pes school of engineering - pesit south campus€¦ · · 2016-05-30engineering physics lab...

PHYSICS LAB MANUAL PESSE

PES INSTITUTE OF TECHNOLOGY (BANGALORE SOUTH CAMPUS)

LABORATORY MANUAL

I & II SEMESTER

ENGINEERING PHYSICS LAB (10PHYL17/27)

Faculty In-charge: Dr. Syed Khasim Mr. Gajanan V Honnavar Mrs. Mohana Lakshmi Dr. Muhammad Faisal

Name of the Student : BRANCH : UNIVERSITY SEAT NO. : SEMESTER & SECTION : BATCH :

ENGINEERING PHYSICS LAB (10PHYL 17/27) 1 I/II SEM


CONTENTS

Sl. No. Name Of The Experiment

Page No.

01 LCR Series and Parallel Resonance Circuits 03

02 Zener Diode Characteristics 07

03 Transistor Characteristics 11

04 Photo Diode characteristics 15

05 Laser diffraction 19

06 Verification Of Stefan’s Law 23

07 Determination of Fermi Energy 25

08 Determination of dielectric constant 27

09 Y by uniform bending 31

10 Torsional Pendulum 35

11 Newton’s rings 38

SCHEME OF EVALUATION - VTU PRACTICAL EXAMINATION

Details of Evaluation

Max. Marks

1. Formula with units, circuit diagram and tabular column. 2+1+2=5

2.Experimental Setup, measurement and conduction of experiment 3+9=12

3.Calculation, graph and result 4+1=5 4.Viva –voce 3 Total marks for one experiment 25



Experiment No. - 1

L.C.R SERIES AND PARALLEL RESONANCE CIRCUIT

Circuit diagram:

Formula:

1. The inductance of the given inductor is Cf4π

1L

22r

= ………………henry

Where fr resonant frequency of the LCR circuit in series/parallel

C capacitance of the capacitor used

2. Band width, B.W = f2 − f1……….hertz

3. Quality factor , 12. ff

rfrfQ WB −

==



Experiment No. - 1

L.C.R SERIES AND PARALLEL RESONANCE CIRCUIT

Aim: 1. To study the frequency responses of the Series and Parallel Resonance circuits. 2. To determine the unknown value of the given inductor, bandwidth and quality

factor for the series and parallel resonance circuits.

Apparatus: Audio frequency oscillator, Inductance of unknown value, resistor and capacitor of known values, a.c. millimeter, circuit unit and patch cords. Procedure:

Series Resonance:

1. Connect the circuit as shown in the diagram (fig 1), with suitable values of C & R

2. The output of the oscillator is adjusted suitably and is kept constant through out

the experiment.

3. Switch on the power supply and set the amplitude to maximum.

4. Increase the frequency from 1000 Hz to 10000 Hz (in suitable steps) and note

down the corresponding readings of the current in the milliammeter.

5. During this variation of frequency, the frequency fr for which current reaches its

maximum value (Imax), called the resonance frequency, must be measured with

maximum accuracy.

6. A graph of frequency taken along the X-axis against the current along Y-axis is

plotted and fr and Imax are marked.

7. A straight line is drawn parallel to frequency axis at the point Imax/ 2

(= 0.707 Imax approximately) on Y-axis.

8. The line intersects the curve at two points which correspond to frequencies f1 & f2

respectively. From graph, the quality factor is evaluated by using the equation,

Q= WBf r

. where, B.W = f2-f1 is the band width.



Observations: R =__________ Ω C =__________ µF

Tabular Column:

Series LCR circuit Parallel LCR circuit

Parallel Resonance Frequency

(Hz) I (mA )

Series Resonance Frequency

(Hz) I (mA )



Parallel Resonance:

1. Connect the circuit as shown in the diagram (fig 3), with suitable values of C & R

2. The output of the oscillator is adjusted suitably and is kept constant through out

the experiment.

3. Switch on the power supply and set the amplitude to maximum.

4. Increase the frequency from 1000 Hz to 10000 Hz (in suitable steps) and note

down the corresponding readings of the current in the milliammeter.

5. Plot a graph of current Vs frequency. You will get the curve as shown in figure 4

6. Note down the frequency corresponding to minimum current (Imin), it is called

resonance frequency (fr).

7. Multiply the minimum value of current by 2 . Draw a straight line through this

point (Irms value), which runs parallel to x-axis. This line cuts the curve at two

points, which correspond to frequencies f1 & f2 respectively.

8. Using graph, calculate quality factor using the relation Q=WBf r

.,

where B.W = f2 – f1 (band width).

9. Using the values of capacitance and resonating frequency calculate the value of

inductance by using the formula L = 1/ (4π 2fr2C).

Result:

Type of Resonance

Resonant frequency

fr(Hz)

L (H)

Band Width B.W(Hz) Q=

WBf r

.

