Tyb sc semester v manual

R. D. National College, Dept. of Physics
T.Y.B.Sc.Physics Semester V Lab Manual, 2013 - 2014 Page 1
R.D.NATIONAL COLLEGE OF COMMERCE &
ARTS & W. A. SCIENCE COLLEGE
DEPARTMENT OF PHYSICS
T. Y. B.Sc. PRACTICAL LABORATORY MANUAL
SEMESTER – V
2013 – 14

Syllabus for Semester V
Program: B.Sc.
Course: Physics
(Credit Based Semester and Grading System with
effect from the academic year 2013–2014)
Practicals:There will not be any internal examination for practical. The External
examination per practical course will be conducted as per the following scheme,
Sr. No. Particulars of External Practical Examination Marks%
1. Laboratory Work 80
2. Journal 10
3. Viva 10
TOTAL 100
A candidate will be allowed to appear for the practical examination only if the candidate
submits a certified journal of TYBSc Physics or a certificate from the Head of the
Department to the effect that the candidate has completed the practical course of TYBSc
Physics as per the minimum requirements.
The T. Y. B. Sc. Syllabus integrates the regular practical work with a series of
demonstration and skill experiments. During the teaching and examination of Physics
laboratory work, simple modifications of experimental parameters may be attempted.
Attention should be given to basic skills of experimentation which include:
i) Understanding relevant concepts.
ii) Planning of the experiments.
iii) Layout and adjustments of the equipments.
iv)Recording of observations and plotting of graphs.
v) Calculation of results and estimation of possible errors in the observation of results.
i) Regular Physics Experiments: A minimum of 8 experiments from each of the course
are to be performed and reported in the journal.
ii) Skill Experiments: All the skills are compulsory and must be reported in the journal.

Skills will be tested during the examination through viva or practicals
The certified journal must contain a minimum of 16 regular experiments (8 from each
group), with all Skills in semester V. A separate index and certificate in journal is must
for each semester course.
There will be two turns of three hours each for the examination of practical courses.
(Practical Course – USPHP05)
1. Determination of “g” by Kater’s pendulum.
2. Flat spiral spring (Y)
3. Stefan’s constant σ
4. Koenig’s method
5. R.P. of grating
6. Goniometer
7. R.I of liquid using laser
8. Rydberg’s constant
9. Edser’s A pattern
10. Diameter of lycopodium powder
11. Determination of e/m
(Practical Course – USPHP06)
1. Mutual inductance by BG.
2. Hysteresis by magnetometer
3. Maxwell’s bridge
4. Band gap of energy.
5. Diode as temperature sensor.
6. Log amplifier using OPAMP
7. High pass (first order active filter)
8. Low pass (first order active filter)

9. Wien bridge oscillator
10. Hall effect
11. LM-317 as voltage regulator
12. LM 317 as current regulator
Skills:
1. Estimation of errors.
2. Soldering advanced circuit.
3. Bread board circuit using IC’s.
4. Optical Leveling of Spectrometer.
5. Laser beam profile.
6. Use of electronic balance: radius of small ball bearing.
7. Dual trace CRO: Phase shift measurement.
8. BG: C1 /C2 by comparing θ1 / θ2.
References:
1. Advanced course in Practical Physics: D. Chattopadhya, PC. Rakshit & B. Saha (8th
Edition) Book & Allied Pvt. Ltd.
2. BSc Practical Physics: Harnam Singh. S. Chand & Co. Ltd. – 2001.
3. A Text book of Practical Physics: Samir Kumar Ghosh New Central Book Agency
(4rd edition).
4. B Sc. Practical Physics: C. L. Arora (1st Edition) – 2001 S. Chand & Co. Ltd.
5. Practical Physics: C. L. Squires – (3rd Edition)Cambridge University Press.
6. University Practical Physics : D C Tayal. Himalaya Publication.
7. Advanced Practical Physics : Worsnop & Flint.

CONTENTS
Expt.
No.
Name of Experiment Page
no.
Signature
Practical Course – USPHP05
1. Determinationof “g” by Kater’s pendulum.
2. Flat spiral spring (Y)
3. Koenig’s method
4. R.P. of grating
5. Goniometer
8. Diameter of lycopodiumpowder
9. Determinationof e/m
1. Mutual inductance by BG.
3. Band gap of energy
4. Diode as temperature sensor

CONTENTS
Expt.
No.
Name of Experiment Page
no.
Signature
5. Log amplifier using OPAMP
6. Highpass (first order active filter)
7. Low pass (first order active filter)
8. Wienbridge oscillator
9. Hall effect
10. LM-317 as voltage regulator
Skills
1. Estimationof errors
2. Soldering advancedcircuit
3. Breadboard circuit using IC’s
4. Optical Leveling of Spectrometer
5. Laser beam profile
6. Use of electronic balance:radius of small ball
bearing
7. Dual trace CRO:Phase shift measurement

8. BG: C1 /C2 by comparing θ1 / θ2
Practical Course –USPHP05
Mechanics and Properties of Matter,
Heat and Optics

1.Kater’s Pendulum : determination of g
Aim: To determine the intensity of gravitational field (g) & the relative error in “g”
using Kater’s Pendulum.
Apparatus: Kater’s Pendulum, telescope, stop-watch, knife-edge, meter scale, etc.
Formulae:
1.
4π2
g
=(
1
2
) [
T1
2+T2
2
𝑙1+𝑙2
+
T1
2−T2
2
𝑙1−𝑙2
] => g =
8π2
[
T1
2+T2
2
𝑙1+𝑙2
+
T1
2−T2
2
𝑙1−𝑙2
]
Where T1& T2 are the periods of oscillations about knife edges K1& K2
respectively, 𝑙1&𝑙2 are the distances of the corresponding knife edges from the
center of gravity of the pendulum.
2. g = 4π2 Le
Te
2
where 𝐿𝑒is the equivalent length of the simple pendulum which is the distance
between the center of oscillations and the center of pendulum.
3. Relative error in g is
dg
g
= (
dt1
t1
+
dt2
t2
) + [
𝑑𝑙
𝑙
]when|
T1
2−T2
2
𝑙1−𝑙2
|<<
T1
2+T2
2
𝑙
Diagram:

Procedure:
1. Arrange the metal masses B& W and the wooden masses B’& W’ on either side of
the center of gravity and set the two knife-edges K1& K2 about 80 cm apart.
2. Suspend the pendulum from a rigid support on the knife-edge K1. Attach a pin at
the lower end of the bar, focus the telescope on the pin Oscillate the pendulum,
keeping the amplitude very small. Find time for 10 oscillations & calculate the
period of oscillation T1. Similarly find the period T2 about the other knife edge
K2.
3. If the difference between T1& T2 is large then shift the mass W towards/
away from K2 through a small distance. Again find the periods T1 & T2 about
the knife edges. If you find that the difference between T1& T2 increases then
shift W in the opposite direction and find the periods T1& T2 once again.
Continuing in this manner adjust W so that the periods T1& T2 becomes nearly
equal. (The two periods may differ by 0.02 sec but not more).
4. When you find that the periods T1& T2 are nearest possible, find time for 100
oscillations about the knife K1& K2& hence calculate T1& T2. Take 3 readings for
knife edge. Measure the distance between K1 & K2& call it ‘𝑙’.
5. Find the position of C.G. of the pendulum by balancing it horizontally on the
given wooden knife edge.
6. Measure distance 𝑙1&𝑙2 of the knife edges K1& K2 from the C.G.
7. Calculate the value of ‘g’ using formula1.
8. Now, without disturbing any other arrangement shift the knife edge K1 slightly
(say through 2cm).Repeat steps (4) to (7).

9. Plot a graph of T against 𝑙. Join the points corresponding to T1 for (l= 80cm) & T1
for (𝑙= 80±2 cm) for knife edge K1. Similarly, join points corresponding to T2 for
(𝑙= 80cm) & T2 for (𝑙 = 80±2 cm) for knife edge K2. Obtain the coordinates
(𝐿 𝑒, 𝑇𝑒) of the point of intersection of these two lines. 𝑇𝑒 is the common time
period about two knife edges &𝐿 𝑒 is the length of the equivalent simple
pendulum.
10. Calculate (g) using the formula: g=4π2 𝐿 𝑒
𝑇𝑒
2
Observations:
Preliminary adjustments for equal periods:
Adjustments Time for 20 oscillation Period Inference
T1 ~ T2 secAbout K1
t1 sec
About K2
t2 sec
T1 =
t1/20
sec
T2 =
t2/20 sec
Error calculation:
𝐝𝑙 = Least count of scale =______cm
dt1 =
max( 𝑡1
′ ,𝑡1
′′ ,𝑡1
′′′)−min(𝑡1
′,𝑡1
′′ ,𝑡1
′′′)
√3
, dt2=
max( 𝑡2
′,𝑡2
′′,𝑡2
′′′)−min(𝑡2
′ ,𝑡2
′′,𝑡2
′′′)
√3
𝑙
cm
𝑙1
Cm
𝑙2
cm
About k1 About k2
t1' t1'
'
t1''' Mean
t1
sec
dt1
sec
𝑇1 =
𝑡1
100
sec
t2' t2''’
t2''' Mean
t2sec
dt2
sec
𝑇2 =
𝑡2
100
sec
𝑑𝑔
𝑔

Calculations:g =
8𝜋2
[
𝑇1
2+𝑇2
2
𝑙1+𝑙2
+
𝑇1
2−𝑇2
2
𝑙1−𝑙2
]
For 𝒍=80 cm
T1
2=__________sec2; T2
2= _________sec2
𝑙1= __________cm ; 𝑙2=_________cm
T1
2+T2
2=_______________sec2; T1
2-T2
2= _________sec2
𝑇1
2+𝑇2
2
𝑙1+𝑙2
= _________ sec2/ cm
𝑇1
2−𝑇2
2
𝑙1−𝑙2
=___________sec2/cm
∴ 𝑔=__________cm/sec2=_________N/kg
For 𝒍= (80±2) cm
T1
2=__________sec 2 ; T2
2=_________sec2
l1= __________cm ; l2=_________cm
T1
2+T2
2=_______________sec2; T1
2-T2
2= _________sec2
𝑇1
2+𝑇2
2
𝑙1+𝑙2
= _________sec2/ cm
𝑇1
2−𝑇2
2
𝑙1−𝑙2
=___________sec2/cm
∴ 𝑔=__________cm/sec2=_________N/kg
g=4𝛑 𝟐 𝑳 𝒆
𝑻 𝒆
𝟐
from the graph, Le=_______cm; Te=______sec; Te
2=________sec2
∴ 𝑔=__________cm/sec2=_________N/kg
for 𝑙= 80cm,dg =
𝑑𝑔
𝑔
× 𝑔(𝑎𝑡 𝑙 = 80𝑐𝑚)=__________
for 𝑙=(80±2) cm, dg =
𝑑𝑔
𝑔
× 𝑔(𝑎𝑡 𝑙 = 80 ± 2𝑐𝑚)=__________

Result:
1. Intensity of the gravitational field (by Bessel’s formula )for 𝑙= 80cm,
g+dg=______________N/Kg
2. Intensity of gravitational field (by Bessel’s formula )for 𝑙=(80±2)cm,
g+dg=______________N/Kg
3. Intensity of gravitational field (from graph)
g=_____________N/Kg

2. Flat spiral spring: (Ү)
Aim:
To determine Young’s modulus (Y) of the material of the flat spiral spring.
Apparatus:
Flat spiral spring, hanger with slotted weight, cylindrical bar with two movable identical
disc, stop watch, telescope, vernier calipers, micrometer screw gauge, etc
Formulae:
1. Y=
32π2NIR
r
4
T2
2
Where I = moment of inertia of the system; 𝑇2 =period of oscillation in horizontal plane.
2. I = I0 + 2M′
x2
= M (
L2
12
+
r′2
4
) + +2M′
x2
Where 𝑀′
= mass of each disc; M= mass of bar; L= length of bar, 𝑟′
= radius of bar.
3. Error in Y:
𝑑𝑌
𝑌
=
𝑑𝑁
𝑁
+
𝑑𝑅
𝑅
+
4𝑑𝑟̅
𝑟̅
+
𝑑( 𝑠𝑙𝑜𝑝𝑒)
𝑠𝑙𝑜𝑝𝑒
4. Standard error in r: 𝑑𝑟 = √
∑( 𝑟 𝑖−𝑟̅)2
𝑛−1
Procedure:
1. Count the total number of turns of the spring.
2. Weigh the spring and find its mass “m”.
3. Find inner diameter (D1) and the outer diameter of the screw (D2) using vernier
calipers, hence find mean radius𝑅.
4. Using a micrometer screw find the diameter of the wire of the spring at ten
different places, hence find the mean radius𝑟.
5. Clamp the spring at its upper end in a stand and suspend it vertically.
Oscillations in a horizontal direction:
6. Take a long cylindrical bar having a small radius. Attach it to the lower end of the
spring. Mount the two identical, movable disc on the bar keeping one disc at each
side. Distance (x) of each disc from axis of rotation should be same.
7. Fix a pin vertically at one end of the bar. Focus the vertical cross wire coinciding
with the pin.

