Ex. No.: …………………… Date:………………………….

ULTRASONIC INTERFEROMETER Aim: To find i) the velocity of sound in the given liquid ii) the characteristic acoustic impendence of the liquid Apparatus: The main Parts of the interferometer are the high frequency generator

and the measuring cell. The high frequency generator is designed to excite the quartz

crystal fixed at the bottom of the cell at its resonant frequency to generate ultrasonic

waves in the experimental liquid taken in the cell. The high frequency generator

consists of an analog current meter which records the change in the anode current.

The deflection in this meter can be adjusted using the knobs provided in the

instrument. The measuring cell is a specially designed double walled cell for

maintaining the temperature of a liquid constant during the experiment. A fine

micrometer screw has been provided at the top which can lower or raise the reflector

plate in the cell.

Principle: Mechanical, longitudinal waves of frequency more than 20 KHz are

known as ultrasonics. These waves can be generasted either by piezo-electric or

magnetostriction methods. A suitably cut quartz crystal when subjected to an

alternating electric field undergoes alternate compressions and expansions (parts per

million) there by producing longitudinal waves. If the applied frequency coincides

with natural frequency of the crystal 550021

21[ ×===

tY

tvf

ρλ

1

resonance will occur and hence amplitude of the waves will be large. The waves so

generated will travel in the liquid taken in a cylindrical column and is made to reflect

from a metallic plate. The ongoing waves and reflected wave superpose to form

standing wave. These standing waves are characterized by nodes and antinodes. The

distance between two consecutive nodes or antinodes is half and wavelength of the

ultrasonic waves. If the liquid column length between quartz crystal and the reflector

is an integral multiple of λ/2, then the situation is called resonance. In this condition,

surfaces of both reflector and quartz crystal are positions of nodes (considering the

waves as displacement waves) or antinodes (considering the waves as pressure

waves). Under resonance condition the waves draw more power from the source and

accordingly the current meter show a maximum reading. In other words maximum

2

deflection of current meter indicates that the reflector surfaces is the position of node

(considering the waves as displacement waves ) and can be noted on the micrometer.

Moving the reflector plate either up or down using the micrometer screw takes the

reflector plate to series of resonances indicated by maximum current meter readings

the peaks decrease in amplitude as the distance from the source (quartz crystal) is

increased. For low attenuation, the resonance peaks are sharp and the decrease in

amplitude with distance is small, but with high attenuation the peaks are broad and die

down rapidly. The non-parallelism of quartz crystal and the reflector plate and also of

diffraction effects may give rise to the appearance of unwanted additional peaks.

Acoustic impedance: There is a similarity between the variations of sound wave

characteristics and those of certain quantities used in electrical a.c theory. Thus

acoustic pressure (p) may be regarded as being analogues to electrical voltage,

particle velocity (u), to electric current and particle displacement (y) to electrical

charge using the acoustic equivalent of Ohm’s law a quantity known as the specific

acoustic impedance Za, equivalent to electrical impedance may be defined as Za=p/u.

Like electrical impedance, Za is in general a complex quantity but for a plane

progressive wave, the imaginary component disappears leaving the real quantity.

This real quantity is called the characteristic impedance Ra and is equal to the product

of the density ρ and the velocity v of sound for the material i.e, Ra = ρv kgm-2s-1

Procedure: The measuring cell is connected to the output terminal of the high

frequency generator through a shield cable. The cell is filled with the experimental

liquid. When the high frequency generator is switched on, lthe quartz crystal

produces ultrasonic waves in the liquid. The waves move normal to the crystal and

are reflected back from the movable metal plate, producing stationary waves in the

liquid medium. The micrometer is moved slowly till the anode current meter shows a

maximum reading. At this instant, the micrometer reading (position of the reflector

plate) is noted down. In this way, the micrometer readings are obtained for a number

of successive maxima readings of the anode current. The wavelength of the ultrasonic

waves produced by the high frequency generator is noted down. The velocity of the

ultrasonic waves in the liquid is calculated.

Result: Velocity of sound in the given liquid = Characterstic impedance of the liquid=

3

Observations and Calculation:

(1) To find least count of the micrometer screw:

head screw thegiven to rotations ofNumber

scalepitch thealong travelledDistance Screw theofPitch =

= Total no. of division on the head scale =

H.S.DofNo. TotalPitch count Least =

= mm

(2) To find the wavelength of ultrasonic waves in the given liquid:

Order of Mamima (n)

Micrometer reading for Maximum

2λ=(Xn+4∼Xn) (mm)

PSR (mm) HSD PSR+(HSD × LC) mm

1

2

3

4

5

6

7

8

Mean 2λ= mm Wavelength of the ultrasonic waves, λ=

(3) Frequency of ultrasonic waves , f = (4) Density of the given liquid δ = (5) Velocity of the ultrasonic waves in the liquid V = fλ

4

(6) Characteristic impedance of the liquid Ra = δV

SERIES AND PARALLEL RESONANCES

Aim: To study the frequency response of the series and parallel resonance circuits

and to determine the inductance of the given inductor, and the quality factor of the

circuit.

Apparatus: Audio frequency oscillator, wide band AC millimameter, inductor,

capacitor, resistor, connecting wires.