Series Resonance

Parallel Resonance



Experiment No. - 2

ZENER DIODE CHARACTERISTICS

Circuit Diagram:

Graph:

Formula:

Forward resistance RF is given by ABBCRF = =------------------ Ω

Zener dynamic resistance RZ is given by RZ = BACB′′′′ =---------- Ω

IF (mA)

IR (mA)

A

BC

VZ

A′

B′ C ′

VK

VR VF



Experiment No. - 2

ZENER DIODE CHARACTERISTICS

Aim: To draw the I-V characteristics of a Zener diode and to determine the knee voltage, Zener voltage and input resistance. Apparatus: Zener diode, 0 to 20 V DC power supply, digital voltmeter (DVM), digital DC milliammeter (DCM), resistor, circuit unit and patch cords.( All the devices are inbuilt in a transistor kit) Principle: A Zener diode is a junction diode with heavily doped p and n regions. A forward biased Zener diode conducts like an ordinary p-n junction diode, when the biasing exceeds the junction barrier potential. When reverse biased, the reverse saturation current is very small of the order of µ A until the breakdown voltage is reached. At one particular reverse voltage (called breakdown voltage), the resistance of the diode becomes very low and the reverse current increases abruptly. Since the voltage across the diode is almost a constant as long as it is conducting, it is used as a voltage regulator. Procedure:

Forward Bias Characteristics:

1. The circuit for studying the forward bias characteristics of a Zener diode is as

shown in the figure1.

2. First identify the terminals of Zener diode, there will be a black colored circular

band on one side of the Zener diode. It is read as n-type of Zener diode and the

other as p-type.

3. Connect p-type side to positive terminal and n-type of the Zener diode to the

negative terminal of the battery.

4. Before switching on the power supply, turn the power supply knob to minimum

and also set the digital ammeter towards milliammeter reading.

5. The applied voltage VF is increased from zero volt in steps of 0.1 V (using

adjustment knob) till the DCM reads a value of current (say about 0.6 V).

6. Then using fine adjustment knob vary the voltage in steps of 0.04 V (or 0.05 V)

up to a maximums of 0.8 V and the corresponding reading of current IF is noted at

each step and are tabulated.



Tabular Column: Forward bias characteristics Reverse bias characteristics

VF (in V) IF (mA)

VF (in V) IF (mA)

Result:

For the given Zener diode, it was found that, 1. The knee voltage, VK =________ V

2. The zener breakdown voltage, VZ =________ V 3. The forward resistance, RF = ________Ω. 4. The dynamic resistance, RZ= ________Ω.



Reverse Bias Characteristics

The circuit for studying the reverse bias characteristics of a Zener diode is as shown in the figure 2. To modify a forward bias circuit into reverse bias circuit, two changes have to be done.

1. First, interchange the terminals of Zener diode and secondly switch over the

DCM from milliammeter to micro ammeter.

2. Also the power supply knob is turned to minimum. The applied voltage VR

is increased from zero volt in steps of 1 V till the milli ammeter (DCM)

reads a value of current.

3. Once a small increase in current is observed, the voltage is increased in

steps of 0.1 V

The plot of V-I characteristics graphs 1. Take a suitable graph sheet divided into four quadrants. In the first quadrant

choosing appropriate scale plot the VI characteristics of forward bias. In the

third quadrant Plot the VI characteristics for reverse bias mode choosing

appropriate scale.

2. A graph of current versus voltage for both forward bias and reverse bias of

zener diode looks as shown in figure 3.

3. To determine the forward bias knee voltage, linear portion of forward

characteristics curve, is extrapolated downwards to cut x-axis. The voltage

corresponding to that point is called forward knee voltage VK.

4. To determine break down voltage in reverse bias characteristics, identify a

stage after which the reverse current rises steeply. The portion of curve that

forms a straight line is extrapolated upward to meet at X-axis. The voltage

corresponding to that stage on –ve x-axis is called reverse breakdown

voltage VRB.



Experiment No. - 3

TRANSISTOR CHARACTERISTICS Circuit Diagram: I µA mA

Where, VBB and VCC = Power Supply VBE = Base emitter voltage

VCE = Collector emitter voltage B = Base, C = collector, E = emitter IB = Base current, and IC = Collector current.

Formula:

1. Input Resistance, Ri = ABBC

=-----------------------Ω

2. Output Resistance, Ro = BACB′′′′=----------Ω

3. β=B

C

II

∆∆

= IIII

BB

CC

12

12

−

−

Where, β is the current amplification factor, =BI∆ II BB 12

− is the change in base current,

= CI∆ II CC 12− is the corresponding change in collector current.

4. β+

β=α

1

C

+

-

B IC

Earth

+

_ - +

VCCVCEVBB

-

+

VBE

B

E

NPN



Experiment No. - 3

TRANSISTOR CHARACTERISTICS Aim: To study the input and output characteristics of the given NPN transistor in the common emitter mode and calculation of input resistance, output resistance & amplification factor.

