Light and sensor

1. -
UNT-
GET REMOTE SENSONGG
s L I R c t i n e
m enein
naidenta
acted ay
s12 Les afnetacti
Te ndt m e d myandthe sa
ein thesameplane
The mtio of the ine oftheangieof mcide the
e age of refirtio isacnmtan
3.13. Refractiwe index
ofthe medium b)(o
Seela aw
The atio f the sine of the angledfinciden tot
e f theandeofredractioniscalledrefractiveindexof
the medium
Bdrctiveindexy=

2. rom dense
ttravels rom den
3 . 1 , 4 . T o t a l
I n t e r n .
I-47
2
a of hght
travels fror
Phenomenon cations of total internal reflection
(imsider
4
a y
of
g
3.1.6
A p P l i c a t i o n s
of total
2) Endoscope 3) Periscope
( g l a s s i
t o
r a r e r
nedum
( a i r )
1) Fibre optics
5) Prisms
4 ) B i n o c u l a r s
=90
Rar
3 . 1 . 7 F I b r e O p t i c s
The
transmission
and reception of light waves through
able is known as fibre optics
Dense
(AS
o p t i c a l
fibre cable
is
known
ble (OFC) as a wave gulde.
3.1.8
Optical
fibre
cable (OPc) as a wa
P r i n c i p l e :
ORC is based on the principle of total internal reflor.
Fig 2
Fig3
Fig
lore115
the angle
of incidence
and r is t
tion.
Fig
1. Here11s
the
angle
nce i is
ncreased
ace of sepera tion.
Construction :
Ontical fibre cable (OFC) 1s a flexible, cylinderical di.
o f
r e f r a c t i o n .
r e t r a c t e d
r r
g r a z e s
the
surface
ofsepe
the angle
of
e t r a c t i o n
is
90°
known as
critical
angle.
(1
= c.r
= 90°
Fig2.
The
angle
of
n c i d e n c e
90 This angle of
incide
That In OFC. the inner cylinder made
ofglass plastic is
led core.
The core has high refractive index n. The core is
lectric (glass or plastic)
wave guide. It's radius is 150um
s u r r o u n d e d
by a cylinderical shell of lower refractive index
2
Fig. 3 When the ungle of incidence is
calle
cladding.
The cladding is covered by outer jacket to
critical angle, the incident
ray totally refie.
in the protect from
moisture and abrasion
denser medum self This 18 called total internal
re
tion(1>c)
Cladding(n2)
3.1.5 Conditions for total internal
reflection
1) Laghtray must travel trom a
densernedium toa
medium
Coreln)
Jacket
2) The angle of incadenoe must be greater thano
angle
ert
Working
When a beam of light enters at one end ofthe fhre it
trikesthe wallsof claddingat an angle greator
thnn
rritical

3. nterna
t
beam
u n d e r g o e s
totai
tota
fibre.
the
l e n g t h
of the
ithout
e. Fir
nergy log
t r o n
many
times
a l o n g
b e a m
eomes
o u t
a t
t l h e
o t h e r
e n d
O F C
acts
a s
a
wave
g u i d e .
- 49
n g l e
alwas
T h e
l i g h t
y Collimator
to convert the source of light into
C o l l i m a
is used to
p a r a l l e l
b e a m
of
light.
I t c o n s i
. of a slit and a convex lens fitted to co-axial
within the other. The distance between the
slit
a n d
the
convex
lens can
andpinion arra
lens can be adjusted by means of a rack
n gement and a parallel beam of rays can be
ly fixed, with its axis horizontal to
b e s o n e s l i d i n g
3 . 1 . 9
Advantages
( M e r i t sof
O p t i e c a l
duetolight weight
got.
T h e
c o l l i m a t o r
is rigidly
Cable I
ofof Optical Fibre
the tripod
b a s e
of
t h e
s p e c t r o m e t e r
Prism
o f t h e s p e c t r o m e t e r .
d flexib.
Table
C o i l i m a t o r
Telescoppe
) E a s y
h a n d l i n g
d u e
to light
w e i g h i
2)
It
has
high
b a n d
w i d t h
4) It is not
c a r r y i n g
any
c u r r e n t . So
h a r m l e s s
3)
Loss
of
e n e r g y
1s
low..
nt. So it is
saf
VERA
5) It is free
from
c r o s s - t a l k ,
tion is possible.
ss-talk, so noise ee commu
atmospheric condition
i) Prismtable
T+ is a circular table mounted at the centre of the instru-
6) It can
withstand
at any atm
7) It is
economical
with high quality ment. It can be levelled, raised or lowered, rotated or fixed by
adiusting the suitable screws. A clip is provided for clamping
the prism on the prism table. The circular scale is also rotated
along with the prism table by using side screw lock.
8) Tapping
(overhere
secrets) of informationi
is impos
3.1.10 Spectrometer
mine
Spectrometer is an
instrument used to determ
refractive index of the material ot a prism and to.
i) Telescope
The telescope is an astronomical one consisting of an
obiective and an eye-piece fitted to co-axial tubes, one sliding
spectra.
Spectrometer consists of three essential parts.
within the other. The distance between the objective and the
are () colimator 6i) prism table (ii) telescope.
eye-piece can be adjusted by means of a rack and pinion
arrangement. The telescope is attached to a circular scale.