8. Give a small angular displacement to the bar. Find the time for 10 oscillation and
hence the period of torsional oscillation (T)
9. Change the distance (x) of the disc from the center of the mass and find T again
take at least 5 readings.
10. Plot a graph of T2 against x2. Calculate slope. Choose end point coordinates of
slope that are far apart, do not select plotted points for slope calculation.
Hence calculate Y.
Observations:
Total number of turns in the spring =N= ………..
Mass of the spring (m) =………….gm
L.C. of the vernier calipers =………..cm
Zero error =……….cm
Sr.no Inner
diameter
D1 cm
Outer
diameter
D2 cm
Radius=
R=
𝐷1 +𝐷2
4
Cm
R1- 𝑅
Cm
(R1- 𝑅)2
cm2
∑(𝑅1 − 𝑅)2
𝑐𝑚2 𝑑𝑅 = √
∑(𝑅−𝑅̅)2
𝑛−1
cm
1
2
3
4
5
6
7
8
9
10
Mean 𝑅=

Diameter of the wire of the spring (d):
L.C. of the micrometer screw = ………..cm, Zero error =……….cm
Sr.no d cm r=d/2
cm
𝑟𝑖- 𝑟
Cm
( 𝑟𝑖- 𝑟)2
𝑐𝑚2
∑(𝑟𝑖 − 𝑟̅)2
𝑖
𝑐𝑚2
d 𝑟 =√
∑ (𝑟𝑖−𝑟̅)2
𝑖
𝑛−1
cm
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
Mean 𝑟̅ =
Reading of oscillation in horizontal plane:
Mass of each disc =M=………….gm
Obs
No
Distance of
each disc
from
axis’ 𝑥’cm
Time for 10 oscillations Period
T2=t/10
T2
2
sec2
𝑥2
cm2
t1
sec
t2
sec
Mean t
sec
1
2
3
4
5
6

Graph:
Calculations:
1. Y=
32π2NIR
r
4
T2
2
Since 𝐼 = 𝐼0 + 2𝑀′
𝑥2
= 𝑀 (
𝐿2
12
+
𝑟′2
4
) + +2𝑀′
𝑥2
𝐼1 = 𝑀 (
𝐿2
12
+
𝑟′2
4
)+ 2𝑀′
𝑥1
2
and 𝐼2 = 𝑀 (
𝐿2
12
+
𝑟′2
4
) + 2𝑀′
𝑥2
2
𝐼 = 𝐼2 − 𝐼1 = 2𝑀′( 𝑥2
2
− 𝑥1
2)
Y=
32𝜋2 𝑁𝑅
𝑟
4 ×
𝐼
𝑇2
2 =
32𝜋2 𝑁𝑅
𝑟
4 ×
2𝑀′( 𝑥2
2−𝑥1
2)
(𝑇2
2−𝑇1
2)
,
Y =
32𝜋2 𝑁𝑅
𝑟
4 × 2𝑀′
× (𝑠𝑙𝑜𝑝𝑒𝑜𝑓𝑇2
𝑣𝑒𝑟𝑠𝑢𝑠𝑥2
)-=………….dyne/cm2………….N/m2
2. Error in N:
dN = smallest number of turns = ………..; N = …………..;
𝑑𝑁
𝑁
= ……………..
.

3. Error in 𝑅 :
d𝑅̅= L.C. of vernier = …………. cm, 𝑅̅= ……….. cm,
𝑑𝑅
𝑅̅
=……………
4. Error in 𝑟 :
d𝑟= L.C. of screw gauge = ………..cm, 𝑟= ……..cm,
𝑑𝑟
𝑟̅
= …………
5. Maximum possible error in Y:
From the plot of T2 versus x2
𝑑( 𝑠𝑙𝑜𝑝𝑒)
=
𝑑( 𝑇)2
∆𝑇2
+
𝑑( 𝑥)2
∆𝑥2
𝒅( 𝑻) 𝟐
: least count of T2
2 axis = ………..sec 2
d( 𝑥)2
: least count of x2 axis = …………cm2
𝑑𝑌
𝑌
=
𝑑𝑁
𝑁
+
𝑑𝑅
𝑅
+
4𝑑𝑟
𝑟
+
𝑑(𝑠𝑜𝑙𝑝𝑒)
=…………..
𝑑𝑌 =
𝑑𝑌
𝑌
× 𝑌 =…………..dyne/cm2
Results:
1. Young’s modulus of the material of the wire =𝑌 ± 𝑌 =………….±…………..N/m2

3. Y by Koenig’s method.
Aim:
To determine Young’s modulus of the material of a beam by Koenig’s method.
Apparatus:
Rectangular metal beam scale, slotted weights, telescope, two small plane mirrors, two
knife edges fixed on rigid support, lamp, vernier calipers, micrometer screw gauge,
stirrup having a hook etc.
Formulae:
Young’s Modulus of the beam:
Y =
3𝐿2(4𝐷+2𝑎)
4𝑏𝑑3
𝑤
𝑥
=
3𝑔𝐿2(4𝐷+2𝑎)
4𝑏𝑑3
𝑀
𝑥
M = mass attached to hanger,
g = acceleration due to gravity =980m/sec2
L = Distance between two knife edges; b = mean breadth of beam;
d = mean depth of the beam; x = depression, D= distance between the scale &
mirror opposite to it,
a= distance between the two mirrors.
Maximum possible error in Y:
𝑑𝑌
𝑌
=
2𝑑𝐿
𝐿
+
𝑑𝑏
𝑏
+
3𝑑′
𝑑
𝑑
+
𝑑( 𝑀 𝑥⁄ )
𝑀 𝑥⁄
𝑑𝑌
𝑌
=
2𝑑𝐿
𝐿
+
𝑑𝑏
𝑏
+
3𝑑(𝑑)
𝑑
+
𝑑(𝑠𝑙𝑜𝑝𝑒)

Diagram:
Procedure:
1. Support the beam symmetrically on the two knife edges.
2. Make chalk marks on the beam so that they coincide with the knife edges.
Measure the distance between them. This is the length ‘L’ of the beam under
consideration.
3. Find the midpoint of the length ‘L’. Mount the stirrup on the beam at this
midpoint.
4. Fix the two plane mirrors M1& M2 rigidly to the ends of the beam, equidistant
beyond the two knife edges (at 5cm) facing each other. Mirrors should be almost
normal to the beam.
5. Arrange the meter scale S vertically, exactly behind mirror M1. Illuminate the
scale with light from the lamp. Keep the telescope behind the mirror M2& direct it
towards the mirror M1.
6. Look into the mirror M1& from the side of the telescope with direct eye. Adjust
the orientation of the mirror M1& get the image of mirror M2 in M1. Then adjust
the orientation of M2 (& if required that of M1) so that within the image of M2,
you can see the image of S, looking into M1.
7. Direct the telescope towards the final image of the scale S in the mirror M1, &
focus the telescope on the image.
8. Take the reading x0 of the division of the scale coinciding with the horizontal
cross wire of the telescope.
9. Suspend the hanger on the stirrup. Wait for a half a minute so that the depression
of the beam is completed. Take the reading x1 of the new division coinciding with
the horizontal cross wire. Find the difference x= x1 ~ x0 for mass M (of hanger).

10. Repeat steps (9) & (10) for all the given weights. These are the readings while
loading.
11. Take readings while unloading also.
12. Measure the distance (D) between the scale S & mirror M2 opposite to it.
13. Measure the distance (a) between the two mirrors M1 & M2.
14. Using vernier calipers, measure the breadth (b) of the beam. Take 5 readings.
15. Using micrometer screw, measure the depth (d) of the beam. Take 10 readings.
16. Plot the Graph M v/s x.
Observations:
1. Breadth of the wire (b):
Least count of the vernier calipers = ______________________cm.
Zero Error: _______________cm.
Sr. no. b
cm
1
2
3
4
5
Mean b = ͞b = __________________cm.
2. Depth of the beam (d):
Least count of the micrometer screw = _________cm. Zero Error: ________cm.
Sr. no. d
cm
1
2
3
4
5
6
7
Mean d = ͞d = __________________cm.
3. Distance between the two knife edges = L =___________cm.
4. Distance between the two mirrors = a = ____________cm.
5. Distance between the scale & the mirror opposite to it = D ____________cm

6. 2D + a = _________cm.
Obs.
No.
Mass
Suspended
M gm.
Reading the scale coinciding with the horizontal
cross wire of the telescope while
Shift in the scale
reading 𝑥 cm.
Loading
cm.
Unloading
Cm
Mean
cm
1 0 x0= 0
2 x1= x1 ~ x0 =
3 x2= x2 ~ x0 =
4 x3= x3 ~ x0 =
5 x4= x4 ~ x0 =
6 x5= x5 ~ x0 =
7 x6= x6 ~ x0=
Calculations:
1. From the plot M v/s x,
∆M = ___________grams; ∆x = __________cm;
. . Slope =
Δ𝑀
Δ𝑥
= ___________gram/cm.
Young’s Modulus Y = —
3𝑔𝐿2(4𝐷+2𝑎)
4𝑏𝑑3
𝑀
𝑥
=
3𝑔𝐿2(4𝐷+2𝑎)
4𝑏𝑑3 𝑋 (Slope)
= ____________________dyne/cm2
2. Maximum possible error in Y:
𝑑𝑌
𝑌
=
2𝑑𝐿
𝐿
+
𝑑𝑏
𝑏
+
3𝑑′ 𝑑
𝑑
+
𝑑( 𝑀 𝑥⁄ )
𝑀 𝑥⁄
𝑑𝑌
𝑌
=
2𝑑𝐿
𝐿
+
𝑑𝑏
𝑏
+
3𝑑(𝑑)
𝑑
+
= _________________

Graph:
Results:
1. Young’s modulus of the material of the given beam = _________________ dyne/cm2
2. Maximum possible error in Y = ________________