Apparatus: Given Transistor (NPN), variable DC power supply, DC micro ammeter, DC milliammeter, DC voltmeter, patch cords. (All these devices are internally connected in the kit).

Principle: Transistor is a three terminal semi-conducting device basically used for amplification. It is operated in three different modes viz., CE mode, CB mode and CC mode. In any transistor emitter-base junction is always forward biased and collector-base junction is reversed biased.

In CE mode, the following characteristics are studied.

Input characteristics: The study of variation in input current (base current) with input voltage (base−emitter voltage) at constant output voltage (collector−emitter voltage). Output characteristics: The study of variation in output current (collector current) with output voltage (collector−emitter voltage) at constant input current (base current). Procedure:

1. The common emitter circuit for studying the transistor characteristics of a

NPN transistor is as shown in the figure.

2. Identify the base, the collector and the emitter leads of the given NPN

transistor and then insert it into the transistor socket in the circuit.

3. Before switching on the circuit, turn all power supply knobs to the minimum

position.

Input characteristics: 1. The DC voltmeter is connected across collector-emitter junction.

2. The collector emitter voltage VCE is set to 1 volt by varying VCC.

3. The voltmeter is disconnected and then connected across base-emitter

junction.

4. Keeping VCE = 1 volt ,as constant , the base-emitter voltage VBE ( input

voltage) is increased from zero volt in steps of 0.1 V up to 0.8 V, by varying

the knob VBB and the corresponding values of base current IB are noted from

the micro ammeter.

5. A graph of VBE along X-axis and IB along Y-axis is plotted.



Tabular Column: Input Characteristics Output Characteristics

Dependence of IB on VBE Dependence of IC on VCE for constant IB

for constant VCE

IB = 75µA IB=100 µA VCE (volts) IC ( mA ) IC ( mA )

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7 0.8 0.9 1.0

VCE = 1 V

VBE volt

IB

(µA ) 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Graph:

IC2

IC3

IB (µA)

VBE (Volt)

VK

ENGINEERING PHYSICS LAB (10PHYL 17/27)

IC

IC1

VCE (Volt)

13 I/II SEM


Output Characteristics:

1. To study the output characteristics of the transistor, again turn all the power

supply knobs to minimum position.

2. The input current IB is set to 75 µA by varying VBB. Keeping IB =75 µA apply

different values of collector-Emitter voltage VCE and note down

corresponding collector current values IC in milli amperes.

3. Tabulate all the values in relevant tabular column for out put characteristics.

Care should be taken that while taking each reading of IC, IB should read the

constant values i.e. IB = 75 µA.

4. Now for other trial set base current IB for 100 µA and repeat the same

procedure. Now a graph of VCE along X-axis and IC along Y-axis is plotted

5. A graph of output voltage VCE along X-axis and output current IC along Y-

axis is plotted for input current IB for 75 µA and 100 µA as shown in the

diagram.

6. The value of β can be calculated using the formula , β= IIII

BB

CC

12

12

−

−

Result:

For the given NPN transistor,

1. The input and output characteristics are obtained,

2. The knee voltage, VK =______________ V

3. The value of input resistance =_____________Ω

4. The value of output resistance= _____________Ω

5. The value of β = ______________

6. The value of α = ______________



Experiment No. – 4

PHOTO DIODE CHARACTERISTICS

Circuit diagram:

Tabular Column: Table -1

IPD (µA) VPD (V) PLED =20mW PLED =30mW 0

-0.1 -0.2 -0.3 -0.4 -0.5 -1.0 -2.0

Variation PD voltage with current Negative voltage and current indicate the reverse bias

Graph:

PD I-V characteristic curves




PHOTO DIODE CHARACTERISTICS

Aim: To study the I-V characteristics of the given photo diode (PD) in reverse bias and also to study the variation of photocurrent as a function of reverse voltage & intensity

Apparatus: Photodiode experimental setup consisting of 0-3V regulated power supply, 0-2mA digital dc current meter, 0-20V digital dc volt meter, white light LED module and photo diode LED type. A transistor drive for LED is used. The LED power (PLED=VLED ILED) is directly read from the dial marked on the LED power supply.

Principle: Photodiodes are semiconductor devices responsive to high-energy particles and photons. Radiation-sensitive junction is formed in a semiconductor material whose resistivity change when illuminated or by the photon. Photodiodes operate by absorption of photons or charged particles and generate a flow of current in an external circuit, proportional to the incident power.

Procedure:

I-V Characteristics of PD

In this part of the experiment, PD current and voltage are recorded for different LED input power.

1. The LED (white light) and PD are placed face to face as shown in Figure-1,

and the light arrangement is switched on. LED power is set to 10mW by

positioning the knob to its minimum position. After confirming that the LED

is glowing and PD current in the meter, the cover is placed so that external

light will not affect the readings. Positive of the PD is connected to negative

of the power supply and Negative of the PD is connected to positive of the

power supply. This reverse biases the photo diode.