4. I-50
3.1.11 Angle ofminimum
deviation .
In a prism.
as the angle of
incid
angle of deviation tieereases upto a
minin
it will nerease. 7he.minimum angle th
e me
ugh whi,
led as
angle of
mi
of minn
devvate the light rays is called
3.1.12 Epression for the
refractive
lnder of .
faces of the prism and BC, its base. Let a
be
on
Sndexof
and Ac
B
Consider a glass prism ABC, AR.
A
nd
the face AB This ray is refracted
along QR an
at R along RS from the other face Ac
Ds th
Let A is the angle of the prism and
nd ref
minimum deviation. The angle of inciden
D
and
the two faces are 11, Ii l2 and i,
respectively
In the qudrilateral AQOR, since the angles at
are right angles.
.(1)
A+ 1QOR = 180°
2)
In AQOR, r tr+ |QOR =
180°
Comparing (1) and (2) r +r = A
In AEQR, the exterior angle,

5. 2
Sin4930
sin29 30
-53
h
a n
experient
thea
i n i m u m
d e v i a t i o
the priam
A+D
Sin
angleof
60+38
a n g h
of
m i n i m u m
d e t i a t i o n
a n d
4 0 0 .
F i n d '
2
8In
ere found t
Refractive
Index u
=
A
iationwere
undtob S1n
6O
the refh
ractive ind
of sin49-1.5064
rial
of
the
p r i s m
s i n 3 0
Here
Angle
ot
prism
A = 5g
tion D =40°3
Calculate
the angle of minimum deviation for an
eguilateral
glass prism of refractive index 1.51.
Angle
of
maunimum
d e v i a t i o n
n -
Oct.16)
A+D
Given:Theprism is equlateral. A G0
SI Refractiveindex = 1.51
A+D
Sin
2 A+D
Sin
Sin
2
A
xSin
39'52 40°30
2
A
SIn
59952
SIn
60
60+D 1.51sin 0.75
Sin
2
2
2
Sin
50'11
Sin2056
60+2=sin (0.75)= 4835
2
4 1 . 5 3 9
60°+D 2x 48°35" =
97°10
D 97°10 -60° 37°10
material
3Calculate therefractiveinderoftheme
equilateral
prism. heangleofminimudeti
is 38.
3.113 Experiment to determine refractive index of the
prism using spectrometer
Given: Theprismis equilateral A =
60 The preliminary adjustments of the telescope, collima
ter and the prism table ot the spectrometer aremade. The
refractive index is determined by knowing the angle ofprism
Angle ofrninimum deviation D=
38°
and the angle of minimum deviation.

6. I 54 55
noted. The diffe
g l e o f m i n i m u m
fference bet
deviation
prism and the direct ray readings are
between these two
readings gives the
R e m o v e
(D).
s i n t D
2
R e f r a c t i v e i n d e x =
A
sin 2
3.2 LASER
Fig. (2)
Fig. (1) The wordd ASER stands for Light Amplification by
of Radiation. The laser is a device
which
mplifies light w a v e s .
Characteristics (Properties) ofLASERR
Cmission
Angle ofprism (A)
It is used as a source of light.
refre
Stimulated En
ing edge facing the collimator (fig. 1) The slit is illu act
by a sodium vapour lamp.
The prism is placed on the prism table with
is
illuminated
its
g
The telescope is rotated to one of the reflectin. The laser beam
the
Then the image of the slit is made to coincide wit ( i ) i s m o n o c h r o m a t i c
The readings ot the verniers are
noter
vertical crosswire.
Similarly the telescope is rotated to the other reflectin.ed
and do the same things as before. The vernier
readinge
(ii) is coherent
face iii) is highly intense and
again noted. (iv) does not diverge at all.
3.2.2
Principle of Laser
Laser works on the principle of quantum theory of
The difference between these two rea dings gives 9
From this, calculate the angle of the prism A.
radiation. When an atom may undergo transition between
two energy states Bi and B2: 1t emits a photon of energy
(i) Angle of minimum deviation (D)
The prism is placed such that one of the polished s
face face the collimator (fig. 2). The telescope is rotated to th.
refracted image of the slit and should be in the field of vie
Now the prism table and the telescope are rotated in the
same direction. The slit also moves in the same
direction.At
one stage, it is found that the image of the slit comes to stop
and retrace its path. This is minimum deviation position.
The vertical erosswire is made to coincide with the image and
the vernier readings are noted.
E2 -
E= hv.
h - Plancks' constant
v frequency of the photon.
3.2.3 Population inversion
In a system of thermal equilibrium, the number of
atoms in the ground state
is greater than the number of
atoms in the excited state. This is called normal population.

7. -57
3.2.6Constructr
1 0 0 %
reflecting
mirror
truction and Wor
ofRuby Laser
II-56
the excited
The atoms in the ground state are taken to the ev.
state with the help of light is called optical pumping.
Lser
stat
Definition: The number ofatoms in the
excited
is called
18 greater than the numberofatoms in ground state is e Partialy
reflect:ng
population inversion.
Xenonflash lamp
mirror
mium oxide. It is a rod of length 10cm and 0.8 cm
diame
One
end is fully silvered and the other end is par-
Construction :
Ruby
is a mixture
of alu
Excited state
a-N2 nixture of aluminium oxide and chro-
E
Na >N
E
d i a m e t e r .
- N1
Ground stale
3.2.4 Spontaneous emissiona:
tially silvered.
During the transition of atoms from excited state to
ground state, emits energy spontaneously is known as
span.
It is
surrounded by a Xenon flash lamp in the form
ofspiral
taneous emission.
Excited state
Excited state
E2 E2 2
Photon Meta stable state
E
E
Ground stale
hv hv
3
3.2.5 Stimulated emisssion hv
During the transition of atoms from metastable state to
ground state, emits energy with the help of photon is known
as stimulated emission.
E1 Ground state
Metastable state
E2
Working:
.When the ruby rod is irradiated by Xenon flash
lamp, chromium ions are shifted from ground state
E E, to excited state E, and then to metastable state
Eg without giving energy.
Ground state
During transition from Eg to E, a photon is emitted.