4. R.P. of grating
Aim:
To find the resolving power of a Diffraction grating
Apparatus:
Sodium source, diffraction grating, prism and spectrometer
Formulae:
 R P of Grating: R.P =
e
nb
where, e = grating element {e= 1/N, where N = number of lines / cm; N =
2.54
000,15
lines/ cm},
n = order of the spectrum,
b = minimum width of the grating required to resolve the sodium doublet
 b=
𝑎
𝑐𝑜𝑠𝜃
where, a = the width of the slit, θ = angle of diffraction
 n λ = eSin θ
where, λ = wavelength of light, e = grating element, n = order of the spectrum
 Theoretical Resolving power = λ/dλ
Daigram:
Procedure:
1. Focus the eyepiece of the telescope on the cross wires so that they are in sharp
focus
2. Adjust the spectrometer for parallel light using Schuster’s method

3. Fix the grating stand on the prism table
4. Insert the grating in the stand in such a way that the surface on which the lines are
etched faces the telescope.
5. For making the plane of the grating parallel to the axis of rotation of the grating
table (i.e. optical levelling by means of grating), follow the following steps :
a. Fix the grating table, with grating plane perpendicular to the incident light
b. Take the direct reading of the slit on any one window of the spectrometer
c. Turn the telescope through 900 and fix it
d. Turn the grating table to obtain the reflection image of the slit so that the unetched
side of surface of the grating faces the telescope. This is shown in diagram A :
e. Bring the reflected image of the slit to coincide with the vertical cross wire of the
telescope
f. There are three screws at the base of the grating table. These form the vertices of
an equilateral triangle, level the grating table by any two of these screws so that
the reflected image of the slit lies at the centre of the telescope i.e. the horizontal
cross wire of the telescope divides the slit exactly half.
g. Now rotate the grating table so as to get the reflected image of the slit from the
etched (other) surface of the grating
h. Repeat step f.
i. Level the grating table by means of the third screw provided at the base of the
grating table.
j. Repeat steps d, e, f, g, h and i alternatively so that the image of the slit does not
move up or down when viewed through the telescope.
k. Now the grating table is levelled in such a way that the plane of the grating is
parallel to the axis of rotation of the grating table.
6. To set the grating for normal incidence rotate the grating table so as to get the
reflected image of the slit from the unetched surface as shown in diagram (A).
Now the angle of incidence is exactly 45o
7. Note the reading of the reflected image of the slit on any one window of the
spectrometer.
8. Now rotate the grating table through 45o so that the plane of the grating becomes
perpendicular to the incident light i.e. the angle of incidence is 0o.
9. Keep the grating table fixed and unlock the telescope.
10. Rotate the telescope to bring it on the r.h.s. second order spectrum as indicated in
figure B. Fix the telescope.
11. Move the fine adjustment screw of the telescope so that the vertical cross wire of
the telescope lies almost at the centre of the yellow doublet (second order).
12. Note the readings on both the spectrometer windows A and B

13. Rotate the telescope to the left and bring it on the first order spectrum on the same
side of the direct reading
14. Note the reading on windows A and B
15. Repeat steps 10, 11, 12, 13 and 14 for the l.h.s. of the direct reading
16. Calculate the angle of diffraction θ for first and second order.
17. Determine the grating element from the expression: n λ = e Sin θ
for λ = 5.890 x 10 -7 m = 5.89 x 10 -5 cms.
18. Bring the sodium lines in the first order spectrum into the filed by means of the
given auxiliary slit placed in front of the telescope objective determine the
minimum width b of the grating required to resolve the sodium doublet. If a is the
width of the slit, b =
𝑎
𝑐𝑜𝑠𝜃
. Calculate R.P = nb/e
19. Repeat for the second order spectrum.
Observations:
To determine the value of “e”
Obs.
No.
Order of
the
spectrum
‘n’
Readings of the
spectrometer
2 θ
= A ~ A΄
= B ~ B΄
Mean
2θ
Θ sin θ
R.H.S. L.H.S.
1 First A =
B =
A΄ =
B΄ =
2 Second A =
B =
A΄ =
B΄ =
Readings for the auxiliary slit for the doublet
Order ‘n’ Width while
closing 𝑎1cm
Width while
opening𝑎2cm
Mean
a cm
1
2
Calculations:
Calculation for minimum width of the grating required to resolve the sodium doublet ‘b’
Order ‘n’ Slit width ‘a’ cm θ cosθ b =
𝑎
𝑐𝑜𝑠𝜃
1
2

Calculation for ‘e’ grating element
Order ‘n’ λ cm n λ sinθ
𝑒 =
𝑛𝜆
𝑠𝑖𝑛𝜃
1
2
Calculation for R.P. =
e
nb
Order ‘n’ b nb e
R.P. =
e
nb
1
2
Result :
Resolving Power for grating
1. for 1st order spectra =
2. for 2nd order spectra =

5. Goniometer
Aim:
To find the equivalent focal length and the principal points of the given system of two
lenses by Searle’s goniometer.
Apparatus:
Lens system, goniometer, plastic scale fixed on a stand, lamp, reference pin with a
holder.
Formulae:
1. F =  𝑙 × (
ℎ
ℎ′
) = 𝑙 × (Slope of plot of h vs.h' ) = 𝑙 ×
∆ℎ
∆ℎ′
2.
1
𝐹 𝑐𝑎𝑙
=
1
𝑓1
+
1
𝑓2
−
𝑑
𝑓1 𝑓2
∴ 𝐹𝑐𝑎𝑙 =
𝑓1 𝑓2
𝑓1 + 𝑓2 − 𝑑
3. Relative error in F :
𝑑𝐹
𝐹
=
𝑑𝑙
𝑙
+
4.
=
𝑑(∆ℎ)
∆ℎ
+
𝑑(∆ℎ′)
∆ℎ′
Where 𝑙 = length of goniometer arm, F = equivalent focal length of the lens system,
h = distance moved by the vertical pin on the object scale, h' = reading at the edge of
the goniometer scale, f1 and f2 are the individual focal lengths of the two lenses as
found by the auto-collimation method, d(∆h) is the least count of the h-axis, d(∆h') is
the least of the h'-axis, dl is the least count of the measuring scale (0.1cm)
Ray Diagram:
L2L
1
L2L1
OR

Procedure:
1. Use the method of auto-collimation to set the vertical pin in the focal plane of the
goniometer lens. For this purpose, fix a plane mirror behind the goniometer lens.
Adjust the vertical reference pin attached to the movable goniometer arm so as to
remove parallax between the pin and its image as seen in the mirror. The distance
of the pin from the goniometer lens at this position is equal to the focal length of
the lens.
2. Place the system of two lenses (whose equivalent focal length is to be determined)
coaxially with the goniometer lens.
3. Mount an object scale beyond the lens system and perpendicular to its axis.
Adjust its distance so that the image of any one of its centimeter marks coincides
with the vertical wire without parallax. Set the goniometer arm to make the index
wire of the goniometer scale coincide with the central division mark.
4. Measure the length  of the goniometer arm from the center of the goniometer lens
(pivot) to the edge of the goniometer scale.
5. Also measure the distance d between the two lenses of the system and the distance
‘a’ from the object scale to the lens facing it.
6. Turn the arm of the goniometer on one side of the central division mark to make
the image on a line (on object scale) at a distance h from the center of the object
scale to coincide with the vertical pin.
7. Read the distance h| by which the index wire is displaced laterally on the
goniometer scale. Take a set of such readings by increasing h in suitable steps of
0.5 cm or less.
8. Repeat steps (6) and (7) by moving the goniometer arm towards the other side of
the central division mark.
9. Now rotate the lens system through 180 anmeasure the distance ‘b’ from the
object scale to the lens facing it. Repeat steps (6), (7) and (8)
10. Plot graphs of h versus h' for set I and set II. Hence calculate the focal lengths F1
and F2 from the respective slopes.
11. Estimate the possible errors in the values of F1 and F2.
12. With the values of a, b, d, F1 and F2 draw a diagram to scale of the lens system.
13. Measure the focal lengths of the two lenses f1 and f2 (of the system) by auto-
collimation method and calculate Fcal.
Observations:
1. Distance between the two lenses of the system = d = _______________ cm
2. Length of the goniometer arm = 𝑙 = __________________ cm
3. The distance between the horizontal scale and the lens near to it = a =
___________ cm
Set -1:

Obs. No.
Object Scale
Reading x1 (cm)
x1
= _____ cm
GoniometerScale
Reading y1 (cm)
y1
= _______ cm
h = x1
– x1
cm
h1
= y1
– y1 cm
L.H.S.
R.H.S.
4. The distance between the object scale and the lens near to it (after rotation of the
lens system through 180 = b = _____________ cm.
Set 2: After rotating through 180O
Obs. No.
ObjectScale
Reading x' (cm)
X1 = _____ cm
Goniometer Scale
Reading y1 (cm)
Y1 = _______ cm
h = x' – x1 cm h1
= y' – y1 cm
L.H.S.
R.H.S.
5) Individual focii of the lenses in the system: f1 = _____cm; f2 = _______cm
6) 𝐹𝑐𝑎𝑙 =
𝑓1 𝑓2
𝑓1+𝑓2−𝑑
=______________cm

Calculations:
Relative Error in F:
Distance of the 1st principal plane P1from lens L1= α =F1-a=__________cm
Distance of the 2nd principal plane P2from lens L2= β = F2-b=__________cm
Graphs: SetI & II
Results:
1. F cal = ___________ cm
2. F1 = ___________ cm
3. F2= ___________ cm
4. Mean F obs =___________cm
5. Relative error in F1 = (dF1/F1) =_________cm
6. Relative error in F2 = (dF2/F2) =_________cm

Aim:
To determine the refractive Index of liquidusing He-Ne Laser
Apparatus:
Laser source, liquid, vernier, mirror with stand, microscope etc.
Formulae:
1. Critical angle θc = tan-1 𝑅
2𝑑
2. Refractive index of liquid 𝑛𝑙 =
1
𝑠𝑖𝑛𝜃𝑐
Diagram :
Experimental arrangement:
This experiment of measurement of refractive index of liquid using laser is based on
the principle of total internal reflection of light in any medium.In case of liquid
medium, a flat bottom rectangular plane acts as a good scatterer and screen.
When a laser beam is incident on liquid, all condition for total internal reflectionscattered
specious waveformsinside liquid when satisfied leads to formation of circular ring
pattern. The circular ring pattern consists of a perfect shadow region. The circular line is
much sharped so that the diameter of ring pattern can be very precisely measured.
If R is the radius of the ring formed and‘d’ is depth of liquid medium then (
𝑅
2𝑑
)= 𝑡𝑎𝑛𝜃𝑐.
According to Snell’s law,
𝑛 𝑎
𝑛𝑙
=
sin 𝑖
sin 𝑟
, Where, 𝑛 𝑎 = 𝑟𝑒𝑓𝑟𝑎𝑐𝑡𝑖𝑣𝑒 𝑖𝑛𝑑𝑒𝑥 𝑜𝑓 𝑎𝑖𝑟; 𝑛𝑙 =
𝑟𝑒𝑓𝑟𝑎𝑐𝑡𝑖𝑣𝑒 𝑖𝑛𝑑𝑒𝑥 𝑜𝑓 𝑙𝑖𝑞𝑢𝑖𝑑.
At total internal reflection, 𝑖 = 𝜃𝑐 , when r = 90º;𝑠𝑖𝑛𝑐𝑒, 𝑛 𝑎 = 1, sin 90 = 1; we can find
the refractive index of the liquid using 𝑛𝑙 =
1
Procedure:
1. Set up the apparatus as shown in the diagram.
2. Adjust the laser beam to fall on the mirror adjusted approximately at an
inclination of 45º. Don’t move mirror till the end of experiment
3. Add some liquid in a porcelain container (tray) and measure the depth of liquid.