2. The LED power is set to 10mW on the dial and VPD is set to -0.10V and the

IPD is noted

3. Trial is repeated by increasing VPD in suitable steps up to maximum of 2V and

the corresponding IPD is noted in Table 1.

4. Experiment is repeated by increasing the LED power to 20 and 30mW. In

each case variation in VPD and corresponding IPD are noted in Table 1.

5. A graph is drawn taking VPD along X-axis and IPD along Y-axis as shown in

figure. The equal spacing between characteristic curves indicates linearity of

photo current with light intensity.



Tabular Column: Table-2

VPD = 1 V PLED

(mW) IPD (µA) 10 11 12 13 14 15 18 21 24 30 38 50

PD current variation with LED power Graph:

Variation of PD current with LED po

Formula:

1. Responsivity of the photodiode, Rλ =LED

PD

PI =

BCAB

2. Actual responsivity of the photodiode = 66.0λR

=----

ENGINEERING PHYSICS LAB (10PHYL 17/27) 17

A

w

=-

--

B
C
er (VPD=-1V)

------------AW-1

----------- AW-1

I/II SEM


Variation of PD current with Intensity In this part of the experiment, voltage across the PD is set to -1 V and the PD current

IPD is recorded for different LED input power.

1. To study the variation of PD current as a function of intensity, initially the

voltage across PD is set to -1V by varying 0-3V power supply and the PD

current IPD is noted.

2. The LED power is increased to 11mW and VPD is again set to -1V and the

corresponding PD current is noted.

3. Trial is repeated for input power 12, 13mW etc up 50mW. In each case VPD is

set to -1V and IPD is noted in Table 2.

4. A graph showing the variation LED power on X-axis and PD current on

Y-axis is drawn as shown in figure and a straight line graph is obtained.

Result:

For the given photo diode,

1. The current-voltage characteristics of the given photodiode in reverse bias

and the variation of photocurrent as a function of reverse voltage and

intensity are studied.

2. Responsivity of the given photodiode, Rλ =---------------- mA/W.

3. Actual Responsivity of the photodiode =------------------- mA/W.



Experiment No. - 5

DIFFRACTION GRATING Ray Diagram:

Left Right

Order-m1 12 2 77

Diffraction Pattern

Formula:

1. The grating constant is determined by using the formula ,d = 1/N meter

Where N is the number of lines on the grating

2. Wavelength of laser source λ is given by λ = d sinθm / m

Where d is grating constant or the distance between two consecutive rulings on

grating and m is the order of diffraction maxima.

Observations:

1. Distance between the grating and screen, f = ------------- m.

2. Grating constant or the distance between two consecutive rulings on grating

For 250 LPI, d = ------------m

For 500 LPI, d = ------------m



Experiment No. - 5

DIFFRACTION GRATING Aim: To determine the wavelength of the Laser light using diffraction grating. Apparatus: Diffraction grating (500 LPI & 250 LPI), diode LASER source, image screen, meter scale. Principle: Laser is a monochromatic, coherent and intense beam of light. When laser

falls on a grating, it undergoes diffraction and produces alternative bright spots on the

screen. The spots become well observable if the grating constant is comparable with the

wavelength of the laser. If θm is the angle through which light is diffracted to give the mth

order diffraction then the condition to be satisfied is

d sin θm = mλ

Where, m is the order of the spots

λ is the wavelength of the laser light

d is the grating constant and

θm is the angle of diffraction

In the experiment, grating of known value of grating constant is used. When laser is

incident on it, the spots produced due to diffraction are recorded on the screen. If ‘f’ is

the distance between the grating and the screen, Xm is the distance of the mth spot from

the central maximum, then the angle θm can be measured using

θm = tan-1f

Xm

If N is the number of lines per unit length of the grating, then the grating constant is

determined by using the formula

d = 1/ N meter



Calculation of d: We know that d = 1/N, where N is the no. of lines on grating. 1 inch = 2.5 cm For 250 LPI, d = (2.5/250) ×10-2 meters = 100×10-6 m For 500 LPI, d = (2.5/500) × 10-2 meters = 50 ×10-6 m Tabular Column:

Table-1

500 LPI grating, f =100 cm

Diffraction Order

m Distance

2xm (cm)

Diffraction angle

θ m = tan-1f

x m Sinθm

Wavelength λ = d sinθm / m

(nm)

1 2 3 4 5 6 7

Average λ1 =…….……….nm

Table-2

250 LPI grating, f =100 cm

Diffraction Order

m

Distance2xm (cm)

Diffraction angle

θ m = tan-1f

x m

Sinθm

Wavelength λ = d sinθm / m

(nm)

1 2 3 4 5 6 7

Average λ2 =……………….nm

λ = (λ1+ λ2)/2 = nm



Procedure:

1. The laser is placed on a study table and switched on. At about a meter away on

the path of the laser a white laminated wooden screen is placed. The leveling

screws of the laser are adjusted such that the laser beam exactly falls on the centre

of the screen. The exact distance between the grating stand and image screen are

noted, f = 1 meter = 100 cm.