8. - 58
I 59
within the
This photon makes multiple
reflections with.
ruby rod and induce new photons.
3.3.1
T y p e s
o t r e m o t e
Remote
sensing have t
singand (ii)
sensing
mote sensing:
msing have two
types. They are (i) Active
These reflections add the
induced emission.
a coherent laser beam emerges
out through thall
tially silvered end.
r e n
emote sensing aa ssive remote sensing.
the par- A c t i v e r e m o t e
enerates and uses its own
energy to illu
T h e s y s t e m g e n e r a t e s
and the
information obtained by
3.2.7 Uses of Laser
minate
the
d i s t a n t object n
1) Laser is used to drill fine holes in hard mat.
like diamond and tungsten.
t h e r e f l e c t e d
(Eg.) Radar, Sonar
w a v e s is known as active remote sensing.
2) It is used in welding and to cut thick sheets of h. an
Passive
r e m o t e sensing
ss of obtaining information by the reflected
metals.
The process of
rce of energy (sunli or U.V. rays) from the
3) It is used to test the quality of the materials,
natural source of
dist
is known as passive remote sensing.
istant object is
4) In medical field it is used in eye surgery, to reme.
kidney stone and c a n c e r
treatment.
(Eg.) Photography, Radiometers
ove
3.3.2.
C o m p o n e n t s
of :
The general process ot remote
sensinghas threa
remote sensing:
5) It is used to study the molecular structure.
6) It is used in OFC (Optical Fiber Cable)
components.
They are () Data acquisition and (ii) Data
7) It is used in CD writing and reading (CD Rw)
8) It is used in holography to generate three dimen.
sional images of objects.
analysis
) D a t a a c q u i s i t i o n
The schematic diagram of data acquisition
3.3 REMOTE SENsING
Introduction
Reference
data
The collection of information about a distant object
through a special device is called remote sensing.
Pictorial
The device used to detect the electro magnetic radia-
tion emitted or reflected from the distant object is called as
remote sensor' or 'sensor'. (Ex) Cameras, Radars etc.
Digita!
Conversion
5)
The vehicle used to carry the sensor is called as 'plat
form'. (Ex) Aircraft, satellites. 3)

9. the
cess comprises th
followin acty
(2)
P r o p a g a
tion
of
e n e r g y
t h r o u g h
aton
eflected ene
The
d a t a
acquisiton
proces
comprises
The date
-61
through atomosphere
with
earth's
surface obje
(1)Energysources
(2) To
c a l i b r a t e a sensor
(3)
E n e r g y
nteraction
with
e a r t )
(4)
Space
b o r n e
sensors
r e c o r d
the
) T o
(3) To verify the
information extracted from remote
sensing data.
(5)
G e n e r a t i o n
of
s e n s o r
d a t a in the fa.
digitalinformations.
form of picta
3 . 3 . 4 R a d a r
The ADAR is an acronym derived from RAdio Detec
Ranging. It is used to find the location and the
tion A n d
i i l
D a t a a n a l y s i s
T h e r e
a r e
two
metho
methods to analyse the pictoria
r a n g e
of
the
distance objects.
and
digital
d a t a s
o b t a i n e d
by
.
Refarencedata
data acquisitie
P r i n c i p l e
Radar works on the principle of 'radio echoec
C o n s t r u c t i o n :
The block diagram or a simple radar system is showr
consists of both transmithng system and receving
Visual
in
I n l e r p r e t a t i o n
Information
system.
Products Users Duplexer
Switch
Digitalimage
process
The process
of
analysing
pictorial dat
data is known
Transmittors Receiver
Visual image
i n t e r p r e t a t i o n
technique
The process
ofanalysing
the digital data Usin
Puser indicator
ng comp
ers is known as digital image
process technique, A
by usen
Timer
ing datas are
viewed in the
information products hu
The transmitting system consists a transmitter and a
pulser. The receiving system consists of a receiver and an
indicator. A single antenna connected with duplexer switch
is used for both transmission and reception.
3.3.3 Reference data
Reference data is also called as ground truth or Working
s e u
10
DOtn transmission and reception
check. Reference data are used in the tolowing proces
(1) To analyse and interpret remotely sensed data
The transmitter and pulser produces short periodir
pulses. These short periodic pulses are fed to the antenna
which radiates them into the space

10. I 1 - 6 2
W h e n
the
transmitted
p u l s e s
hits
a n .
t
the receive
target
W r i t e
the
important
parts of a
spectrometer.
Light
xpan.
Amplitication by Stimulated Emission of Radia-
The collection of information about a distant object
signa
returns
to
t h e
s a m e
antenna.
N o w
iver. The receiv
a.
Nowthe
duplex
I 63
d e m o d u l a
ted
pulses
a r e
fed
to
t h e
i n d i c a t o r
The
i n d i c a t o r
CRT
r e c o r d s
the
t r a r
se
with a small
he range of the
p u l s e s
a r e
a m p l i f i e d
a n d
demodulatedby
t h .
the transmitted
o n n e c t
the
antenna
w i t h
t h e
r e c e i v
con E x p a n d
the acronym LASER.
i)
Collimater
) Prism table i
Telescope
well
a s
the
r e t u r n i n g
e c h o
p u l s e
with a s n
This
displacement
is a
measure
ofthe ran
Ap.17,18)
Du
displa
well
tion.
What
is
r e m o t e sensing ?
9.
Q U E S T I O N S
necial device is called remote sensing..
through a special.
PART A
es of remote sensing?
(Apll
es from one
10.
What
a r e
th types
or remote sensi
i) Active
remote sensing
1
The
bending
oflight
when
it
p a s s e s
1 . D e f i n e r e f r a c t i o n .
i)
Passive
remote sensing
uum? (Ap.10,0
11.
what are the components of remote sensing
other
m e d i u m
is
known
as
r e f r a c t i o n .
2
What is the
velocityoflight
in v a c u u m ? (A
a)
Data
acquisition (1) Data analysis
(What is the
value ofvelocity oflight)
Velocityoflight v
=
3 x
10°ms
12.
Expand
the acronym RADAR.
RAdio
Detection And Ranging
(Ap.18,0ct.18)
3.
Define
critical
angle
3.
PART B
The angleofincidence
at which angle of refrad
is called
critical angle
4. What is fibre optics?
efraction is State laws of refraction.
(Ap.16)
1. The incident ray, refracted ray and the normal, all
4.
The
transmission
and reception of lightwaves
optical fibre cable is known as tibre optics'.
ght waves
lie in the same plane.
thro 2. The ratio of the sine of the angle incidence to the
sine of the angle of refraction is a constant.
5. What is the value ofrefractive index ofglass?(0
5.
Refractive index ofglass
= 1.5
6. What is a spectrometer.
2.
Define refractive index ofa medium. (Oct16,17, Ap.17)
6.
Spectrometer is an instrument used to determine
refractive index of the material of a prism andtoe eun.
The ratio of the sine of the angle of incidence to the sine
of the angle of refraction is called refractive index of the
medium.
spectra.
Sin
Sin r