4. Now focus the laser beam into the liquid and observe the ring formed over the
liquid surface.
5. Measure the diameter of ring.
6. Take 3-4 reading for different depths of the liquid.
7. Using formula calculate θc& R. I.
8. Repeat steps 2 to 7 for another liquid.
Observations:
LIQUID I : WATER
Obs.
No.
Depth
d (cm)
Diameter
D (cm)
Radius
R (cm)
𝑅
2𝑑
= tan 𝜃𝑐
𝜃𝑐
= 𝑡𝑎𝑛−1
𝑅
2𝑑
sin 𝜃𝑐
1
𝑛𝑙
=
1
1
2
3
4
5
6
Refractive Index (Mean) = __________________
LIQUID II : SUGAR SOLUTION
Obs.
No.
Depth
d (cm)
Diameter
D (cm)
Radius
R (cm)
𝑅
2𝑑
= tan 𝜃𝑐
𝜃𝑐
= 𝑡𝑎𝑛−1
𝑅
2𝑑
sin 𝜃𝑐
1
𝑛𝑙
=
1
1
2
3
4
5
6
Refractive Index (mean) = ______________
Results:
1. Refractive index of liquid 1 (water) is ___________________
2. Refractive index of liquid 2 (sugar solution) is ______________

Aim:
To determine the wavelength of the given monochromatic light using Edser’s ‘A’ pattern.
Apparatus:
Sodium light source, 2 ‘A’ patterns, two wire gauges telescope, microscope etc.
Formula:
λ =
D
ld
2
; where,
λ = wavelength of light (monochromatic) in cms,
l = length of the cross bar of ‘A’
d = element of wire gauze &
D = distance between the ‘A’ pattern and the gauze
Daigram:
Procedure:
1. Determine the length of the cross bars of the 2 given ‘A’ patterns, using the
travelling microscope.
2. Determine the elements of each wire gauze by measuring the spacing between
four successive vertical wires, at least four times for each.
3. Place the ‘A’ pattern plate in the inverted position ( ) at a short distance from
the sodium source.
4. Keep the telescope, a little beyond 2 meters away from the ‘A’ pattern and
focus it on ‘A’ (A real and inverted image of the inverted  will be observed)
5. Introduce the wire gaze with its plane perpendicular to the axis of the telescope
and close to the telescope objective. A number of secondary images of ‘A’ (due
to diffraction) along with the principal or primary image of ‘A’ will be
observed.
6. Adjust the position of the wire gauze, till the point of intersection of the first
pair of secondary image of ‘A’ lies at the mid-point of the bar of the principal
image of ‘A’ as is shown in the diagram.

7. Measurethe distance ‘D’ between the plane of the ‘A’ pattern plate and the wire
gauze plane, for the adjustments mentioned in the preceding step 6.
8. Repeat steps 5, 6 and 7 for the other wire gauze
9. Repeat steps 3,4,5,6,7 and 8 for the second ‘A’ pattern
Observations:
To determine the length of the cross bar ‘𝑙’:
Least count of the travelling microscope = __________ cms
No. Microscope Readings 𝑙 = 𝑥~𝑦 𝑐𝑚𝑠 Mean ′𝑙′
𝑐𝑚𝑠
Left end
‘x’ cms
Right end
‘y’ cms
A1
A2
To determine the gauze element‘d’
Gauze
No.
Vertical.
wire No.
Microscope
reading ‘cms’
4d ‘cms’ Mean 4d ‘cms’ Mean d
1 1
5
9
13
17
Gauze
No.
Vertical.
wire No.
Microscope
reading ‘cms’
4d ‘cms’ Mean 4d ‘cms’ Mean d
2 1
5
9
13
17
Readings for ‘D’
A Gauze No. Distance between ‘A’
plate and wire gauze
D ‘cms’
A1 1
2
A2 1
2

Calculations:
To calculate the wavelength the λ: λ =
D
ld
2
A Gauze
No.
′𝑙′cms ‘d’ cms ‘D’cms ′𝑙𝑑′cms 2D cms
λ =
D
ld
2
cms
A1 1
2
A2 1
2
Mean λ = ___________cms ____________ A.U.
Results:
The mean wavelength of the monochromatic light = _____________A.U.

8.Diameter of lycopodium powder
Aim:
To determine the diameter of lycopodium power particle.
Apparatus:
Lycopodium power, glass plate, card board with hole at the center, Sodium source
Formula:
The angle between the direction of principal maximum and the 1st minimum =
1.22
𝑑
The angle between the direction of principal maximum and the 2nd minimum =
2.23
𝑑
Where,‘d’ is the diameter of the aperture or obstable,  is the wavelength of light used.
Diagram:
Procedure:
A hole of 1/8th inch diameter is made on a card board and small pin holes are made at
distances from these holes along two perpendicular direction. The central hole (1/8th inch
diameter is illuminated by yellow light (sodium source) and it is observed through a glass
plate sprinkled with lycopodium powder. A no. of circular rings seen when satisfied that
the first two sharp dark rings are observable following procedure be adopted.
1. Adjust the distance between the glass plate and the card board by moving the
glass plate such that the 1st dark ring fits the 1st pin hole i.e. the ring just touches
the 1st hole. Let ‘r’ be the radius of 1st ring in the 1st hole and ‘D’ be the distance
between the card board and the glass plate. Since the angle (θ) is small θ = r/D.
Measure ‘r’ and D.
2. Repeat the above procedure by ‘fitting’ the 1st ring in all the remaining holes and
record ‘r’ & ‘D’ everything.
3. Now repeat the same procedure by fitting the 2nd dark ring in all the pin holes.

4. Draw the graph of ‘r’ against ‘D’ for both the rings.
Observations:– Readings for
1st ring fitted in various holes 2nd Ring fitted in various holes
Ob.
No.
Distance from the
central hole to the
pin holes ‘r’ cm
Distance
between
cardboard and
glass plate ‘D’
cm
Ob.
No.
Distance from
the central hole
to the pin holes
‘r’ cm
Distance between
cardboard and glass
plate ‘D’ cm
1 0.5 1 0.5
2 1 2 1
3 1.5 3 1.5
4 2
5 2.5
Calculations:
= 5893 A.U.
Slope of the graph for 1st ring =
1.22
𝑑
, d =
1.22
=
Slope of the graph for 2nd ring =
2.23
𝑑
, d =
2.23
=
Graph:
Result:
The diameter of the lycopodium powder particle is ________________cm.

9. Determination of e/m
Aim:
To determine e/m of electron using Thomson’s cathode ray tube
Apparatus:
Thompson’s cathode ray tube, power supply, bar magnets, magnetometer, a wooden
platform, a wooden bench (Thomson’s bench), a voltometer, connecting wires.
Formulae:
1. 𝑣 =
𝐸
𝐵
Where E is electric intensity between the horizontal plates of CRT
B is magnetic induction which nullifies the deflection of electron
2. 𝐵 = 𝐵 𝑜 𝑡𝑎𝑛𝜃
Where B is magnetic induction at distance x from the aperture
Bo is horizontal component of earth’s magnetic field
θ is mean deflection of needle ‘sn’ in the magnetometer
3.
𝑒
𝑚
=
𝑣𝑦
1
2
𝑙2 𝐵̅+∫ (𝑙−𝑥)ℎ𝑑𝑥
𝑙
0
Where
𝑒
𝑚
is specific charge of electron
v is velocity of electron
y is deflection of electron by electric field
𝑙
𝐵
is distance of screen from aperture
is average of B
x is distance of point of aperture
h = | 𝐵. 𝐵̅|
Diagram:

Procedure:
1. Keep the Thomson’s C.R.T. with its length parallel to magnetic meridian on a
wooden platform placed in E-W direction.
2. Adjust the focus of C.R.T. to get a fine spot on the screen at its centre O.
3. Apply a p.d. V between the horizontal plates to get vertical deflection y of about
1 cm.
4. Place two bar magnets coaxially on the wooden platform with their axis in E-W
direction on two sides of the C.R.T. so that a magnetic field B is produced at
right angles to the electric field. Adjust the position of the magnets placed
symmetrically such that the deflection of the spot is nullified and the spot
comes back to O.
5. Without disturbing the positioning of the magnets, remove the CRT. Place the
wooden bench in position of the CRT which has its top surface in level with the
wooden platform. Draw a line on the top of the bench at its centre which
concides with the axis of the CRT. Mark the positions of aperture and the
screen of CRT on this line.
6. Keep magnetometer on this line with 90-90 div coinciding with the line at
equidistant points from the position of aperture to the position of the screen, the
needle being at the height of the axis of the tube. Note deflections θ1 and θ2 of
the needle at the ends of the aluminium pointer in the magnetometer and
distance x of the point from the aperture.
7. Plot a graph of (l-x) h against x, where l is distance between aperture and the
screen and h is difference between magnetic induction at distance x and average
value ______ of the magnetic induction.
Observations:
1. P.D. between the horizontal plates = V = ---------- volts
2. Deflection of the spot = y = --------- cm
3. Distance of the screen from aperture = l = --------- cm
4. Distance between the horizontal plates = d = ------ cm / m2
5. Horizontal component of earth’s magnetic field = B0 = ---- Wb / m2

Practical Course –USPHP06
Electricity, Magnetism and
Electronics

1. Mutual inductance by BG
Aim:
To determine mutual inductance between two coils by ballistic galvanometer.
Apparatus:
2 V source, two coils, plug key, stop watch, commutator, Rayleigh key, tap key, one
resistance box (0-1-10,000 Ω), one resistance box (0-0.1-50 Ω), B.G. lamp and scale
arrangement, connecting wires.
Formulae:
1.θ0
̅̅̅= θ1 (
θ1
θ3
)
1/4
2. M=
T
2π
×
r
ϕ
× θ0
̅̅̅
Where, M is the mutual inductance between the two coils; T is the period of the ballistic
galvanometer coil oscillating freely; r is the resistance across secondary and the ballistic
galvanometer. ϕ is the steady deflection in the ballistic galvanometer corresponding to r;
θ1 and θ3are the successive throws of the B.G. coil on the scale on the same side.
3. Relative error in M=
dM
M
=
dt
t
+
d(r ϕ⁄ )
r/ϕ
+
dθ0
θ0
dt is the least count of the measuring clock used.
(r /ϕ)=Slope =
∆r
∆ϕ
where Δr and ∆ϕ are as shown in the graph of r versus ø.
d(r ϕ⁄ )
r/ϕ
= relative error in slope =
d(∆r)
∆r
+
d(∆ϕ)
∆ϕ
d(Δr)= least count of r-axis; d(Δ ϕ)= least count of ϕ -axis.
4. Standard error in θ0
̅̅̅ = dθ0
̅̅̅ = √∑ (θ0i−θ0)
2n
i=1
n−1

Circuit Diagram:
Procedure:
1. Set up the B.G. and lamp and scale arrangement such that light incident on the
mirror in B.G. from the lamp reflects to produce a well defined bright spot of light
on the scale.
2. Connect the circuit as shown.
3. Keep R sufficiently high (≈2000Ω) and r equal to zero. Connect segment 1 and 2
of the commuter key (4 quadrant key).
4. Press the damping key across the B.G. to arrest the throw at zero. Then press the
Rayleigh key (k1 and k2). First release the damping key and then the Rayleigh
key. Note the first and second successive throw of B.G. coil on the scale on the
same side of zero division.
(θ1 and θ3) respectively. Take 10 readings.
5. Now connect segment 1, 3 and 2, 4 (disconnect the segment 1 and 2) of the
commutator. Do not change R.
6. Keep r = 0.1 Ω . Press Rayleigh key and note the steady deflectionϕ of the B.G.
coil on the scale.
7. Repeat step 6 for r = 0.2, 0.3, 0.4, 0.5, 0.6 Ω . So thatϕranges from 1cm to 19cm.
8. Plot a graph of r versus ϕ.
9. Disconnect the circuit. Allow the coil to oscillate freely. Hence determine period
T of the B.G.