2. The 500 LPI grating is now placed on the grating stand close to the laser source

and the diffraction pattern is observed as shown in the figure. (The equally spaced

diffracted laser spots are observed on either side of central maxima. The central

maximum is very bright and as the order of diffraction increases the brightness

decreases).

3. The center of the spots of the diffraction pattern are marked placing a paper or

graph sheet on the screen using pencil and after marking the diffraction pattern,

the image screen is removed and the distances between consecutive order of

diffraction is measured using a scale.

4. The distance between the two first order diffraction spots is measured as 2x1 cm.

5. Similarly the distance between second order diffraction spots is measured and

recorded as 2x2 cm. This is continued up to 8th order, 2x8 cm and the readings are

tabulated.

6. Using equation, θm = tan-1f

Xm diffraction angles are calculated for various

orders of diffraction and are noted in Table.

7. Using equation, λ = d sinθm / m wavelength of given laser source is calculated for

various orders of diffraction and the average wavelength is obtained.

8. The experiment is repeated for grating 250 LPI and readings are tabulated in

Table-2.

Result: The wavelength of given laser light by diffraction method using grating is…………nm.



Experiment No. - 6

VERIFICATION OF STEFAN’S LAW Circuit diagram: + --_

_

+

Bulb

V

A

+

Battery

Tabular Column:

V (volt)

I (ampere)

R = V/I (ohm)

P = VI (watt) Log P Log R

5.0 5.5 6.0 6.5 . .

15.0

Graph:

C B

A Log P

EN

Log R

GINEERING PHYSICS LAB (10PHYL 17/27) 23 I/II SEM


Experiment No. - 6

VERIFICATION OF STEFAN’S LAW

Aim: To verify Stefan’s law of radiation with a suitable graph.

Apparatus: Electric bulb, digital dc voltmeter, digital dc ammeter, power supply

Principle: According to Stefan’s law, the energy radiated per unit area per unit time by a

prefect black body is directly proportional to 4th power of its absolute temperature.

If E is the energy radiated and T is the absolute temperature, then according to

Stefan’s Law, dissipation of energy, E α T 4 or E = σ T4 ,

Where σ is Stefan’s constant.

The energy E is related to power P and temperature T is related to resistance R.

(P α E and R α T)

Therefore the above equation can be written as

P α R 4 P = σ R 4

Log P = log σ + 4log R

A graph of log p versus log R is a straight line whose slope is 4.

Procedure:

1. The circuit connections are made as shown in the circuit diagram.

2. By adjusting the battery knob, suitable voltage is applied till the bulb starts

glowing.

3. The voltage applied across the bulb is varied in regular steps (From 5 V to 15

V) and the corresponding current is noted.

4. The resistance of the bulb and the power dissipated is calculated in each case

and the readings are tabulated.

5. A graph of log P against log R is plotted and the slope of the resulting straight

line is determined.

Result:

The slope of the graph is found to be , which is close to 4.

Thus Stefan’s law is verified.




DETERMINATION OF FERMI ENERGY Diagram:

Observations:

Length of the copper wire, L =___________ m

Radius of copper wire , r = __________ m

Area of cross section of copper wire, A = = ___________ m2rπ 2

Density of copper, D= 331096.8 −× mkg

Resistance unplugged in the resistance box, S = Ω

Tabular Column:

Temperature t

( oC )

Temperature T(K)

T= (t+273) Balancing length

l (m)

Ω−

=l1

SlR 1KTR −Ω

85 80 75 70 65 60 55

=⎟⎠⎞

⎜⎝⎛

meanT

R _______________




DETERMINATION OF FERMI ENERGY

Aim: To determine the Fermi energy of copper using meter bridge.

Apparatus: meter Bridge, copper wire, battery, galvanometer, Resistance box, hot bath and thermometer.

Principle: Metals have positive temperature coefficient of resistance. When the temperature of a metal increases its resistance also increases. By noting the change in resistance with temperature for copper metal and knowing the density of copper, its Fermi energy can be calculated using the formula.

Formula:

The Fermi energy of copper is given by mean

15F T

RLAD

101.35E ⎟⎠⎞

⎜⎝⎛×= − in joules.

Where, D Density of copper in 3−mkg

A Area of cross section of the wire in m2

L Length of the copper wire in m R Resistance of the material at temperature T (in K)

Procedure: 1. The given copper coil is kept in a hot bath and its ends are connected to the left gap of

a meter bridge. A standard resistance box is connected in the right gap of the meter

bridge

2. A suitable resistance is unplugged from the standard resistance box. The sliding

contact is checked for opposite deflection in the galvanometer by pressing the wire

with sliding contact at ‘A’ and ‘C’.