11. I I - 6 4
d,
W h a t
is
t o t a l
i n t e r n a l
reflection ?
3.
oct
(Oc
efe ter than the o
Il-65
he cri
a n g l e ,
the
i n c i d e n t
r a yis
t o t a l l y
retlectedin
t h e h e
m e d i u m .
This
is
c a l l e d
t o t a l
i n t e r n a l
r e f l e c t i o
M
internal reflect
T h e
n u m b e r
of
atoms in #h
the
n u m b e r
of
a t o m s
p o p u l a t i o n i n v e r s i o n .
11.
What
is
s p o n t a n e o u s em
0.
W h a t
is
p o p u l a t i o n
inversion?
or of atoms in the excited state is greater than
W h e n
t h e
angle
of
incidence
is
g r e a t e r
t h o .
atoms in the ground state. This is called
n.
taneous emissic
1.
Light
r a y
m u s t
t r a v e l
f r o m
a
dense
be greater
W r i t e
the
conditions
f o r
t o t a l
in
edium
nser medi
4.
transition ot atoms from excited state to
During the trar
emits energy aneously is known as
spon
und state emit
r a r e r m e d i u m .
than cr
12.
W h a t
is ind
sion?
t a n e o u s e m i s s i o n .
. . induced emision (or) stimulated emis-
2.
The
angle
of
i n c i d e n c e
m u s t
be g r e a t
5.
Write
the
a p p l i c a t i o n s
of
t o t a l
i n t e r n a l
2 ) E n d o s c o p e
internal reflectio
angle.
(Ap.16,18)
the transition of atoms from metastable state to
3) Periscope
gro
round
state,
emits
9 s s t i m u l a t e d e m i s s i o n .
During the transiti
ground
state,
e m i t s energy with the
etastable
its energy with the help of photon is known
1) Fibre Optics
Optical Fibre Caki 13.
Write any
two uses
oflaser
5) Prisms
6.
Write any
two
a d v a n t a g e s
of
Optical Fib
flexible
4 ) B i n o c u l a r s
2) It has high
band
width
and
low energy loss
3) It is not
carry1ng
any
c u r r e n t .
So it is
harmless
1) Easy
handling
due to light
weight and A
ow energy lose
1. Laser is used in eye surgery.
a Tt is used to bore holes in hard substances like
safe
tungsten and diamond.
3 It is used in welding and to cut thick sheets of hard
Define angle
of
m i n i m u m
d e v i a t i o n .
7.
metals
The
minimum angle
through
which the prism de.14.
What is an active remote sen
&What are the properties
(characteristics)
oflaser? (Ap reflected waves is known as active remote sensing.
he prism dev
14, What is an active remote sensing ? (Ap.16)
The system generates and uses its own energy to illumi.
the light rays is called angle of
m i n i m u m deviation.
ate the distant object and the information obtained by the
) Laser is
monochromatic (i) It is coherent (Eg.) Radar, Sonar
9. Write the principle of laseer. 15. What is passive remote sensing ?
Laser works on the principle of quantum theory ofrn
tion. When an atom may undergo transition betweent natural source of energy from
the distant object is known as
(Ap. 16)
The process of obtaining information by the reflected
energy states E and E, it emits a photon of energy passive remote sensing. (Eg.) Photography, radiometer.
Eg- E, = hv.

12. Il-
66 I-67
16.
W h e r e
are
the
reference
d a t a s
u s e d ?
sensed data
used ?
(1)
To
a n a l y s e
and
i n t e r p r e t
r e m o t e l y
s e n .
cted rom
PROBLEMS
r e
the
reference
d a t a s
the refractive index of prism. If the angle of
(3)
To
verify
the
intformation
e x t r a c t e d
sensing data.
C a l c u l a t e
Calc is 59° and angle of minimum deviation is 40
the prism
is 59° and
(2)
To
c a l i b r a t e
a
s e n s o r
( A p . 0 6 )
(Ans:1.544)
af prism is 60° and its angle of minimum
If the
angle of
is 38°42' Caleulate the refractive index.
Part C 2)
The angle of a glass prism is 59, Calculate the angle of
the material is 1.512. Calculate the angle of minimum
total internal reflec
(Ans. Sec314 m i n i m u m
deviation, if the refractive index of the prism
4)
The angle of a prism is 60 and the refractive index of
( A p . 1 7 . O c t . 1 7 )
1)
Explain
the
p h e n o m e n o n
of
tota
(Oct. 17.18)
Explain
the
working of
optical
tibre c a b i
gude
3 ) W r i t e
the
a d v a n t a g e s
(or)
m e r i t s
ofopticalf .
(Ans: 1.525)
fibre cable as a
(Ans. Sec.3.1
is 1.642 (Ans: 48°53).
cab)
(Ans. Sec3.1 deviation. (Ans: 38°13)
4 ) D e r i v e
an
expression
for
r e t r a c t i v e
index ofth.
of the prism
using
angle
of
m i n i m u m
Ap.16)
the mate
(Ans: Sec.3.1
tive
5)
Describe an
exper1ment
to
d e t e r m i n e the ref
dex ofthe prism using
s p e c t r o m e t e r . (Ap.1810
5
Ans: Sec.3.1
6) Explain
population
inversion.
s p o n t a n e o u s emise
stimulated
emission.
(Oct. 17)
(Ans:Sec.3.2.3.3
7Explain the construction
and working of a Ruby
with a neat diagram.
(Ap.16.17. Oct.16,17,18)
(Ans. Sec. 32
(Ans. Sec.32
2.3,3.2.4,
8) Write the uses of Laser.(Ap. 18,19)
Explain the components of remote sensing.
(Ap.18.Oct. 18)
9)
(Ans. Sec33
10) Explain the working of RADAR with block diam
(Ap.16,17.19 Oct. 17) (Ans. Sec33

