= 1 C/V.

EXAMPLES

Example; 11.2 Capacitance, Page 293, Chapter 11: Fields, International A/AS Level

Physics, by Mee, Crundle, Arnold and Brown, Hodder Education, United Kingdom,

2008.

EXAMPLES



2008.

C A PAC I TO R S C O N N EC T E D

I N S E R I E S


I N S E R I E S

Vsupply


I N S E R I E S


I N S E R I E S• The diagram on the previous slide• The diagram on the previous slide

shows 3 capacitors connected with eachother in series.• Electrons flow from negative terminal of

the power supply to plate Y, and chargeplate Y negative• Electrons also flow from plate A to the

positive terminal of the power supply,thereby causing plate to acquire apositive charge.• What about the other plates B, M, N

and X?


I N S E R I E S


I N S E R I E S

• The sum of the p.d. across the 3

� � � ��

��

• The sum of the p.d. across the 3capacitors must equal the supplyvoltage, or �� ,• The charge stored on each capacitor is

the same, or ��

• Hence�

��

�

��

�

��

�

��,or

�

��

�

��

��

�,


I N PA R A L L E L


I N PA R A L L E L


I N PA R A L L E L


I N PA R A L L E L

• The diagram on the previous slide• The diagram on the previous slideshows 3 capacitors connected in parallelwith each other.

• Charges flow into the capacitors untilthe potential difference across eachcapacitor is equal to the chargingvoltage, V.

• Hence, the potential difference acrossthe capacitors are the same, V.


I N PA R A L L E L


I N PA R A L L E L

• � � � or ��

� � �

• � � � or ��

� � � .

• On simplification, we obtain

� � �

EXAMPLES

Example 24.5 and Diagrams 24.8 and 24.9, pages 793, 794 and 795, Sear’s and

Zemansky’s University Physics, Young and Freedman, 13th edition, Pearson

Education, San Francisco, 2012.

EXAMPLES

Example 24.6, page 796, Sear’s and

Zemansky’s University Physics, Young

and Freedman, 13th edition, Pearson

Education, San Francisco, 2012.

EXAMPLES

Exercise 24.16, page 812, Sear’s and


Freedman, 13th edition, Pearson Education, San

Francisco, 2012.

EXAMPLES

Exercise 24.16, page 812, Sear’s and


Freedman, 13th edition, Pearson Education,

San Francisco, 2012.

EXAMPLES



2008.

EXAMPLES

Questions; Section 11.2 Capacitance, Page 303, Chapter 11: Fields, International

A/AS Level Physics, by Mee, Crundle, Arnold and Brown, Hodder Education, United

Kingdom, 2008.

E N E R G Y S TO R E D I N

C A PA C I TO R S


C A PA C I TO R S

• Capacitors are capable of storing electric• Capacitors are capable of storing electricenergy.

• How do we calculate the amount of energystored in a capacitor?

• Recall that the potential difference across acapacitor is directly proportional to theamount of charge stored in it.

• What sort of graph would we get if we plotp.d. versus amount of charge stored?


C A PA C I TO R S


C A PA C I TO R S


C A PA C I TO R S


C A PA C I TO R S

• To calculate the amount of electric

� ��

�

� � !�

• To calculate the amount of electricenergy transferred from the batteryto the capacitor, we need to find thearea under the curve.• Note that the p.d. across the capacitor

increases as the amount of chargestored in it increases.• Hence, the energy stored by the

capacitor, ��

��

�

� since

� � !�

E X A M P L E S



2008.

E X A M P L E S

May/Jun 2008, Paper 4, Question 5.

E X A M P L E S

May/Jun 2008, Paper 4, Question 5 (cont’d).

E X A M P L E S


E X A M P L E S


E X A M P L E S

May/Jun 2009, Paper 4, Question 5.

E X A M P L E S


E X A M P L E S


E X A M P L E S


E X A M P L E S


H O M E W O R K

1. Winter 09, Paper 42, question 4.

2. Summer 10, Paper 42, question 5.



5. Summer 11, Paper 42, question 3.


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Chapter 18 Capacitance