3. Boiling water is poured in to the hot bath connecting the copper coil. At a temperature

of the around 850 C, the sliding contact is moved on the wire of the meter bridge from

terminal ‘A’ till the deflection in the galvanometer becomes zero. The corresponding

balancing length is noted. The experiment is repeated for every 50 C decrease in

temperature till 600 C and the corresponding balancing lengths are noted and the value

of resistance is calculated for each trial using the formula.

4. By using the mean value of R/T, the Fermi energy is calculated using the formula

Result: The Fermi energy of given copper wire is found to be ----------------------eV



Experiment No. – 8 DIELECTRIC CONSTANT

Circuit diagram:

VBa S1

S2

Discharge

Charge

Re-setter

C

R

A

B

M N S

T

P

Q

X

Where, Ba = Battery, S1 and S2 = Dual switches,

C = Electrolytic Capacitor, and R = Resistor.

Formula: Dielectric constant,

Y

+

Halt-start

K = 1.44X10-3.TP.d / (εo AR) Where, A is anode foil area in mm2,

d is the separation between the foils or the thickness of the paper in mm,

R is the resistance in ohms,

TP is in seconds,

εo = 8.85x10-12 F/m, is the permittivity of free space.

Dimensions of the capacitors:

Capacitor C1 C2 C3Length (mm) 47 114 183 Breadth (mm) 5 5 6 Separation (mm) 0.075 0.075 0.075

Area of the plate of the capacitor, A = l × b = _____________ mm2




DIELECTRIC CONSTANT

Aim: To determine dielectric constant of a dielectric material of the given capacitor by charging and discharging method.

Apparatus: 5V DC power supply, RC charging and discharging experimental setup consisting of digital stop clock 0.1 second resolution, digital dc voltmeter, set of resistors and set of capacitors of known dimensions.

Procedure: 1. The circuit connections are made as shown in circuit diagram. Select R as 100K

and Capacitor C1 and connect them in the circuit using patch cords.

2. The digital stop clock is to be reset by pressing reset button. The display indicates

00.0.

3. Switch S1 (Charge-discharge) is to be thrown to the charge position and switch

S2 (Halt-Start) is to be thrown to the start position keeping an eye on digital stop

clock and voltmeter.

4. The values of voltmeter are noted at an interval of every 10 seconds each without

pausing in between.

5. Trial is to be repeated and the capacitor is charged until voltmeter reaches steady

state (up to 4.5 Volts). In each case the capacitor voltage is to be recorded at an

interval of 10 seconds in Table.

6. When the capacitor is charged to maximum voltage (4.5V and above), the

charging is stopped and the charge discharge switch is thrown to discharge

position and the stop clock is reset simultaneously.

7. The voltage across the discharging capacitor is noted at an interval of every 10

seconds. This is done until the capacitor is discharged fully.

8. Draw a graph by taking time on X-axis and voltage along the Y-axis as shown in

Figure. The charging and discharging curve intersects at a point P, where the

voltage across the capacitor during charging and discharging remains the same

and it is measured as TP = Seconds.

9. Determine Dielectric constant using equation, K = 1.44X10-3.TP.d / (εo AR)

10. Experiment is to be repeated for C2 and C3 capacitor. Tabulate the readings in the

table and calculate K.



Tabular Column:

Voltage (V) C1, R=100KΩ



Time (sec) Charge Discharge Charge Discharge Charge Discharge

0 10 20 30 40 50 60 70 80 90 100

Graph:

Charging and Discharging curves



Result: The value of dielectric constant of the material in the capacitor is found to be

a) For C1, K = -------------

b) For C2, K = -------------

c) For C3, K = -------------



Experiment No.-9

Y BY UNIFORM BENDING

Diagram:

Formula:

1. Least count of T.M = value of one M.S.D/Total no. of V.S.D’S

L. C = cm

2. T.R = MSD+ (CVD×L.C)

3. ⎥⎥⎦

⎤

⎢⎢⎣

⎡=

hb

xmgY

dl

3

2

2

3 newton/meter2

Where, Y, is the Young’s modulus of the material of the meter scale

m, is the load for which the elevation is found

g, is the acceleration due to gravity

l, is the distance between the knife edges (m)

x, is the distance between the knife edges and near load (m)

b, is the breadth of the scale (m)

d, is the thickness of the scale (m)

h, is the mean value of elevation (m)



Experiment No.-9

Y BY UNIFORM BENDING

Aim: To determine Young’s modulus of the material of a given bar by uniform bending

method.

Apparatus: Meter scale with known dimensions, traveling microscope, two knife edges,

two scale pans, weights, round pin, reading lens.

Procedure:

1. The material of the beam (meter scale) whose Young’s modulus is to be

determined is placed horizontally on two knife edges, such that equal lengths

project from each knife edge.