13. - 69
- 68
UNIT y 4.1ELECTRICAL CIRCUITS
network
containing abattery
ELECT
A n e l e c t r i c a l
CITY i n s t
struments and
d connecting wires is ry,
called an elec electrica
4.1.1. Ohm'slaw:
AL constant temperature
tric circuit
the
strength of the
Introduction :
of the cur
a conductor is
directly
proportional to the
the strength of the current flows
through the
of motion
p o l e n
ntial
difference
between two en
Let I be
The current
electricity
deals with the study oe
l o w i n g t h r o u g h
of electric charges.
When the two ends of a conduos
higher poten.
to
tial to lower potential.
Here the charges means the s
free electrons. The direction of electric current is opne
connected to a battery, the charges
flows from
ns
highe
the flow ot
nd V is the potentis
difference between its ends.
resistance of the conductor and its unit is ohm(
c o n d
Then V aI (or) V=IR where R is a
constant
that of direction of flow of electrons.
n o w n a s ,
Current (
of eled
ctric
second. The
charges that flows through the conductor per second
4 . 1 . 2 .
L a w
of.resistances
()
Resistances in series :
When a
number of resis-
The strength of current is the amount of
Te connected in series then the effective
resistance in
is equal to the sum of the individual resistances
TE three resistances Rj.R2 and Rg are
connected in
series
symbol for current is I and unit is ampere, A.
Charge (Q)
When a current of I ampere
flows through the con.
.
tor for t seconds. Then, quantity ofcharge Q =
It.
The symbol for charge is Q and unit is coulomb, c
then
Effective resistance in series
R,= R+ R2 +R
R R3
Potential difference (or) voltage (V) R,
For the movement of free electrons an external force
necessary. This force is called electro motive force (e.m.
is
G) Resistances in parallel: When a number of resis.
Because of e.m.f. theends of the conductor are at different tancesare connected inparallel, thereceiprocal of the effective
electric potentials. This difference in potential iscalled po
tential difference or voltage. The symbol for potential differ-
resistance in parallel is equal to the sum of the reciprocals of
the individual resistances.
ence is V and the unit is volt. If three resistances R. R2 and R, are connected in
parallel.

14. l 71
4.1.6 Meissner effect
The expulsion of magnetcic flux wh
To
calculate current or
potential erence in
compli-
Kirchoff's I law says about the
junctions and Ind law
I I - 7 0
R
ww-
R conductor in a
magnetic field.
n a material
RR'RR
Ra
M W
comes s u p e r c o
be-
ffs laws
-Rp
4.1.7. Kirchoffa l a
4.1.3.
R e s i s t i v i t y
(or)
Specific
r e s i s t a n c e (p)
cate
c i r c u i t s
Kirchoffs laws are used. The
complicated cir-
crossectic
Consider a
conductor
of length
t and area ofcrose
ys
about the closed networks.
I law:
(Current Law)
The
c u i t
contain
large number of
junctions and closed networks.
A has resistance R.
Thus
R =p.A
The algberic sum ofcu rents meeting at any junction is
Resistivity p
= ",4
zero.
When A= 1m^ and/= 1 m,
then p
=
R
The resistivity is defined as the resistance ofth
having unit length and unit area of
crossection.
the
junction
O. The currents
I,, l and Is are flowing towards
the junction.
The currents I, and
Lare
flowing away trom the
Consider the currents
lh2.lg,'4 and ls are
meetingat
wire
Let r be the radius of the wire, then A =
nr
p-R.n junction.
The algebric sum of cur-
ohm-metre
The resistivity
-wwO
rents flowing towards the junc-
tion is equal to the algebric sum
of currents flowing away from
4.1.4. Conductivity (o)
The reciprocal ofresistivity is called conductivity
ww.
ww
conductivity a =
the junction.
Then +l+Is ht4
4.1.5. Super Conductivity
tlt ls-h-4 =
0
The ability of certain materials to conduct electricitv
with zero resistance at critical temperature is called super
conductivity.
The algebric sum of currents is equal to zero.
The materials which exhibits super conductivityare
called super conductors. (Eg) Hg, Pb

15. -73
-72
resistan. P, Q, Rand S:
F o u r
re
nnected to form
II Law:(VoltageIaw
c l o s e d
n e t v
e
G
is
c o n n e c
et n e c t e d as shown in the
figure. 1, isthe current
et
I,l2,1, and I, are the
currents
vork.
A
battery, key and a
galvandmeter of res
ic sum of
In any elosed netuork ofconductors, the algebrics
equal
the product ofcurrent and resistance of each branch is o through
u g h v a r i o u s
galvanomete; Let
t a m
ugh 1s branches are
indicat in the
s
branches are' sand
lsthe .
Applying
K i r c h o f f ' s I law
AtB,I
+'g
to the algebric sum ofthe e.m.fs in the circuit. fig.
throug
B
w w
RI
(1)
At D,
+ 4
(2)
R ER2 pplying
Kirchoff's II law
ForBCDB,Q-Sl4
-
G1,= 0
The deflection in the galvanometer. That is I, =
0.
L4
(3)
F o r
A B D A
Pl, +
G
-
RI,= 0
www-
R3
(4)
E2
Considera closed circuit ABCDA. The currents I,, I
and I4 are passing in the same direction of ABCDA and I, io
in opposite direction of ABCDA. The e.m.f. E is in the me
direction and E is in opposite direction of ABCDA.
The values of P, Q. R and S are adjusted such that
Put I, =0 in the above four equations
2 and =l
The algebric sum of the product of current and resis.
tance = 1 R, +1,R2 - 1,R, +l4 R4
Pl,
-
RI
= 0
RI
P (5)
The algebric sum of e.m.fs = E, - E2
Ql-Si,= 0
Q Sl
Then 1,R+1,Rg - I_Rg+ 1,R, = E^ - Eg2 (6)
4.1.8 Wheatsones bridge
P RI
Eqn.(5)/Eqn. (6), Ql, SI4
ww
www.
P P-R
This is the condition for balancing the Wheatstone's
bridge. It is used to find the value of unknown resistance.
S
D
Ba
K

