Note Physics 2 SP025

o Capacitance, C of a parallel-plate capacitor is
 proportional to the area, A of its plates
()

 inversely proportional to the plate separation, d
()

 depends on type of dielectric insert between

two plates ( )

42

Dielectric

o is defined as a non-conducting (insulating)
material placed between the plates of a
capacitor.

o When a dielectric (such as rubber, glass or
waxed paper) is inserted between the plates of
a capacitor, the capacitance increases by a
factor which is called the dielectric constant
(relative permittivity) of the material.

43

o The advantages of inserting the dielectric
between the plates of the capacitor are

increase in capacitance

increase in maximum operating voltage
possible mechanical support between

the plates, which allows the plates to be
close together without touching,
thereby decreasing d and increasing C

44

How dielectric
increase the
capacitance ?

45

46

 Q Eo  Q

o As battery is
removed, charge, Q
on the plates
remains constant.

o Electric field
between the plates
is Eo.

47

o Dielectric is o From ,
placed o As

between the

plates , the

dipoles o From :

Q  Q orient  QAs E  Eo  Q

themselves

Ed o A `reverse`

electric

 field, is
E0
created.
o

)

o Electric

field E is

reduced. 48

Battery, dielectric E decreases, so does V.
V0 Capacitor, VC But because the
circuit remains
connected, charges
are able to flow to
charge C until VC = V0

Since V remains
constant, C increases

From Q = CV, so Q
increases

49

Is the capacitor connected to a
battery when you modifying a
capacitor?

Battery is Battery still
disconnected connected

50

Dielectric constant,

o is defined as ratio of permittivity of dielectric
material, and permittivity of free space,

εr  ε C  V0  E0
ε0  C0 V E

where : Capacitance with dielectric

: Capacitance of air filled (vacuum)

: voltage across capacitor with dielectric

: voltage across air filled (vacuum) capacitor

: electric field strength of capacitor with dielectric

: electric field strength of air filled (vacuum)

capacitor 51

o is dimensionless (no unit) & is greater than 1.

o Different insulating material has different value of

Material Dielectric constant,
Vacuum 1.0
Air 1.00059 = 11.1 F
Teflon 2.1
Silicone oil 2.5 52
Paper 3.7
Ruby Mica 5.6
Water 80.4

Example LO 2.3

A parallel-plate capacitor has plates of area 280 cm2 are
separated by a distance 0.550 mm. The plates are in vacuum.
If a potential difference of 20.1 V is supplied to the capacitor,
determine

a. the capacitance of the capacitor.

b. the amount of charge on each plate.
c. the electric field strength was produced.

(Given permittivity of free space, o = 8.85  1012 C2 N1 m2)
Solution : A  280 104 m2; d  0.550 103 m;V  20.1 V

a. By applying the equation of capacitance for vacuum
parallel- plate capacitor,

  C 
C  ε0 A 8.85 1012 280 104
d 0.550 103

C  4.511010 F 53

Solution : A  280 104 m2; d  0.550 103 m;V  20.1 V

b. The amount of charge on each plate is given by

Q  CV

 Q  4.511010 20.1

Q  9.07 109 C

c. From the relation between uniform E and V , therefore

V  Ed

 20.1  E 0.550 103

E  3.66 104 V m1

54

Example LO 2.3

A vacuum parallel-plate capacitor has plates of area A = 150 cm2
and separation d = 2 mm. The capacitor is charged to a potential
difference V0 = 2000 V. Then the battery is disconnected and a
dielectric sheet of the same area A is placed between the plates

as shown in Figure below.
dielectric

d

In the presence of the dielectric, the potential difference across
the
plates is reduced to 500 V. Determine
a. the initial capacitance of the capacitor,
b. the charge on each plate before the dielectric is inserted,

55

c. the capacitance after the dielectric is in place,

continue :

d. the relative permittivity,

e. the permittivity of dielectric material,

f. the initial electric field,

g. the electric field after the dielectric is inserted.