2. Two identical scale pans are suspended symmetrically at either ends of the scale

at equal distances from the free ends.

3. A pin is fixed exactly at the centre (i.e. on the 50 cm mark) of the scale such

that, it stands with its tip pointing vertically upwards.

4. A traveling microscope (T.M) is brought in front of the scale and its microscope

is focused such that its horizontal cross wire is just in level with the image of

the tip of the pin (seen as pointing downwards).

5. The reading on the vertical scale is noted, which corresponds to the zero load

state of the scale.

6. A load of 50gm is placed in each of the pans due to which the beam bends, and

the pin gets displaced. The microscope is again focused to the image of the pin

tip and the corresponding reading is noted.



Observations:

m = load for which the elevation is found =150gm=150×10-3 kg g = acceleration due to gravity= 9.8 m/s2

l= distance between the knife edges =…………m x = distance between the knife edges and near load=…………m b = breadth of the scale=…………m d = thickness of the scale =…………m h = mean value of elevation=…………m Tabular Column:

TRAVELLING MICROSCOPE READINGS

LOAD INCREASING LOAD DECREASING

Trial No.

Load (gm)

MSR

CVD

1 00 2 50 3 100 4 150 5 200 6 250

TrialNo.

Load(gm)

MSR

CVD

1 250 2 200 3 150 4 100 5 50 6 00

T.M Readings in cm T.M Readings in cm Trial No.

Load (gm)

Load Increasing

TR = MSR+(LCXCVD)

Load Decreasing

TR = MSR+(LCXCVD)

Mean TR R2

(cm)

Load (gm)

Load Increasing

TR = MSR+(LCXCVD)

Load Decreasing

TR = MSR+(LCXCVD)

Mean TR R1

(cm)

Elevation for

150gm h= R2-R1

(cm)

1

00

150

h1=………..

2

50

200

h2=………..

3

100

250

h3=………..

Mean elevation for 150 gm, h = (h1+h2+h3)/3 =……………cm =……………m



7. The load in each of the pans is increased in steps of 50gm, and the

corresponding readings of T.M, are noted for each step under the heading

LOAD INCREASING (I), till the accumulated load becomes 250 gm.

8. The load in each of the pans is then decreased in same steps of 50gm, till zero

load state is reached, and the corresponding readings are entered in the column

LOAD DECREASINF (D).

9. The mean value of (I+D)/2 is evaluated and the elevation ‘h’ at the centre of the

beam for a load (m) of150 gm is found in each case whose mean value is also

evaluated. 10. The Young’s modulus of the material of the scale is calculated using the

formula: ⎥⎥⎦

⎤

⎢⎢⎣

⎡=

hb

xmgY

dl

3

2

2

3 Nm-2

Result:

The Young’s modulus of the material of the given meter scale is Y = ------------Nm-2



Experiment No.-10

TORSIONAL PENDULUM

Aim: To determine the moment of inertia of a circular disc about its axis of suspension and modulus of rigidity of a given wire by the method of Torsional oscillations.

Objective:

To understand the concept of moment of inertia and modulus of rigidity using pendulum. Apparatus:

Circular disc with chuck, suspension wire, stop clock, screw gauge and meter scale

Formula:

Moment of inertia of the disc is given by ----------- (1)

Modulus of rigidity of the material of the wire is given by

---------- (2)

where

Diagram:

Fig: Torsional Pendulum



Theory:

Torsion pendulum consists of a metal wire clamped to a rigid support at one end and carries a heavy circular disc at the other end. When the suspension wire of the disc is slightly twisted, the disc at the bottom of the wire executes torsional oscillations such that the angular acceleration of the disc is directly proportional to its angular displacement and the oscillations are simple harmonic.

Procedure:

One end of a long, uniform wire whose rigidity modulus is to be determined is clamped by a vertical chucknet. To the lower end, a heavy uniform circular disc is attached by another chuck. The diameter of the wire is accurately measured at various places along its length with screw gauge. From this, the radius of the wire is calculated. The circumference of the disc is measured by using a thread wounding round on the circular disc. The radius of the disc is calculated. The length (L) of the suspension wire (from the top portion of chucknet to the clamp) is fixed to a particular value (say 60 cm). The suspended disc is slightly twisted so that it executes torsional oscillations. The first few oscillations are omitted. By using the pointer made on the disc the time taken for 10 complete oscillations(to and fro oscillations) are noted. Three trials are taken. The mean time period ‘T’ i.e. time for one oscillation is found. The above procedure is repeated for the three different lengths of the pendulum wire. From the above values of ‘L’ and ‘T’ calculate The moment of inertia of the disc and the rigidity of modulus of the wire are calculated using the given formulae. Precautions to be taken:

The suspension wire should be well clamped, thin long and free from kinks The period of oscillations should be measured accurately since they occur in

second power in the formula Radius of the wire should be measured very carefully using screw guage since it

occurs in fourth power

Observations:

1. Determination of the diameter (d) of the suspension wire using screw gauge:



Sl.No P.S.R (x 10-3 m) H.S.R (Divisions) 1.