16. -75
I - 74
he
charge across each
I n series connection
A capacitor is a device for storing charges tem
It is also known as condensor
*L.9 Capacitors (or)
Condensors
porarily lifferent apacitor is
me
butthepotential difference is
VI
A capacitor consists of two parallel plates sepDe.
a small distance. It allows A.C but blocks D.C. perated hby CHE
4.1.10 Capacitance
Hence
tial difference creates
between them. As the chareoe
When an electric charge is given to a capacitor
charge adde
atial
quantity of charge is directly proport10nal to the no.
nstant known
Let V V2 and V3 be the
potentia' difference across
increases the potential difference also increases,
the
c a p a c i t o
C, C2 and C3. V is the
applied potential.
difference.
V V1t Vg+V3 ... (1)
(i.e) Q a V or Q =
CV, where C 1s a constant 1
Q V V=
VC1
as the capacitance of the conductor.
tio of its
charge
The capacitance ofa capacitor is the ratio ofits 3
Let C. is the equivalent capacitancein series. For the
to its potential. The unit is farad. (F)
V 9
C
otential
V applied, the charge is Q.
C
Capacitance b o
The above values are substituted in equ (1
4.1.11 Farad
-
The capacitance ofa conductor 1s one farad when
coulomb of charge added to it increases the potential by .
volt.
one
one
The effective (equivalent (or) resultant) capacitance in se
ries C, 1s given by
The practical units of capacitance are pF and pF.
1
1uF 10F; 1pF =
10 F
C C1 C2 Ca
4.1.12 Capacitors inseries
4.1.13 Capacitors in parallel
Let three capacitors with capacities C ,
C2 and C
Let three capacitorswith capacitiesC,C and Cgare
onnected in series to a battery of voltage V.
connected in parallel to a battery of voltage V.

17. 1-77
II-
76
n parailel connection the potential difference
etch capacitor is same but the charge is different.
ce acro WORKED EXAMPLES
thin uwire of radius 0.2 mm has .
as a
istance of7
the wire is
hms. Ifthelength.
2m. Caleulate the
C1 resistivity
of the materin
of the wire (Ap. 2003)
G i v e n : r
0.2 mm =
0.2x-
10 m, R=7Q, I=2m
R = 7z3.14x(0.2x10-32
p 2
Calculatethe resistance of a wire of length 1.5
material ofthe wire is 45x10
p
0.4396 x 10- ohm-m
m
and
d i a m e t e r
0.5 mm
The specific
ire or
resistance of
each capaci.
Let Q,,Q, and Q be the charges across each cane ohm-m.
Given: p =45x 10 ohm-mI=1.5 m, d 05 mm
tors C, C, and Cg. Qisthe total charge.
9,+ r
0.25 mm
= 0.25 x 10m
,-C,V = CV: C,V R r
p
. R = p
Ttr
Let C is the equivalent capacitance in parallel, B.
the potential difference V applied. the charge is Q. 1.5x 45x 108
= 3.439 ohm
R
Q=CV
3.14x
(0.25 x 1032
The above values are substituted in equ (1), Calculate the length of the mangunin wire of resis-
3)
tance 20 and diameter 0.4 mm. The specific resist.
ance is 4 x
107 ohm-m
CV C,V CV CV
The effective (equivalent (or) resultant) capacitance in
parallel C, is given by Given: R 2 ; d = 0.4 mm, r 02 mm 02 10
Cp C1 C2+Ca p 4x 107 ohm-m.
4.1.14 Application of Capacitors R ar
p
R r
Capacitors are used in power storage, power condition
ing. tuned circuits, electric motor, fans, decoupling, filter
carcuts, signal processing etc
2x3.14x (0.2 10 -0.628 m
4x 107

18. -79
Find the resultant
o f
c a p a c i t a
II- 78
capacitan
wire
l of a
4) Calculate the
resist ith a diameter of 0.2
uE , 30 uF wh
pacitance 10 u, 20 u
of hree ecapas
acitors
the resistivity ofa material
of 0.32m
they are
Given:C1
=
10uF; C2 20 F, C F
they are
ected in
series, the
resultant
whose resistance is 1.52 with a diameter of o connected (i) in series and (ii)
30
in
parallel.
and length 80cm. (Ap.17,18)
Given i ) W h e n
R 1.5Q apacitance C, is given by
r= -0.32
2
r = = 0.16 cm =0.16 x10 m
6+3+2 11
60
8Ocm =80 x 10 m
60
RA R Tr
C
60 = 5.45 F
11
1.5x 3.14 x(0.16 x10)
p
i)
When they are connecte in parallel, the resultant
80x 10-2
capacitance , 1s given by
P 15.07x 10 sm C. = C+C2+ C3 10 + 20 + 30 = 60
F
.5m
5) Calculate the resistance ofa wire of length 1.5
and diameier 0.8mm (resistivity p = 45 x I0m
5)
adeulate the effective capacitanee of three Ca
4ar af capacitance 1 F, 2uF and 4uF respec-
when they are connected in series and
Given
parallel connection inacircuit. (Ap.16, Oct. 16)
l= 1.5m
r = =
=0.4 mm =
0.4 Given
2 2
C
= 1p F
P 45x 10 Qm
R = ?
= 2uF
C
RA
C3 4F
P
C = ?
R =
P=Pl
CP
45x10x1.5 Series connection
R =
3.14x
(0.4 x 102
R =
1.343 ohm

19. I-80 -81
lentical capacitors each of ca
"hree i d e
Thrnected in the form of a
triangle. Calculate
C 9
a r e c o n n e c
the effectve capacitance
apacitance C
etween two corners.
C itable triangle. Any two
capacitors are
con
1-
1+2+3 =Z
4
C
Draw a suitabi
neca
nected
in
s e r i e s
and t third is connected in
parallel to the
4
Cs=uF=
0.57uP
a b o v e i n s e r i e s .
Cs
Parallel connection
Cp =
C+ C2+ C
Cp=1+2 +3
Cp
=
1+2+4 B
Cp 7 uF
Effective capacitance if any two in seri
COn.
8) Shouw that when three equal capacitors
ine times the
nected in paralle,
the system
has nine tio
capacity of that obtained
when they are con 4
in series.
C
C, 2
Let C Cy CC ffetive capacitance of C, 1n parallel with the third capacitor C
C= C +C +C
= C+C+C 3C
(1)
C C, + C = C =3C
2
3C 1.5 C
C 2
C 10) The resultant capacitance of two capacitors con-
nected in series is 0.95 juF. The resultant will
change to 0.74 uF when a third capacitor is con-
nected in series to the above. Find the value of the
third capacitor.
ButC
3
C
C 3x 3 C 9C