(Given permittivity of free space, 0 = 8.85  1012 C2 N1 m2)

Solution : A  150 104 m2;d  2 103 m;V0  2000 V;
V  500 V
a. The initial capacitance of the capacitor is given by

ε0 A  C0 
C0  d 8.85 1012 150 104
2 103
C0  6.63 1011 F

b. The charge on each plate is

Q0  C0V0  Q0  6.631011 2000

Q0  1.33 107 C 56

Solution : A  150 104 m2;d  2 103 m;V0  2000 V;
V  500 V
c. In the presence of the dielectric, the charge on each plate is

the same as before the dielectric was inserted. Therefore the

new capacitance is 1.33 107  C500

Q0  CV C  2.66 1010 F

d. From the definition of the dielectric constant, thus
C 2.66 1010
εr  C0 εr  6.63 1011

e. the permittivity of dieleεcrtric4m.0a1terial is given by

 ε  εrε0

ε  4.01 8.85 1012

ε  3.55 1011 C2 N1 m2 57

Solution : A  150 104 m2;d  2 103 m;V0  2000 V;
V  500 V

f. By applying the relationship between E and V for uniform

electric field, the magnitude of the initial electric field is

E0  V0
d
2000
E0  2 103

E0  1.00 106 V m1

g. The electric field after the dielectric inserted is given by
E0
εr  E OR E  V
d
1.00  10 6
E
4.01 

E  2.49 105 V m1 58

CAUTION !!! Capacitors are located inside of all laboratory equipment. They
come in many different shapes and sizes. Capacitors can remain energized and
produce harmful shocks long after a piece of equipment has been unplugged.

End of Chapter 2 59

CHAPTER 3
ELECTRIC CURRENT AND DIRECT-CURRENT CIRCUITS

(2 HOURS)

3.1 Electric Conduction
3.2 Ohm’s law and Resistivity
3.3 Variation of resistance with temperature
3.4 Electromotive force (emf), internal resistance and potential difference
3.5 Resistors in series and parallel
3.6 Kirchhoff’s Rules
3.7 Electrical energy and power
3.8 Potential divider
3.9 Potentiometer

1

Learning outcomes

At the end of this topic, the student should be able to:

3.1 Electrical Conduction
(a) Describe microscopic model of current

(Lecture : C1, CLO1, PLO1, MQF LOD1)

(b) Define and use electric current, .

(Lecture : C1, CLO1, PLO1, MQF LOD1)
(Tutorial : C3, CLO3, PLO4, CTPS3, MQF LOD6)

(c) Use electric current,

(Tutorial : C3, CLO3, PLO4, CTPS3, MQF LOD6

2

Learning outcomes

At the end of this topic, the student should be able to:

3.2 Ohm’s Law and Resistivity

a) State and use Ohm’s law

(Lecture : C1, CLO1, PLO1, MQF LOD1)
(Tutorial : C3, CLO3, PLO4, CTPS3, MQF LOD6)

(b) Define and use resistivity,

(Lecture : C1, CLO1, PLO1, MQF LOD1)
(Tutorial : C3, CLO3, PLO4, CTPS3, MQF LOD6)

(c) SketchV-I graph (Experiment 2: Ohms’s Law)

(Tutorial : C4, CLO3, PLO4, CTPS3, MQF LOD6) ; (Practical : P3, PLO2, MQF LOD2)

(d) Verify Ohm’s Law(Experiment 2: Ohms’s Law)

(Tutorial : C4, CLO3, PLO4, CTPS3, MQF LOD6) ; (Practical : P3, PLO2, MQF LOD2)

(e) Determine effective resistance of resistors in series and parallel by
graphing method (Experiment 2: Ohms’s Law)

(Tutorial : C4, CLO3, PLO4, CTPS3, MQF LOD6) ; (Practical : P3, PLO2, MQF LOD2)

3

Learning outcomes

At the end of this topic, the student should be able to:

3.3 Variation of resistance with temperature
(a) Explain the effect of temperature on electrical resistance in metals.

(Tutorial : C4, CLO3, PLO4, CTPS3, MQF LOD6)

(b) Use ,

(Tutorial : C3, CLO3, PLO4, CTPS3, MQF LOD6)

4

Learning outcomes

At the end of this topic, the student should be able to:

3.4 Electromotive force (emf), internal resistance and potential
difference

(a) Define emf, and internal resistance r of a battery.

(Lecture : C1, CLO1, PLO1, MQF LOD1)

(b) State factors that influence internal resistance.