Observations:
To determine θ0
R=_________Ω
Sr.
no
n
θ1
cm
θ3
cm
θ0
= θ1 (
θ1
θ3
)
1/4
Cm
(θ0i − θ0)
cm2
(θ0i-θ0
̅̅̅)2
cm2
∑(θ0i − θ0)
2
n
i=1
cm2
dθ0
̅̅̅
=√∑ (θ0i−θ0)
2n
i=1
n−1
cm
Mean θ0=θ0 = ______________ cm
To determine steady deflection ϕ
Obs No. r (Ω) ϕ. Cm
1
2
3
4
5
6

To determine T
No. of oscillation (n) Time t (sec) T (sec) = t/n
Calculations:
R= _______Ω
1.From the graph of r versus ϕ, ∆r = _____________Ω; ∆ϕ. = _____________ cm
∴Slope =
∆r
∆ϕ
= ___________ cm
2. M=
T
2π
×
r
ϕ
× θ0
̅̅̅
=
T
2π
× (slope) × θ0
̅̅̅ = ___________ Henry
3. Error in T
dt = Least count of measuring clock used = ______ sec ; t=_________ sec
dt
t
=________ sec
4. To Calculate
d(r ϕ⁄ )
r/ϕ
:
d(∆r) = _____________ Ω ; d(∆ϕ) = ________________ cm
d(r ϕ⁄ )
r/ϕ
=
d(∆r)
∆r
+
d(∆ϕ)
∆ϕ
= ________________
5. Standard error in θ0:
dθ0=√∑ (θ0i−θ0)
2n
i=1
n−1
= _________________ cm;
dθ0
θ0
= ______________
6. Maximum possible error (dM) in M:

Relative error in M =
dM
M
=
dt
t
+
d(r ϕ⁄ )
r/ϕ
+
dθ0
θ̅0
= _________________
∴ dM=
dM
M
x M = _________________ Henry
Graph:
Results:
1. Mutual inductance between coils = M=____________ Henry
2. Corrected value of mutual inductance M ± dM =______±______ Henry

Aim:
To determine the inductance, a.c. resistance and Q-factor of a coil having a large D.C.
resistance using Maxwell’s Bridge.
Apparatus:
Resistance boxes, null detector (CRO), capacitance box, signal generator, connecting
wires.
Formulae:
1. L =R2 R3 C1
2. r =
R2
R1
×R3
3. Q=
ωL
r
Where ω = 2πf
4. Standard error in the mean value of L. = ΔL̅ = ±[
∑ (Li−L̅)i
n(n−1)
2
]
1/2
5. Standard error in the mean value of r. Δr = ∆r̅ = ±[
∑ (ri−r)2
i
n(n−1)
]
1/2
Where L = inductance of coil, r = a.c. resistance of coil, Q = quality factor, L̅ = mean
value of L, n is the number of observations, r̅ is the mean value of r, f is the applied
frequency = 1 kHz.
Circuit diagram:
A.F.
Generator
1 kHz

Procedure:
1. Connect the circuit as shown, having a coil of large d.c. resistance (Low –Q)
2. Set the frequency on the sine wave generator to 1kHz.
3. Set R1= R2 = R3 = 1000Ω and C1= 0.1µF
4. Connect a CRO as a null detector. Keep the CRO in X-Y coupling. Adjust the
amplitude of the signal generator so that the trace is as large as possible
(Vertically).
5. Adjust C1 to get minimum possible amplitude in the CRO.
6. Readjust the amplitude of the signal generator once again to obtain trace with
amplitude greater than that obtained in (5).
7. Now adjust R1 to further minimize the amplitude of trace.
8. Adjust C1 and R1 alternately to get the least possible amplitude of trace in the
CRO.
9. Note down the final values ofC1 and R1 so obtained. Calculate L and r.
10. KeepR2 fixed at 1000Ω, varyR3 in the following steps : 400Ω, 600Ω, 800Ω,
1200Ω, 1400Ω, 1600Ω, 1800Ω.
11. Calculate the quality factor Q.
Observations:
R2=1000 Ω
Obs
No.
(n)
R3
Ω
C1
μF
R1
Ω
L
mH
Li–L
mH
(Li − L)2
(mH)2
∑(Li − L̅)2
(mH)2 ΔL̅ = ±√
∑ (Li−L)
2
i
n(n−1)
mH
Mean L=L̅ = _________ mH

ObsNo.
(a)
R
Ω
ri--r
Ω
(ri– r)2
( Ω)2
∑(ri − r̅)2
( Ω)2 ∆r̅ = ±√
∑ (ri − r)2
i
n(n− 1)
Ω
Mean r = r̅ = __________Ω
Calculations:
Q=
ωL̅
r̅
=
2πfL̅
f̅
= ________________
Results:
1. Inductance of coil =L̅=___________ mH
2. A.C. resistance of coil = 𝐫̅ = ______________Ω
3. Quality factor = Q = ___________
4. ΔL̅ = _______________ mH
5. ∆𝐫̅ = ____________________ Ω
6. Corrected inducance = L̅ ± ΔL̅ =( ______________±_______________)mH
7. Corrected r =r̅ ± ∆r̅ = (___________±_____________)Ω

3. Band gap of Energy
Aim:
To determine the band gap energy in a semiconductor p – n junction diode
Apparatus:
Diode, Power supply (0-5) Volts, Micro ammeter (0-200 µA) water bath, burner,
Rheostat / Pot, connecting wires
Formulae:
1) 𝐼𝑆 = 𝐴𝑇2
𝑒𝑥𝑝 {
−𝐸 𝑔
𝑘𝑇
}
Where Is = reverse saturation current; Eg = band gap energy; k = Boltzmann
constant;
T= absolute temperature at which Is is measured.
𝑙𝑜𝑔10 {
𝐼𝑆
𝑇2
} = 𝑙𝑜𝑔10 𝐴 −
𝐸𝑔
2.303𝑘𝑇
𝑖. 𝑒 𝑙𝑜𝑔10
{
𝐼 𝑆
𝑇2
} = 𝑙𝑜𝑔10
𝐴 −
𝐸 𝑔
2.303𝑘𝑇
∗
1
𝑇
This is of the form y =mx+c
Slope = −
𝐸 𝑔
2.303𝑘𝑇
, 𝐸𝑔 = −( 𝑠𝑙𝑜𝑝𝑒) ∗ 2.303 ∗ 𝑘 where k = 8.6*10-5 eV
2. Relative error in 𝐸𝑔 =
𝑑{∆[ 𝑙𝑜𝑔10(
𝐼 𝑆
𝑇2)]}
∆[ 𝑙𝑜𝑔10(
𝐼 𝑆
𝑇2)]
+
𝑑[∆(
1
𝑇
)]
∆(
1
𝑇
)
Shown in graph of 𝑙𝑜𝑔10 {
𝐼𝑆
𝑇2} vs
1
𝑇
𝑑 {∆ [𝑙𝑜𝑔10 (
𝐼 𝑆
𝑇2 )]} = least count of 𝑙𝑜𝑔10 {
𝐼 𝑆
𝑇2} axis, 𝑑 [∆ (
1
𝑇
)] = least count of
1
𝑇
axis.
Error in 𝐸𝑔 =
𝑑𝐸 𝑔
𝐸 𝑔
* 𝐸𝑔

Circuit Diagram:
Procedure:
1. Connect the circuit as shown in the figure.
2. Insert the diode or transistor used a diode about ¾ deep in the test tube and
immerse the test tube in a water bath taking care that the lower end dose not touch
the base of the bath.
Also insert a thermometer in the test tube such that the of the thermometer lies
close to the outer casing of the diode.
3. At an ambient temperature say room temperature (tr) vary the reserve voltage V
across the diode in convenient steps and note down the corresponding reserve
current I through it till it reaches a saturation value Is Now set the reserve voltage
at 5V.
4. Change the ambient temperature of the diode say by 5°C above t1 by hearing the
water bath and record the saturation current Is This is to be repeated for various
temperatures (tr+5)°C, (tr+10)°C, (tr+15)°C,--------- (tr+30)°C, also take the
reading the while cooling.
5. Plot the reverse characteristics i.e. plot ‘V’ against ‘I’ and determine the
saturation current I, at room temperature.
6. Plot another graph of log10 (Is/T2) against 1/T where T is in Kelvin.
7. Determine the slope, which is negative, and find the value of Eg from the given
formula. Also determine error in slope of graph of log10 (Is/T2) versus I/T.

Observations:
Room temperature (t) = °C.
-V (volts) I (µA) -V (volts) I (µA)
Obs.
No.
t0
C T(K)
Saturation current IS
(µA)
Mean IS
(µA)
IS( pA)
Heating Cooling
1
2
3
4
5
6
7

T (K) 1
𝑇
( 𝐾−1) IS ( pA)
T2
(K2)
𝐼𝑆
𝑇2
(
𝑝𝐴
𝐾2
) log10(
Is
T2 )
Calculations:
From the plot of log10 (Is/T2) versus I/T, ∆ { log10 (Is/T2)
=________;∆(1/T)=__________ K¯1.
Slope =
∆[ 𝑙𝑜𝑔10(
𝐼 𝑆
𝑇2)]
∆(
1
𝑇
)
=______________k
∴Eg= - Slope x 2.303 x k=________eV
To calculate=
𝑑{
𝑙𝑜𝑔
10(𝐼 𝑆/𝑇2)
1/𝑇
}
{
𝑙𝑜𝑔
10(𝐼 𝑆/𝑇2)
1/𝑇
}
d{∆[ log10( Is / T2)]}=___________;d[∆(1/T)] =___________
dEg=
𝑑{
𝑙𝑜𝑔
10(
𝐼 𝑆
𝑇2)
1
𝑇
}
{
𝑙𝑜𝑔
10(
𝐼 𝑆
𝑇2)
1
𝑇
}
=
𝑑{∆[𝑙𝑜𝑔10(
𝐼 𝑆
𝑇2)]}
∆[𝑙𝑜𝑔10(
𝐼 𝑆
𝑇2)]
+
𝑑[∆(
1
𝑇
)]
∆(
1
𝑇
)
Hence Eg = Eg ±d Eg = __________ ± ___________ eV

Graphs:
(a) Reverse characteristics at room
Temperature
(b)
Results:
Average band gap energy Eg of the given semiconductor is found to be =_______eV
Error in Eg ± dEg = ____________eV.
Corrected Eg = Eg ± dEg = __________eV.