20. I1-82
-83
Let C, and C be the capacitance of the firat
pacitors and C, be the capacitance of thethird
Then
twg
capacitoy 2)
res1stance
ofth
of flow ofcurrent ()
aistance ot the conductor
3)
t i m e of
fow
Ha 'Rt
and C
0.95 Ca 0.74
C
(ie.)
0.74 H VIt R
Hent
d e v e l o p e d
H =
0.95 0.74
0.95 0.74 2 . 3 . D e t e r m i
a.2 lHquid using Joule's calorlmeter.
terminatlon of
specifle heat
capacity of a
074 0.96
0.74
3.35
uF
ealorimeter consiBla o1 a
henting coil, copper
42 EFFECTSOFCURRENT vessel with stirrer
placed inside a
cotton or wool
4.2.1. Heating Effect of Eleetric Current
packed wooden box.
Consider a current I passes thwugh a condue
resistance Rfor the time t. The potential difference bet
the two ends is V Amount of work done to take the ch
from theend Ato Bis given by
Battery,
ammeter, calorimeter, rheostat, are con-
h e c t
in series and voltmeter 18
connected parallel
to the coil.
harge Ba K Rh
AR (VA VR)
(e) W V
But, the Ohm's law is V = IR and eharge Q = It
Thermometer Stirror
Amount of work done = IR 1t IRt
This amount of work done is liberated as heat eneru
Swhen a current flows through a conductor heat
energy is
produced
Water
Joule's
Coil
4.2.2 Joule's law of heating
The heat developed (H) n a conductor by the tlow of
the eurrent is
directly proportional to
Mass of empty calorimeter with stirrer
M,is deter
mined. The given iquid is taken upto two thirds of
1square of the current () the calorimeter and its mass M, is determined

21. -84
. The
c a l o r i m e t e risplaced
inside the.
the key is
ciosed.
Adjust
the rheost
5°C rise
woodenbe
for curr
85
stat
When
an
electric c
composed into, ions is cal
Tent
prsaed
through an e
etrilkyte,
electrokysa.
and
p o t e n t i a l
d i f f e r n c e
V.
empe
w i l l b e d e c o m p o s e d
The metallic plates used to pa
The time offlow ofcurrent
t for 5°C
led electrodes. rrent through the
of the liquir
imeter
ture is found.
Let S is the
specific
heat
S, is the specific
hest capacity of the
e l e c t r o l y t e
a r e
calle electrode
Heat developed
=heat gained by calorimter
Heatdeveloped VIt
Heat gained by
c a l o r i m e t e r
and liquid
=
M,5, T
-
T) +
(M2
-
M,)S(T2 -T,)
The electrode connected to
positive o the
battery ia
and liq
c a l l e d a n o d e .
The vessel containing the
electrolyte and
electrodes is
alled
v o l t a m e t e r .
If the
electrolyte is copper sulphate solu
Theprocess of electrolysis is used in
electroplating electro
typing. preparationofmetals:
and purificationo metals
The
electrode connected to negative of the
battery
c a l l e d c a t h o d e .
tion.
it 1s
c o p p e r
voltameter.
Heat deveioped
= Heat gained
4.2.6
Faraday's
laws of electrolyaia
Tlaw: The mass of an element liberated during el
VIt =
M,S, (T,
-
T)- (M
-
M,)S(T, -T
The specific heat capacity of the liquid
M, S Jk'K vsis is directly proportional to the strength of the curren
VIt
M-M,) (T,-
T,) (M,
-
M,) and the time of flow of current.
ma It
4.2.4 Chemical Effect of Electric Current
Zlt where Z is called
electrochemical equivalent of
certain
When an electric current s passed through e an element.
ution
liquids like copper sulphate solution, silver nitrate solte: I law: f the same current passes through different eier
trolytes for the same time, the masses of the different elemeni
liberated are directiy proportional to their equivalent ueighta
ve
etc. Chemical action takes place. It 1s decomposed into.
1ons and -ve ons.
If m, m2 and mz are the masses of the elements
liberated and E. E2 and Eg are their equivalent weights
In case of copper sulphate solution
CuSo Cu+So
respectively.
4.2.5 Electrolysis
Then ma E; m2 a
Ez:m, a
E
Laquids which conducts electricity are called electrolytes
(ex) Copper suiphate solution, silver nitrate solution ete.
-

22. R e m o v e the cathode, cleaned with
Replace the cathode and
-87
4.2.7 Eleetro
r o - c h e m i e e l
equivalent
(e.c.e) ofan
II-86
eleme Re dried and its mass m is determi
ery pape,
determined.
adjustthe rheostat for
w a s h e d
According to Farnday's 1 iaw, m a lt
m
=
Zlt, Here Z is called
electro
chemical equival
of an element
equivalen cur
rent I.
.
Current
is passed for 30 minutes (t) and the circuit
the cathode, washed in a
m
7.1
ned. Remove
1s
a gentle
ied and its mass m in
deter
s t r e a m
of water, dr
m
When I= 1 ampere
and t 1 second then Z =
m i n e d .
is the
The electro chemical equivalent of an element is
the
mass liberated when ofone ampere
current flows through
Mass of copper deposited m = m2 - m
electrolyte for one second.
e.c.e.copper Z kgC
-I
Unit kg/coulomb. (i.e) kgC"
4.2.9
Applications
of eating effect of electrie
4.2.8 Experiment to determine electro-chemical egm c u r r e n t
valent of copper
Heating effect or eleceric current is used in electrio &
lament bulb, electric heaters, electric ovens,
Rh
Ba electric iron, filam
electric
kettle, soldering, electric furnace ete
WORKED EXAMPLESs
2 3
1,3-Anode
2-
Cathode 1) A current of one ampere passing througha copper
voltameter for one hour, liberates 1.2 gm of copper.
Calculate the electro chemical equivalent of cop-
(Ap. 13)
CuSOA
Solution
per.
Given I=1 amp; t= 1 hour =3600s:
m= 1.2 gm= 1.2 x 10 kg
Copper voltameter consists of a glass vessel contain.
ng copper sulphate solution and three copper
plates
1.2x103
Z
It 1x3600
Z =
Battery, ammeter, voltameter and reheostat are con
nected in series.
= 3.33 x10 kg C