2.

3.

Mean (T.R) = d =

2. Determination of Time period of oscillation:

Time for 10 oscillations (second)

Trial No.

Length of the pendulum (L)x10-2 m

Time Period

1.

2.

3.

4.

Mean

Calculations:

Circumference of the disc =

Radius of the disc =

Mass of the disc

Radius of the wire

Result:

Moment of Inertia of a circular disc about the axis passing through its centre

Modulus of rigidity of the material of the wire



Experiment No. –10

NEWTON’S RINGS Diagram:

Formula:

1. ( )λnmDD

R nm

−−

=4

22

Meters

Where, R is the radius of curvature of the given lens (meter)

m, n are the ring ordinal number

Dm & Dn are the diameters of mth & nth rings

λ is the wavelength of sodium light = 5893 x 10-10 m

2. TR = MSR + (HSD X L.C )



Experiment No. –10

NEWTON’S RINGS Aim: To determine the radius of curvature of the given plano-convex lens.

Apparatus: Plano-convex lens, optically plane glass plate, traveling microscope (T.M),

stand with a turnable glass plate, sodium vapour lamp.

Principle: When waves of light are reflected at the surface of a denser medium a phase

changes of λ/2 or π is produced. The regions of crossover with the path difference 2n

(λ/2) forms the bright ring and (2n+1) λ/2 forms dark ring. And the radius of curvature of

lens can be found by measuring the diameter of the rings.

Procedure:

1. The arrangement of the plano-convex lens on the glass plate resting on its curved

surface is placed below the tilting glass plate.

2. This setup is then placed below the objectives of the microscope of the T.M, such

that the axis of the microscope is through the centre of the lens when viewed from

the top.

3. The sodium vapour lamp is switched on. The T.M unit is positioned properly to

receive the light straight to the tilting glass plate.

4. The orientation of the plate is changed slowly so that its upper part makes an

angle of 45° with respect to the direction of the incident light, at which time the

field of view suddenly becomes bright in the microscope.

5. Maximum brightness is obtained by fine adjustments.

6. Operate the rack and pinion screw till the bright patch of light modifies itself into

a series of alternate bright and dark rings.

7. The intersection of the cross-wire is made to coincide with the centre of the ring

system which is a dark patch.

8. The eyepiece is rotated to make one of the cross-wires align in a direction parallel

to the scale of the T.M.



Observations: Pitch of the head scale drum = Distance moved on the main scale

Number of rotations given to the head scale drum.

Pitch = 1mm /1 = 1mm

Total No. of division on the head scale drum, N = 100 divisions.

Least count of the traveling microscope is = Pitch/ N = 1mm/100

L.C = 0.01mm =0.001 cm

Precautions:

1. Traveling Microscope screw should be rotated in one direction only to avoid error

due to backslash.

2. Same position of coincidence of the crosswire for any ring should be considered.

3. Once the experiment is started don’t shake the table or lean on it as this will

disturb the focusing and effect the readings.


PHYS

ENGINEERIN

ICS LAB MANUAL PESSE

G PHYSICS LAB (10PHYL 17/27) 41 I/II SEM

d m d n

The radius of curvature of the given Plano convex lens R =----------------------m

Result:

9. By rotating the tangential screw, the cross-wire are moved towards left from the

center, counting the ordinal numbers of only the dark rings till the 14th dark ring is

reached.

10. Now, reversing the direction of rotation, the readings of the T.M are noted starting

from the 12th ring up tothe2nd ring, for every alternate dark ring and entered in the

L.H.S Readings column.

11. Still continuing further, and after crossing the central dark patch, the readings of

the T.M are noted in the same way from the 2nd ring onwards up to the 12th ring.

12. The readings are entered in R.H.S Readings column, from the 2nd ring to the 12th

dark ring, i.e., in the back track order in the tabular column.

13. The diameters and and also their squares are found for various rings.

14. For three pairs of ordinal numbers which satisfy m-n = 6, the value of ( )dd nm

22 −

is evaluated and their mean is found.

15. The radius of curvature of the lens is then evaluated by using the equation

)()( λnm

dd nm

−

−

4

22

, where λ =5893×10-10 m.


Tabular Column: Left hand side Right had side Left hand side Right hand side Ring

No. m MSR

(cm) HSD TR=R1

(cm) MSR (cm)

HSD TR=R2 (cm)

Diameter Dm=R1~R2

(cm)

RingNo. n MSR

(cm) HSD TR=R3

(cm) MSR (cm)

HSD TR=R4 (cm)

Diameter Dn=R3~R4

(cm)

(Dm2-Dn

2) (cm2)

12

6

10

4

8

2

Mean (Dm2-Dn

2) = …………………. cm2

= …………………..m2


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