4. Diode as temperature sensor
Aim:
To study the variation of the forward voltage with temperature in a forward biased p-n
junction diode.
Apparatus:
A constant current source, a p-n junction, Ge diode, a DMM used on the 0-2 volts range,
a temperature bath, a thermometer.
Formulae:
The forward current in the forward biased p-n junction diode is given by
𝐼𝑓 = 𝐼𝑠 𝑒𝑥𝑝 {
𝑞𝑉𝑓
𝑘𝑇
− 1}
Where, k = Boltzmann constant, q= electron or hole charge, T= temperature (k),
𝐼𝑆 = Reversed saturation current, 𝑉𝑓 = 𝑉𝐷= forward voltage or voltage drop
across the diode.
If𝐼𝑓 ≪ 𝐼𝑠 then 𝐼𝑓 = 𝐼𝑠 𝑒𝑥𝑝 {
𝑞𝑉 𝑓
𝑘𝑇
}
 ln
𝐼 𝑓
𝐼𝑠
=
𝑞𝑉 𝑓
𝑘𝑇
=>𝑉𝑓 =
𝑘𝑇
𝑞
𝑙𝑛
𝐼 𝑓
𝐼𝑠
If Ifis held constant, it is seen from the above equation that the temperature
coefficient of Vf is negative, i.e., Vf= (VD ) decreases with increasing
temperature.
Circuit Diagram:

Procedure:
1. Connect the circuit as shown above (power supply for current source Vcc= 12V )
2. Adding crushed ice (or chilled water) in the outer water jacket, obtain the diode
temperature to be 0⁰C.
3. Set If = 0.01 mA (constant throughout the experience)
4. Measure the voltage drop VD across the diode at 0⁰C. With the help of a DMM
used on the 0-1.999 volt range.
5. Repeat step (4) at regularly increasing temperature 0 – 60⁰C in steps of 5. ⁰C
6. Plot a graph of VD (y-axis) against (x-axis) and determine the slope d VD /dt, at
40⁰C the lowest and the highest values of the temperature range.
7. Repeat the experiment for forward current If = 1mA and plot correspondence
graph. Determine the values of d VD /dt as before.
Observations:
Temperature
℃
For
𝑰 𝒇 = 𝟎. 𝟎𝟏 𝒎𝑨
𝑽 𝑫(𝒎𝑽)
For
𝑰 𝒇 = 𝟏 𝒎𝑨
𝑽 𝑫 (𝒎𝑽)

Graphs:
Result:
Temperature
(o
C)
dVD/dt at 0.1 mA
(mv/sec)
dVD/dt at 1 mA
(mv/sec)
40
Comments:
At If = 0.1 mA. The variation of the forward voltage Vf with temperature is non-linear
resulting in a non-uniform temperature scale. The variation of Vf is dependent on the
reverse saturation current IS. Here, since If is comparable to IS. Variation of Vf with
temperature in non-linear.
At If = 1.0 mA, the variation of the forward voltage Vf with temperature is linear
resulting in an uniform temperature scale.

5. Log amplifier using OP-AMP
Aim:
To study the transistor characteristics of a logarithmic amplifier.
Apparatus:
Op amp modular board ,a  12 volt dual power supply, DVM a Si-diode a 0 to 15 V
power supply, 10kΩ carbon resistor (1/4 or ½ watt) connecting wires
Formulae:
1. 𝑉𝑜 = −𝜂𝑉𝑇 (ln 𝑉𝑖𝑛 − ln 𝐼𝑠𝑅)
2. 𝑉𝑇 =
kT
q
3. 𝜂 =
−𝑉𝑜
2.303 𝑉𝑇 log 𝑉𝑖𝑛
4. 𝐼𝑠 =
𝐴𝑛𝑡𝑖𝑙𝑜𝑔(𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡𝑜𝑛 log 𝑉𝑖𝑛𝑎𝑥𝑖𝑠)
𝑅
Where, VT = Electron volt equivalent to temperature.,
k = Boltzmann’s constant (1.38  10-23 J/K )
T= Absolute temperature , q = electronic charge (1.610-19 Coulombs)
η = Ideality factor, Vin = Input voltage, Vo= Output voltage,
Is = Reverse saturation current
Circuit Diagram:

Procedure:
1. Connect the circuit as shown in the circuit diagram
2. Switch on the dual power supply. Then switch on the input voltage supply and set
its terminal voltage to 10mV,with the help of the digital voltage (DVM),observe
and record the corresponding output voltage(-Vo)
3. Observe and record the output voltage (-Vo) for the remaining input voltage (Vin)
varying from 10m V to 10V.
4. Plot a graph of (-Vo) against log10 Vin from it determine the slope
−𝛥𝑉𝑜
log 𝛥𝑉𝑖𝑛
- and also
the intercept on the log Vin axis. Hence calculate the value of η and Is.
Observations:
Vin(mV)
Vin(nV)
log
Vin
Vo(mV) Vin(mV) Vin(nV)
log
Vin
Vo(mV)
10 600
20 800
30 1000
40 2000
60 3000
80 4000
100 6000
200 8000
300 100000
400
Calculations:
k = Boltzmann’s constant (1.38  10-23 J/K),
q = electronic charge (1.610-19 Coulombs)
T = (toC + 273) K = _______K
VT = (kT/q) = ______mV
.From the plot of log Vin versus –Vo (mv) , slope = ____________mV.
𝜂 =
−𝑉𝑜
2.303𝑉𝑇 log 𝑉𝑖𝑛
=
1𝑥𝑠𝑙𝑜𝑝𝑒
2.303𝑉𝑇
= ________
The intercept on X-axis= ________, -Is= antilog (Intercept) / R = ____nA

Graph:
Results:
1. VT = _______mV
2. 𝜂 = ________
3. Is = _______nA

6. High Pass (1st
order active filter)
Aim:
To study the frequency & phase response of active high pass filter.
Apparatus:
Dual power supply (+12Volts), IC 741, capacitors, resistors, signal generator, C.R.O.
Circuit Diagram:
Formulae:
 𝐹𝐶 =
1
2𝜋𝑅 𝐶
 𝐴 𝑉 = 1 +
𝑅 𝑓
𝑅1
=
𝑉 𝑂
𝑉𝑖𝑛
 Phase shift ( 𝜃°) = ( 𝑡 × 𝐹𝑖𝑛 ) × 360°
= (
𝑡
𝑇𝑖𝑛
) × 360°
Where, 𝐹𝐶 =Cut off frequency, 𝐹𝑖𝑛= Input frequency, 𝐴 𝑉 = Voltage gain, 𝑉𝑖𝑛= Input
voltage, Tin = Input period, V0 = Output voltage, t = Time lag/ lead between 𝑉𝑂 &𝑉𝑖𝑛
Procedure:
1. Connect the high pass filter circuit as shown in the circuit diagram.
2. Study its frequency response over a frequency range of
𝐹𝐶
10⁄ to 10𝐹𝐶 , keeping the
input voltage constant at all the applied frequencies.
3. Determine the phase shift between 𝑉𝑂 and 𝑉𝑖𝑛 for any two frequencies in the Pass
band and at cut-off frequency, using dual trace CRO.

4. Plot a Graph of 𝑉𝑂 versus log Fin. Determine the cut-off frequency and compare it with
the expected value.
Observations:
𝐹𝐶 =
1
2𝜋𝑅 𝐶
= ____________ kHz
𝑉𝑖𝑛= _____________volts (p-p)
Frequency Response:
Fin (Hz) Log Fin V0 ‘volts’ AV
= VO Vin⁄
Fin (Hz) Log Fin V0 ‘volts’ 𝐴 𝑉
= 𝑉𝑂 𝑉𝑖𝑛⁄
Phase:
Obs. No. 𝐹𝑖𝑛 (Hz) t sec 𝜃° Remark

Graph:
Results:
Cut-off frequency (expected) =𝑓𝐶= Hz
Cut-off frequency (from graph) =𝑓𝐶= Hz
Phase Shift:
In the pass band
At 𝑓𝐶= Hz ; θ = degrees
At 𝑓𝐶= Hz ; θ = degrees
At cut-off 𝑓𝐶 = Hz ; θ = degrees

7. Low Pass (1st
orderactive filter)
Aim:
To study the frequency & phase responses of active Low pass filter.
Apparatus:
Dual power supply (+12Volts), IC 741, capacitors, resistors, signal generator, C.R.O.
Circuit Diagram:
Formulae:
 𝐹𝐶 =
1
2𝜋𝑅 𝐶
 𝐴 𝑉 = 1 +
𝑅 𝑓
𝑅1
=
𝑉 𝑂
𝑉𝑖𝑛
 Phase shift ( 𝜃°) = ( 𝑡 × 𝐹𝑖𝑛 ) × 360°
= (
𝑡
𝑇𝑖𝑛
) × 360°
Where, 𝐹𝐶 =Cut off frequency, 𝐹𝑖𝑛= Input frequency, 𝐴 𝑉 = Voltage gain, 𝑉𝑖𝑛= Input
voltage, Tin = Input period, V0 = Output voltage, t = Time lag/ lead between 𝑉𝑂 &𝑉𝑖𝑛
Procedure:
1. Connect the Low pass filter circuit as shown in the circuit diagram.
2. Study its frequency response over a frequency range of
𝐹𝐶
10⁄ to 10𝐹𝐶 , keeping the
input voltage constant at all the applied frequencies.
3. Determine the phase shift between 𝑉𝑂 and 𝑉𝑖𝑛 for any two frequencies in the Pass
band and at cut-off frequency, using dual trace CRO.
4. Plot a Graph of 𝑉𝑂 versus log Fin. Determine the cut-off frequency and compare it with
the expected value.

Observations:
𝐹𝐶 =
1
2𝜋𝑅 𝐶
= ____________ kHz
Vin = _____________volts (p-p)
Frequency Response:
Fin (Hz) Log Fin V0 ‘volts’ Av=V0/Vin Fin (Hz) Log Fin V0 ‘volts’ Av= V0/Vin
Phase:
Obs. No. 𝐹𝑖𝑛 (Hz) t sec 𝜃° Remark

Graph:
Results:
Cut-off frequency (expected) = 𝑓𝐶 = Hz
Cut-off frequency (from graph) =𝑓𝐶= Hz
Phase Shift:
In the pass band
At 𝑓𝑖𝑛= Hz ; θ = degrees
At𝑓𝑖𝑛= Hz ; θ = degrees
At cut-off 𝑓𝐶= Hz ; θ = degrees

8.Wien Bridge Oscillator
Aim:
To analyze practically the working of the given Wien Bridge Oscillator using an
operational amplifier IC.
Apparatus:
Built-up circuit of the Wien Bridge comprising an op-amp (IC 741),2 diodes (IN4148),
resistors, capacitor, a potentiometer, ±12 volt dual power supply. C.R.O, connecting wires
etc.
Formulae:
f =
1
2π√R1R2C1C2
, f =
1
2πRC
, if R1 = R2 = R,C1 = C2 = C
Circuit diagram:
R1=_______KΩ, R2=_______kΩ, R3=________KΩ, R3’=________KΩ,
R4=________KΩ
C1=_______µf, C2=_______µf
D1 and D2 are both IN4148 switching diodes.