(Lecture : C1, CLO1, PLO1, MQF LOD1)

(c) Describe the relationship between emf of a battery and potential
difference across the battery terminals

(d)Use terminal velocity, V= - Ir (Tutorial : C4, CLO3, PLO4, CTPS3, MQF LOD6)

(Tutorial : C3, CLO3, PLO4, CTPS3, MQF LOD6)

5

Learning outcomes

At the end of this topic, the student should be able to:

3.5 Resistors in series and parallel

(a) Derive and determine effective resistance of resistor in series and

parallel. (Lecture : C2, CLO1, PLO1, MQF LOD1)
3.6 Kirchhoff’s Rules (Tutorial : C4, CLO3, PLO4, CTPS3, MQF LOD6)

(a) State and describe Kirchhoff’s Rules

(Lecture : C2, CLO1, PLO1, MQF LOD1)

(b) Use Kirchhoff’s Rules

*(i) Maximum two closed circuit loops

(ii) Use scientific calculator to solve the simultaneous equations

(Tutorial : C3, CLO3, PLO4, CTPS3, MQF LOD6)

6

Learning outcomes

At the end of this topic, the student should be able to:

3.7 Electrical energy and power

(a) Use power, and . (Known as power loss)

(Tutorial : C3, CLO3, PLO4, CTPS3, MQF LOD6)

(b) Use electrical energy,

(Tutorial : C3, CLO3, PLO4, CTPS3, MQF LOD6)

3.8 Potential divider
(a) Explain the principle of potential divider

(b) Use equation of potential divider, (Lecture : C2, CLO1, PLO1, MQF LOD1)

(Tutorial : C3, CLO3, PLO4, CTPS3, MQF LOD6)

7

Learning outcomes

At the end of this topic, the student should be able to:

3.9 Potentiometer
(a) Explain principles of potentiometer and its applications.

(Lecture : C2, CLO1, PLO1, MQF LOD1)

(b) Use related equations for potentiometer,

(Tutorial : C3, CLO3, PLO4, CTPS3, MQF LOD6)

(c) Determine internal resistance, r of a dry cell by using potentiometer.
(Experiment 3 : Potentiometer)

(Tutorial : C4, CLO3, PLO4, CTPS3, MQF LOD6); (Practical : P3, PLO2, MQF LOD2)

8

3.1 ELECTRICAL CONDUCTION

Microscopic Model of Current
o Metal is good electric conductor. In metal (conductor),

the charge carrier is free electron.
o If there no electric field inside a conductor, free

electrons move randomly in all directions.

9

o If an electric field,  is present, electric force,  
E F  qE

causes the free electrons to move slowly along the
conductor (in a direction opposite that of E ) at drift

velocity, vd

–+

o The drift of electrons in one specific direction

producing current. 10

Electric Current (I)

o is defined as total charge, Q flowing through an area
per unit time, t

o Formula : dQ where dQ is the amount of charge
dt that pass through a conductor at
I  any location during the time
interval, dt.

elementary charge

o Base and scalar quantities, S.I. unit: ampere (A).

o 1 ampere of current is defined as one coulomb
of charge passing through the surface area in
one second.

o Can be measured using an ammeter connected

in series in a circuit. 11

o The flow of charge (current) persists for as
long as there is a potential difference.

Analogue to

12

o The direction of the current is opposite
the direction of flow of electrons

Current, I

electron _
flow

Direction of electric current : Positive to negative terminal
Direction of electron flows : Negative to positive terminal

13

Example 3.1

Question 1:
(a) A current of one ampere is a flow of charge

at the rate of _1_ coulomb per second.

(b) When a charge of 8 C flows past any point
along a circuit in 2 seconds, the current is _4_A.

14

Question 2: FIGURE 1 shows a conducting
FIGURE 1 wire. Two cross-sectional areas
are located 50 cm apart. Every 2.0
seconds, 10 C of charge flow
through each of these areas. The
current in this wire is __5__ A.

15

3.2 OHM’S LAW AND RESISTIVITY

Ohm’s Law

o states that the potential difference (voltage) across a
conductor, V is proportional to the current, I flowing

through it if its physical conditions & temperature are

constant. V (V) Materials that obey
Ohm’s law (have
o Expressed mathematically :
constant resistance
V I over a wide range of

voltage) are called

ohmic conductor.

V  IR Gradient, m = R

: resistance 0 I(A)

: potential difference applied across,

: current flow 16

Resistance ( R )

o Is property which opposes or limits current
flow.

o Is defined as a ratio of the potential difference,
V across an electrical component to the
current, I passing through it.

o All electrical devices (heater, light bulb etc) offer
resistance to flow of current.

o Scalar quantity ; SI unit : ohm (Ω) 17
o Symbol to indicate resistance in a circuit :
o In a circuit, if R is constant, as V ↑, I ↑.