23. Il-86
4.2.7 Electro-ch
-chemical
equivalent
(e.c.e) ofa
l -87
an eler
ment
R e p l a c e
the cathode and adjust the rheostat for cur-
Current
is passed for 30
minutes (t) and the circuit
R e m o v e
he cathode, cleaned with ernery paper,
washed,
dried and its mass
m is
determined.
According to Faraday's I law, m a lt
uivalent
m =ZIt. Here Ziscalled
electro
chemical equi.
of an element
rent I.
Z 1t ened. Remove i
the cathode, washed in a
gentle
is open
m
When I= 1 ampere
and t= 1 second then 2 s t r e a m
of water, dried and its mass mo in
deter
mined.
is the
mass liberated when ofone ampere
current flows thro e
electrolyte for one second.
The electro chemical equivalent of an element
hrough the
Mass ofcopper deposited m =
m -
m
e.c.e.copper Z =kgC-1
Unit kg/coulomb.(i.e)kgC
4.2.8 Experiment to determine
electro-chemical
valent of copper
equi 4.2.9
A p p l i c a t i o n s
of heating effect of electric
c u r r e n t
Rh
Heating effect of electric current is used in electric fuse.
lament bulb, electric heaters, electric ovens,
Ba K
e l e c
electric
kettle, dering, electric furnace etc.
1 2 3
WORKED EXAMPLES
1,3 Anode
2-Cathode 1) A current of one ampere passing through a copper
oltameter for one ho0ur, liberates 1.2 gm of copper.
Calculate the electro chemical equivalent of cop-
CuSO4
Solution
per. (Ap. 13)
Given I=1 amp; t= 1 hour =3600s;
m = 1.2 gm = 1.2 x 10 kg
Copper voltameter consists ofa glass vessel contain,
ing copper sulphate solution and three copper
plates. Z = =1.2x10-3
1x3600
Battery, ammeter, voltameter and reheostat are con
nected in series.
= 3.33x10 kg C

24. -89
II-88
2 C a l c u l a t e
the
amount of
current
to be
e.c.e of coppe
passed Given
through
a
copper
v o l t a m e t e r
60 as to
d e p o s i s e d
gm of
c o p p e r
in 2
h o u r s
(e.c.e of
as to dep0stt 3.88
I = 1A
t = 30 nutes =
30 x
60 s=
1800 s
Z 3.33 x
10-7kgC-1
3.33 x 10 kg C"')
m = ?
3 . 8 8 gm =3.88 x 10 kg
Given m
It
t = 2 hours
= 2 x 60 x 60
= 7200 s
m = ZIt
Z= 3.33 x 10 kg C
m m = 3.33 x 10 x 1x 1800
m= 5.99x 10 kg
3.88x10 1.618 A
3.33 x 10'x 7200
4.3 MEASURING INSTRUMENTS
3) When a current 2Apasses through an electrol
bf
double cynamide of gold and potassium, a massaf
ken
4 x
10 kg gold is deposited, what is the time taken
olyte
Measuring instruments are based on the magnetic ef.
for this deposition.
0.68 x10 kgC"
e.c.e. of gold is
(Oct. 16)
fact of electric current. Moving coll galvanometer, ammeter
and voltmeter are some of the measuring instruments. A
oalyanometer is used to detect the direction of current in a
circuit.
Given: m =4x 10d kg, Z=0.68 x
107 kg C"
4.3.1. Force on a current carrying conductor placed in
I 2A
a uniform magnetic fleld.
m
Z tZ1 Consider a conductor of length Iis placed in a uniform
4x
10
0.68 x 10x 2
magnetic field of magnetic induction B.
When a current I flows through the con-
ductor, it experiences a mechanical
t 2941 s (or) 49 minutes
=
B
force. This force is due to interaction of
4) Calculate the mass of copper deposited when a cur
rent of 1A flows for 30 minutes in a copper volta
meter. Electro chemical equivalent of copper 3.33 x
10 kgC
the magnetic field due to current and
uniform magnetic field.
This force (F) on the conductor is
directly proportional to

25. -91
l-90
Let 1be the
current through the
magnetic induction B.
hrough the
coil Consider one turn of the coil
1)the magnetic
induction ofmagnetic
field B'
) the strength of the current I
ii) the length / of the conductor
Iv)sin (eis the angle
between the conductorand
direction of magnetic field)
the
Then Fa Bllsin 0
F B1/sin BIl
B
Case ) Ifthe conductor is placed at right angles
the direction of magnetic field.
to
The forces on sides AD and BC are zero.
Force acting on the side AB = BIL
(1.e.) =
90° sin 90° =1, Then F = BI
Case (i) If the conductor is placed parallel to the diror
tion of magnetic field, (i.e.) 0 =0°; sin 0°=0, Then F 0
Force acting on the side CD = Bu
rec-
These two equal and opposile forces constitule a counle
The direction of motion of the conductor is given by
Flemmings left hand rule.
Moment (or) Torque
of the couple =
One of the torce x
Perpendicular distance
4.3.2. Fleming's left hand rule: BIl x b
=BIA where A =
lx b, area of crossection of thecoil
Stretch the fore finger, the mid
dde finger and the thumb of left hand
Force
If n is the number of turns of the coil, then
in three mutually perpendicular direc-
Torque on the rectangular coil = nBIA
magnetic
field
tions. If the fore finger represents the
arection of magnetic field, the middle
finger represents the direction of cur-
rent, then the thumb represents the
direction of motion of the conductor.
4.3.4 Moving coil galvanometer
Current
Description
A rectangular coil of n turns is suspended between
the poles of a horse-shoe magnet by a phosphor
4.3.3 Torque on a rectangular eoil carrying cur
rent placed in a uniform magnetic field.
bronze wire.
A small mirror M and a spring K is attached to the
Consider a
rectangular coil ABCD of length l breadth b
and number of turns n is placed in a uniform magnetic field
phospor bronze wire. A soft iron piece is placedin
side the coil.