Procedure:
1. Trance the circuit and mention the component values of the given Wien Bridge
Op-Amp oscillator
2. Connect the dual power supply. Switch on the dual power supply. Use d.c.
coupling to the C.R.O.Y input. Adjust the potentiometer (𝑅′3) to obtain a
symmetric sine wave on the C.R.O. screen.
3. Measure the time period and hence the frequency of the observed sine wave using
an appropriate time base setting. Compare the observed frequency value with the
one given by the formula
4. Next determine the signal voltage at the following test points.
a) Non –inverting i/p terminal of Op-Amp (PIN3)
b) Inverting i/p terminal (PIN2)
c) O/P terminal of OP-Amp(PIN6)
(i) Determine the ratio of the negative feedback voltage(PIN2) to the O/P-
voltage(pin6)
(ii) Determine the closed loop voltage gain (ratio of O/P voltage to the
non-inverting i/p voltage) of the OP-AMP
5. Find the product of ratios(i) and (ii).and compare it with the expected values
6. Also determine the frequency of oscillation of the output sinewave using
Lissajous figures by connecting channel 1 of the CRO to a signal generator
(known frequency) and channel 2 of the CRO to pin 6 of the OP AMP (unknown
frequency).
7. Repeat steps (3) to (6) for two more combinations of R1,R2,C1, C2.
Observations and Calculations:
To measure frequency of oscillations:
R1= __________ Ω, R2 = ___________Ω
Obs. No. C1
µ F
C2
µf
T obs
(sec.)
T cal.
(sec.)
F Obs.
KHz
F exp.
KHz

To determine signal voltages:
Obs.
No.
Voltage
(peak to
peak) at
pin 3
(a)
Voltage
(peak to
peak) at
pin 2 (b)
Voltage
(peak to
peak) at
pin 6
(c)
Negative
Feedback/Output
Voltage =b/c
Closed
loop
voltage
gain=
c/a
Observed
(b/c) X
(c/a)
Expected
(b/c) X
(c/a)
To measure frequency of oscillations using Lissajous figures:
Obs. No. C1
µ F
C2
µf
Lissajous
Figure
Known
Frequency
KHz
Unknown
Frequency.
KHz

Results:
R1= __________ Ω, R2 = ___________Ω
Obs.
No.
C1
µ f
C2
µ f
Tobs
sec
Fobs
KHz
Fexp
KHz
Observed
b/c X c/a
Expected
b/c X c/a
Comments:
Conditions for sustained oscillations:
1. The loop gain βAv around the feedback loop should be greater than or equal to
unity, i.e βAv>1.
2. The net phase shift around the feedback loop must an integral multiple of 2π
radians or 360.

9. Hall Effect
Aim:
To determine the Hall coefficient, and hall angle of the given semiconductor.
Apparatus:
Hall Effect module, millimeter, voltmeter, electromagnet separated by specific gap.
Formulae:
1. 𝑉𝐻 =
𝑅 𝐻
𝑡
× B × 𝐼𝑠 × 10-8⟹ 𝑅 𝐻=
𝑡
𝐵
(
𝑉 𝐻
𝑖 𝑆
) × 10+8 =
𝑡
𝐵
× slope x 10+8
2. From the plot of 𝑉𝐻 vs B
𝑅 𝐻 =
𝑡
𝐵
× 𝑠𝑙𝑜𝑝𝑒 × 10−3
3. η=
1
𝑅 𝐻 𝑒
=
1
𝑅 𝐻×1.6×10−19
Circuit diagram:

Importance:
The measurement of the Hall Effect gives the following important quantities.
1. The sign of current carrying charges is determined.
2. From the magnitude of the Hall coefficient, the number of charge carrier per unit
volume can be calculated.
3. The mobility is measured directly.
4. It can be decided that the material is metal, semiconductor or insulator. Hence one
thing should be remembered that not all metal have a (-)ve hall coefficient but some have
(+)ve RH if charge carrier are holes; and if both holes and (𝑒 ̵ ) contribute to the
conductivity, then RHcan be (+)ve or (-)ve depending upon the mobility and relative
density.
Procedure:
Setting up the instrument:
1. Connect the electromagnet to the magnet terminal.
2. Connect the Hall Probe into socket provided on the panel.
3. Keep magnet current control and probe current control in maximum anti-clock
wise position.
4. Plug the instrument into the MAINS and SWITCH ON.
Experiment:
1. Keep the current selector switch in MAGNET position and set the magnet current
at a desired value say Im= 100 mA. Do not disturb this control till one set of
reading is complete.
2. Keep the current selector switch in PROBE position. The meter will indicate
some sample current Is the Probe output may show some reading and the zero
control can be used to nullify the offset voltage of the Probe.
3. Carefully insert the probe through the plastic nut provided on the electromagnet
and the screw it so the plane of the plate is parallel to the face of the pole pieces.
Now the plane of the crystal will be at right angles to the direction of the field.
Slowly turn the probe output meter reads maximum reading. Do not disturb the
probe till end of the experiment.
4. Set the probe current (Is) to various values between 40 mA to 400 mA and note
down the values of probe output (VH) for these values.
5. Repeat the procedure for two different magnet currents say Im = 200 mA and
Im =3 00 mA.

6. Plot the graph of VH (probe output in mV) against Is (probe current) Rʜ, Hall
coefficient of crystal material in cm³/coulomb can be calculated. This coefficient
will be characteristic of the material of the Hall plate. For a given plate Rʜ and t
are constant.
7. The plate gap is 0-20mm adjustable. If the pole is reduced, the magnetic field will
increase and vice-versa. The calibration chart is available for different magnet
current Im for three different pole gaps (10 mm, 15 mm, 20 mm). One can use
this data to get the value of B.
8. Now keep the current selector switch in PROBE position. Set up the current Is to
40mA. Now keep current switch in MAGNET position. Note down the values of
probe output (VH) for various settings of magnetic field by
Im=100,200,300,400,500mA. Find B from calibration chart.
9. Plot a graph of VH versus B. hence calculate RH and η.
Source of Error:
1. Due to the temperature gradient errors are introduced. These errors are eliminated
by reversing the current and taking another pair of readings with magnetic field
normal and reversed.
2. Even in the absence of magnetic field, a potential difference due to imperfect
alignment is developed between A and B, this is eliminated by reversing the
magnetic field and measuring the potential difference between A and B again.
Calibration Chart for Magnetic Field:
Magnet
current mA
Magnetic field in gauss
Increasing current Decreasing current
10 mm 12 mm 20 mm 10 mm 15 mm 20 mm
50 210 130 100 270 170 110
100 390 270 180 480 300 200
150 580 390 220 690 420 300
200 770 510 360 880 550 390
250 970 630 450 1060 670 490
300 1170 760 540 1270 800 580
350 1370 870 620 1420 900 650
400 1570 1000 710 1630 1030 730
450 1770 1120 810 1810 1130 820
500 1960 1240 900 1960 1240 900

Observations:
Part I :
Thickness of the sample = t = 0.0148 cm
lM
mA
B
Gauss
ls
mA
VH (mV) VH
(mV)
lM
+
ls
+
lM
+
ls
-
lM
-
ls
+
lM
-
ls
-
Part 2:
lM
mA
B
Gauss
ls
mA
VH (mV) VH
(mV)
lM
+
ls
+
lM
+
ls
-
lM
-
ls
+
lM
-
ls
-

Calculations:
𝑅 𝐻=
𝑡
𝐵
(
𝑉 𝐻
𝐼𝑠
) × 10+8 =
𝑡
𝐵
× slope x 10- 3
=___________________cm3/Coulomb
η=
1
𝑅 𝐻 𝑒
=
1
𝑅 𝐻×1.6×10−19
= ____________________________/cm3
Graphs:
Results:
1. Hall coefficient RH = ________cm3/Coul
2. η = ____________/cm3.

10. LM 317 as Voltage Regulator
Aim:
To study the use of LM 317 as a variable voltage source
Apparatus:
LM 317, Power supply, resistance , Voltmeter , Current source
Circuit diagram:
I. Design:
𝑉𝑖𝑛 = Volts
𝑉𝑟𝑒𝑓= 1.25 volts
𝐼 𝑎𝑑𝑗 = 100 mA
𝑉𝑂( 𝑚𝑖𝑛)= 𝑉𝑟𝑒𝑓
𝑉𝑂( 𝑚𝑎𝑥) = 𝑉𝑖𝑛 − 3 volts
= Volts

𝐼 𝑚𝑖𝑛 = 50 × 𝐼𝑎𝑑𝑗 = 50 × 100𝑚𝐴 = 5𝑚𝐴
.˙. R1 =
Vref
Imin
=
1.25Volts
5mA
= Ω
𝑅2 = 0Ω
R2 (min) =
Vo(max )
−Vref
Imin
= Ω
Procedure:
1. Determine the values of 𝑅1and 𝑅2 required to construct the above circuit.
2. Connect the circuit.
3. Measure the minimum and maximum values of 𝑉𝑂 . Compare the same with expected
values.
4. Select a suitable value of 𝑉𝑂 . Obtain and plot the load regulation characteristics with
the maximum load current 𝐼𝐹𝐿 lying between 200 mA to 300 mA . Hence determine the
percentage load regulation at IFL.
5. Measure the input ripple 𝑉𝑖𝑟( 𝑝−𝑝)at 𝐼 𝐹𝐿 .
6. Calculate the output ripple for an assumed ripple rejection of 90 dB.
Given ripple rejection in dB = 20 log 10
Vir (p−p)
Vor(𝑝−𝑝)
Observations:
𝑉𝑖𝑛= volts
Measured 𝑉𝑂( 𝑚𝑖𝑛)= volts
Measured 𝑉𝑂( 𝑚𝑎𝑥)= volts
𝑉𝑁𝐿 = 𝑉𝑂 = volts

Obs.
No. RL ‘ k Ω ’ VL ‘volt’ IL = VL / RL ‘mA’
1
2
3
4
5
6
7
8
9
10
Input ripple 𝑉𝑖𝑟( 𝑝−𝑝)(at IFL = mA) = volts (p-p)
Calculations:
1. % Load regulation (at 𝐼𝐹𝐿 = mA) =
VNL−VFL
VFL
x 100 % = %
2. Ripple Rejection in dB = 20𝑙𝑜𝑔10
𝑉𝑖𝑟( 𝑝−𝑝)
𝑉 𝑜𝑟( 𝑝−𝑝)
Given RR = 90 dB
.˙. 𝑉𝑜𝑟 =
Vir(p−p)
antilog (4.5)
= volt (p-p)

Graph:
Results:1. Measure range of 𝑉𝑂 = to volt.
2. 𝑉𝑜𝑟 = volt (p-p)
3. % Regulation (at 𝐼𝐹𝐿= mA ) = %

SKILLS

Skill – 1: Estimation of errors
 WHAT IS ERROR ?
Error in a measurement is the difference between the measured value and the true value
of a physical quantity.
 WHAT IS MEANT BY ERROR ANALYSIS
When the true value is not known, it is necessary to know by what margin the measured
value differs from the true value. This is done by error analysis.
 CLASSIFICATION OF ERRORS:
i] Errors which are due to known sources. E.g. Least count of apparatus, calibration of
instruments etc.
ii]Random: Errors due to unidentifiable causes.
 TYPES OF ERROR
i]Absolute Error or Instrumental Error: It is the maximum uncertainty in a measurement.
As a rule of thumb, it is equal to the least count of the measuring device.
ii]Relative Error: Ratio of actual error to correct (mean) value of the observation.
Iii] Percentage Error: Relative error expressed in percentage.
 PROPAGATION OF ERRORS:
a. If y=x1+x2 then dymax=dx1+dx2
b. For 𝑦 = 𝑥1 × 𝑥2 :
Taking log on both sides
log 𝑦 = log(𝑥1 × 𝑥2 ), log 𝑦 = 𝑙𝑜𝑔𝑥1 + 𝑙𝑜𝑔𝑥2
Differentiating, 𝑑(log 𝑦) = 𝑑( 𝑙𝑜𝑔𝑥1)+ 𝑑( 𝑙𝑜𝑔𝑥2 ),
1
𝑦
𝑑𝑦 =
1
𝑥1
𝑑𝑥1 +
1
𝑥2
𝑑𝑥2
𝑑𝑦
𝑦
=
𝑑𝑥1
𝑥1
+
𝑑𝑥2
𝑥2
c. For 𝑦 =
𝑥1
𝑥2
, using same method as above:
𝑑𝑦
𝑦
=
𝑑𝑥1
𝑥1
−
𝑑𝑥2
𝑥2
, (
𝑑𝑦
𝑦
)
𝑀𝐴𝑋
=
𝑑𝑥1
𝑥1
+
𝑑𝑥2
𝑥2
d. For y=xn 𝑑𝑦
𝑦
= 𝑛
𝑑𝑥
𝑥

ERROR ANALYSIS IN CASE OF RANDOM ERROR:
1. For a sample containing finite number of observations the error is measured by
standard deviation.
𝝈 = √
∑(𝒙 𝟏 − 𝒙̅) 𝟐
𝒏(𝒏 − 𝟏)
Where xi= individual observation 𝑥̅= mean n= Number of observations.
PHYSICALLY SIGNIFICANT FIGURES:
1. When reporting a measurement its precision is expressed in terms of digits or
significant figures.
2. The last figure represents the most uncertain figure.
3. The more significant figures a measurement contains, the more precise it is.
4. As the significant figures increase the percentage error in the measurement
decreases.
IMPORTANCE OF SIGNIFICANT FIGURES
In a single measurement it is very easy to determine the number of significant figures.
Difficulties arise when these are used in calculations producing large number of figures.
In general the, it is better to compute values containing many figures. The rounding off
should be done in the final step to appropriate significance.
Rule: the number of valid significant figure is equal to the number of significant figures
in the least accurate value that entered into the calculation.
 ESTIMATION OF ERROR
In an experiment, Surface Tension of Mercury by Quincke’s method, the
following values were recorded.
Calculate the standard error in T and by using formula: -----
Standard error in X= √
∑(𝒙 𝟏−𝒙̅) 𝟐
𝒏(𝒏−𝟏)
Where x is average of n values of x.