Resistance, of any wire or conductor

Resistance of a wire or other conductor of

uniform cross section is

1) directly proportional to its length,

2) inversely proportional to its cross-sectional

area,

3) proportional to the resistivity of the material

of which the conductor is made, 18

Resistivity ( ρ )

o A measure of a material’s ability to oppose the
flow of an electric current

o is defined as the resistance of a unit cross-
sectional area per unit length of the material

o SI unit is ohm meter ( m)
o Resistivity depends on the type of the material

and temperature.
o A good electric conductors have a very low

resistivities and good insulators have very
high resistivities.

19

Material Resistivity,  ( m)

Silver at 20
Copper 1.59  108
Aluminum 1.68  108
2.82  108
Gold 2.44  108
Nichrome 150  108
Tungsten 5.60  108
1.0  107
Iron 10101014
Glass

20

Example 3.2

Question 1:

Use the Ohm's law equation to determine the missing values
in the following circuit A and C.

3 4
2
2

21

Question 2:
A 1.5 m length of wire has a cross-sectional area
5×10-8 m2. When the potential difference across its
ends is 0.20 V, it carries a current of 0.40 A. The
resistivity of the material from which the wire is made
is ____

Solution:

22

Question 3:
Two copper wires have the same cross-sectional area
but have different lengths. Wire X has a length L and
wire Y has a length 2L. The ratio between the resistance
of wire Y and wire X is……

Solution:

((

23

3.3 VARIATION OF RESISTANCE
WITH TEMPERATURE

Effect of temperature on electrical resistance
in metals

 The electrical resistance (or resistivity) in metal always
increases with increasing temperature.

 As the temperature increases, the ions of the metal
vibrate with greater amplitude.

 This causes the number of collisions between the free
moving electrons and metal atoms increase.

 This impedes the drift of free electrons through the metal
and hence resistance increases.

Make it more difficult 24

Resistance and temperature

o Resistivity of a material varies with temperature.

How to ρ
find value

of ρ at

tempera

-ture T

?

T

25

o Over a limited temperature range, the resistivity
of a conductor varies approximately linearly with
temperature

where  = resistivity at temperature T (in ),

o = resistivity at reference temperature,
(usually taken to be 20 )

α = temperature coefficient of resistivity (at

temperature 20

o Because resistance is proportional to resistivity

( we can write the variation of resistance
as

26

Temperature coefficient of resistivity () is the fractional
increase in resistivity per kelvin temperature rise from
the resistivity value at some reference temperature.

  1 

0 T

where

SI unit for α is

Various material have various values of .
103 –1
e.g : Silver   = 4.10  K
103 –1
Mercury   = 0.89  K

27

Example 3.3

Question 1:
The resistance of tungsten filament of a bulb is 190 Ω
when the bulb is alight and 15 Ω when it I switched off.
Calculate the temperature of the filament is alight .
The room temperature is 30°C and the temperature
coefficient of resistance tungsten is

Solution :

°
28

3.4 ELECTROMOTIVE FORCE,
INTERNAL RESISTANCE &
POTENTIAL DIFFERENCE

Emf,  and terminal potential difference, V

Consider a circuit consisting of a battery (cell) that is

connected by wires to an external resistor R as

shown. R

Battery (cell) ‒B

Aε r
‒

29

emf is not a force at all; it is a special type
of potential difference.

 Electromotive force (emf), is defined as the
energy provided by the source (battery or cell) to
each unit charge that flows through the external
and internal resistances.

 Terminal potential difference (voltage), V is defined as
the work done in bringing a unit (test) charge from the
negative to the positive terminals of the battery through
the external resistance only.

30

o When the current flows naturally from the battery,
there is an internal drop in potential difference (voltage)

equal to Voltage

o Terminal voltage due to internal drop in
internal

resistance, of the battery. resistance,

o The terminal voltage,

o The unit for both and are volt (V). 31

 Terminal voltage,
where : current flow in the circuit
: total external resistance

terminal voltage equals The internal resistance of a

emf only if there is no voltage source affects the output

current flowing. voltage when a current flows.

Battery (cell) Battery (cell) 0.5A

AB IA B

V V smaller the internal
resistance r, the
Voltmeter reads Voltmeter reads greater the current the
voltage source
supplies to its load R