Obs.
No.
Surface Tension
(T) N/m *
Angle of
Contact *
1 0.532 125
2 0.487 133
3 0.495 137
4 0.539 131
5 0.517 127
6 0.502 129
7 0.499 141
8 0.547 139
9 0.517 135
10 0.533 133
(* EXAMINERS MAY PROVE DIFFERENT SET OF
OBSERVATIONS. )
Write the final value of T and θ along with error to proper significant
places.
ERROR CALCULATION IN GRAPH:
METHOD 1:
Slope 𝑚 =
𝐴𝐶
𝐵𝐶
,
=
𝑑𝑦
𝑦
+
𝑑𝑥
𝑥
,
=
𝐿𝐶𝑜𝑓 𝑦 − 𝑎𝑥𝑖𝑠
𝐴𝐵
+
𝐿𝐶𝑜𝑓 𝑥 − 𝑎𝑥𝑖𝑠
𝐵𝐶
=
0.1
𝐴𝐵𝑖𝑛𝑐𝑚
+
0.1
𝐵𝐶𝑖𝑛𝑐𝑚
Note: There is no need to multiply by the scale used for each axis.
METHOD 2:
Mean slope= m=(m1+m2)/2
Error in slope=dm=(m1-m2)/2
d(slope)/slope=dm/m

 PHYSICALLY SIGNIFICANT FIGURES :
When responding a measurement its precision is expressed in terms of
digits or significant figures.
1. The last figure represents the most uncertain figure.
2. The more significant figures a measurement contains, the more precise
it is.
3. As the significant figures increase the percentage error in the
measurement decreases.

Skill – 2: Soldering advanced circuit
1. All parts must be clean and free1 from dirt and grease.
2. Try to secure the work firmly.
3. Coat the iron tip with a small amount of solder. Do this immediately, with new
tips being used for the first time.
4. Clean the tip of the hot soldering iron on a damp sponge.
5. Then add a tiny amount of fresh solder to the cleaned tip.
6. Heat all parts of the joint with the iron for under a second of so.
7. Continue heating, then apply sufficient solder only, to form an adequate joint.
8. Remove and return the iron safely to its stand.
9. It only takes two or three seconds at most, or solder the average p.c.b. joint.
10. Do not move parts until the solder has cooled.
Circuit Diagram:
Connect circuit for transistor as a switch. Connect Vcc=+5 Volts. Measure collector
voltage at zero base voltage and high base voltage.
V in ‘Volt’ V o ‘Volt’
0.0
5.0

Skill – 3: Bread board circuit using IC’s
Aim:
To connect a circuit on breadboard from a given diagram
Apparatus:
Breadboard, circuit components, single strand wires, CRO, multimeter, Power supplies.
Theory:
When building a “permanent circuit” the component can be “grown” together (as in an
integrated circuit) soldered together (as on a printed circuit board) or held together by
screws and clamps (as in house wiring). In lab, we want something that is easy to
assemble and easy to change. We also want something that can be used with that “real”
circuit use. Most of these components have pieces of wire or metal tabs sticking out of
them to form their terminals.
How it works
The heart of the solder less breadboard is a small metal clip that looks like this
The clips is made of nickel silver (which like mock turtle soup, contain no silver), a
material which is reasonably conductive, reasonably springy, and reasonably corrosion
resistant Because each of the pairs of fingers is independent (like the coils of beauty rest
matters) we can insert the end of a wire between any pair without reducing the tension in
any of the other finger. Hence each pair can hold a wire with maximum tension. When
we combine two socket strips, three bus strips , and three binding posts on a plastic base,
we get the breadboard.
The breadboard lets us connect component together and by wiring the bus strips to the
binding posts and the binding post to the power supply, to connect the power supply to

the circuit. Now what we need is a way to bring connection from the rest of the
instruments into the breadboard.
Formulae:
Inverting Amplifier
1. Output voltage = Vo (expected ) = −
𝑅f
Rin
× 𝑉𝑖𝑛
2. Voltage gain = 𝐴 𝑣 =
𝑉0
𝑉𝑖𝑛
= −
𝑅 𝑓
𝑅 𝑖𝑛
Circuit Diagram:
Layout

Procedure:
1. Understand the circuit diagram and draw a rough layout plan as you would place
the device, components and wires on the given breadboard.
2. Insert the device, components and single core wires in the breadboard locations.
3. Test the circuit operation and record at least two observations of different input
and output levels for do signals.
Observations:
Vin (V)
Vout(Observed)
(V)
Vout(Expected)
(V)
Av
Result: Gain of the inverting amplifier Av =_______

Skill – 4: Optical Leveling of Spectrometer
Aim:
Optical Levelling of the prism table.
Apparatus:
Sodium Mercury source, Spectrometer, Prism, Prism Stand.
Diagram:
Procedure:
1. Place the prism on the centre of the prism table with its base BC facing the base stand
and the vertex A pointing towards the collimator.
2. Observe the reflected image of the slit with the naked eye from the face AB of the
prism.
3. Now move the telescope at the position T as shown in the naked eye from the face AB
of the prism.
4. Adjust the screws at X and Z so that the image of the slit is symmetrical with respect to
the horizontal cross wire of the eyepiece of the telescope.
5. Now observe the reflected image of the slit with the naked eye from the face AC of the
prism.
6. Move the telescope at the position T2 as shown in the above diagram so that the image
of the slit is seen in its fie1ld of view.
7. Adjust the screw at Y so that the image of the slit is symmetrical with respect to the
horizontal cross wire of the eyepiece of the telescope.
8. Repeat the steps 2-7 until the image of the slit as seen from the eyepiece of the
telescope is symmetrical with respect to the horizontal cross wire.

Skill – 5: Laser beam profile
Aim:
Study of laser beam intensity across its diameter.
Apparatus:
LASER source, LDR, travelling microscope, convex lens, Reference pin etc.
Procedure:
1. The LASER beam and LDR should be kept at sufficiently large distance
approximately 3 meters, so that we get a beam of appreciable size on LDR.
2. The LDR can be mounted on a travelling microscope and placed in a such way that the
surface of LDR is exposed to the LASER beam. Variation of the intensity of LASER can
be done by slightly varying the LDR exposed area.
3. Starting from one end of the edge of the diverged beam the distance is noted at the
interval of 0.1 cm and and corresponding resistance of LDR is measured by DMM till the
other end of the divergent beam is reached (along the diameter of the diverge beam).
4. Plot a graph of (1/R) versus distance.
ObservationTable:
Microscope Reading X
cm
Resistance “R”
Ω
(1/R) Siemen
Graph:

Skill – 6: Use of electronic balance: radius
of small ball bearing
Aim:
To use pen balance to determine the radius of small ball bearings and the number
of ball bearings.
Apparatus:
Pan balance, ball bearings, bottle with stopper.
Procedure:
1. Find the mass ‘M’ of ‘N’ ball bearings by using single pan balance.
2. If ‘r’ is the radius of the ball bearing then
M = N(
4
3
) 𝜋r3
𝜌
𝜌 = density of the material of ball bearings.
3. Measure the diameter of the ball bearings by using micrometer screw gauge
and hence find the number ‘N’ of the ball bearings.
Observations:
1. Mass of empty bottle with stopper = m0 = ________________ g
2. Mass of bottle + N bearings = m1 = _________________ g
3. Mass of N bearings = (m1 − m0) = M = ______________ g
Density of material of ball bearing = 𝜌 = 7.86 g/cc.
To determine the radius of ball bearings
Least count of screw gauge = ___________________ cm
Zero error of screw gauge = ____________________ cm

MSR
Cm
CSD
Cm
MSR + (CSD ±ZE) LC
Cm
Mean ‘d’
Cm
Radius r
cm
Mean r = _______________ cm
Number N = (
3M
4πr3 𝜌
)
= ___________________
Results:
1. Radius of ball bearings = _________________ cm
2. Number of ball bearings = ________________

Skill – 7: Dual trace CRO: Phase shift
measurement
Aim:
To measure the phase difference between input and outnput voltage for a given circuit.
Apparatus:
Signal generator,dual trace CRO,bult up circuit,connecting wires.
Formulae: Method - 1
Phase difference θ=(t/T)*3600
T=time lag/ lead between input and outpu.
T=Time period of the waveform.
Method - 2
1. Phase difference θ = sin -1 (x/x0) if the ellipse lies in the first and the third
quadrant.
2. Phase difference θ=180-(sin-1(x/x0)), if the ellipse lies in the second and
the fourth quadrant.
Circuit Diagram:

Procedure:
1. Connect the sine wave generator to the input of RC network.
2. Connect channel 1 of CRO to the input channel 2 to the output of circuit.
3. Observe the input and output wavwforms for the cut off frequency fc.
4. Determine the phase shift(θ) : θ=(t/T)*3600
Where ‘t; is the time lag/lead between the input and output .’T’ period of wave forms.
5. Repeat the steps for two more values of the input frequency between(fc/5) 5fc
ObservationTable:
Obs no
Input
frequency
(Hz)
t
(sec)
T
(sec)
θ=(t/T)*3600
1
2
3

Skill – 8: BG: C1 /C2 by comparing θ1 / θ2
Aim:
To determine the ratio of the capacitances C1/C2 using a mirror galvanometer.
Apparatus:
Mirror galvanometer with lamp and scale arrangement, resistance boxes, charge-
discharge key, tap key, dc supply, connecting wires.
Formula:
𝐶1
𝐶2
=
𝜃1
𝜃2
Where 1 and 2 are the ballistic throws obtained in the galvanometer for
capacitances C1 and C2 respectively.
Circuit diagram:
Procedure:
1. Place the lamp and scale arrangement on the table at about 1 meter from the
galvanometer. Obtain a bright spot.
2. Connect the Circuit.
3. Keep P small and Q large.
4. Connect C1.Charge C1 by charge-discharge key. Now discharge the capacitor
through the galvanometer. Observe the ballistic throw 1.

5. For the same value of P and Q,charge C2 and obtain the ballistic throw 2
discharging the capacitor through the galvanometer.
6. Hence, Calculate C1/C2.
Observation:
P=_________; Q=_________ ; E=__________volt.
Capacitor Ballistic Throw(cm)
C1 1=
C2 2=
Calculation:
𝐶1
𝐶2
=
𝜃1
𝜃2
_ = __________
Result:
𝐶1
𝐶2
=

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