Circuit Diagram

Series resonance circuit Series resonance curve

Procedure: Series Resonance: The series resonance circuit is built as shown in the circuit diagram

using an audio frequency oscillator, capacity of known capacitance C, resistor of

known resistance R and an inductor of unknown inductance L. The values of the AC

current are noted for values of the frequency of AC. The points are plotted on a graph

sheet and the series resonance curve is drawn. The resonant frequency (fR) the

resonant AC current )(I2

Imax

max are found from the graph Corresponding to the AC

current

5

the frequencies fA and fB are found from the graph and the band with (Δf=fB-fA is

calculated. The experimental value of the quality factor is calculated (Q=fR/Δf). The

unknown inductance [L = 1/4πf2RC] is evaluated.

)R1

CL

=The theoretical value of the quality factor for evaluated (Q

Parallel Resonance: The parallel resonance circuit is built as shown in the circuit

diagram. The values of AC current are noted for various values of the frequency of

AC. The points are plotted on a graph sheet and the parallel resonance curve is

drawn. The resonant frequency (fR) the resonant AC current (l min) are found from

the graph. Corresponding to the AC current min2I the frequencies f A and fB are

found from the graph and the bandwidth (Δf = fB – fA) is calculated. The

experimental value of the quality factor is calculated ⎟⎠⎞

⎜⎝⎛

Δ=ff Q R

The unknown inductance is evaluated ⎥⎦

⎤⎢⎣

⎡=

Cf R224

1Lπ

The theoretical value of the quality factor for evaluated ⎟⎟⎠

⎞⎜⎜⎝

⎛=

CL

R1Q

6

OBSERVATIONS AND CALCULATIONS

Series Resonance:

Frequency

F

(Hz)

Current

I

(mA)

Resistance. R =

Capacitance. C=

Resonant frequency fR

Maximum current. I max =

. =2

max I

FA= fB=

Band width Δf = fB - fA=

Inductance, Cfr

241L

π=

L = ………………….

Theoretical value of the quality factor.

==CL

R1Q

=

Experimental value of the quality factor.

...................

ffQ R

=

=Δ

=

7

Parallel Resonance:

Frequency

F

(Hz)

Current

I

(mA)

Resistance. R =

Capacitance. C=

Resonant frequency fR

Maximum current. I max =

. ==

=

BA ffmin12

Band width Δf = fB - fA=

Inductance, Cfr

241L

π=

L = ………………….

Theoretical value of the quality factor.

==CL

R1Q

=

Experimental value of the quality factor.

...................

ffQ R

=

=Δ

=

Result: Mean value of the inductance=

Quality Series Parallel

Theoretical

Experimental

8

Expt. No. :………… Date: ………………….

DIFFRACTION GRATING

Aim: To determine the wavelength of the lines in the mercury spectrum by minimum deviation method. Apparatus: Spectrometer, diffraction grating, mercury vapour lamp, spirit level.

Principle: An arrangement of large number of equidistant parallel slits constitutes a grating. It is prepared by drawing fine lines extremely close together on the surface of an optically flat glass plate using a diamond point. The lines act like opacities and region between two lines act like transparencies. If there are N lines in unit length, then there will be N opacities, each of width a and N transparencies, each of width b, then Na+Nb = 1 or N(a+b) = 1

Let a plane wave front AB of a light of wavelength λ incident obliquely on the grating surface XY at an angle i. As per Huygen’s principle, each point in the transparent region behaves like a secondary source and emits secondary wavelets in all the directions. Consider the parallel wavelets proceeding at an angle θ to the grating normal. Then the path difference of the two waves diffracted from the corresponding points such as A & F of transparent spaces is Δ = (EF + FG) = AF sin I + AF sin θ = AF (sin i + sin θ)

= (a+b) (sin i + sin θ)

If the waves were diffracted in the upward direction, then the path differences Δ =

(a+b) (sin i – sin θ). Thus, in general the path difference Δ=(a+b) (sin i + sin θ). If Δ

is an integral multiple of λ then the secondary wavelets will reinforce each other and

this is true for all the adjacent slits. Hence intensity maxima will occur.

i.e, Δ = (a ± b) (sin i ± sin i θ) = nλ where n = 0,1,2…. Is the condition for maxima.

9

In the above figure, the total deviation d=i + θ i.e, deviation d depends upon the

incident angle. Deviation is minimum when d1=0

i.e, i- or 0i(did

=+ θ

-ve sign indicates that θ and i are measured in opposite directions. Let D be the

= θ + θ

=2θ or θ = D/2

with this result, Δ =- 2(a+b) sin θ = nλ of 2(a+b) sin D/2 = nλ is the grasting equation.

Since a+b = 1/N above equation can also be written as

λn N

D/22sin =

Preliminary adjustments:

1. The least count of the vernier of the spectrometer is found out.

2. Initial adjustments of the spectrometer are done as follows:

The telescope is directed towards a white wall and the eyepiece is adjusted to see

the clear image of the crosswise.

• The telescope is focused to a distant object till a clear image is obtained in the

field of view. Now the telescope receives parallel rays.

• Collimator slit is illuminated using the given source of light. The slit is

adjusted for an optimum width. The telescope is brought in line with the

collimator and the collimator is focused till a clear image of the slit is sen in

the field of view.

• The turn table is leveled by means of leveling screws and spirit level.

Procedure:

The grating is mounted vertically on the grating platform. The slit is

illuminated by a light from a mercury vapour lamp and the first order spectrum on the

right or left is viewed. The grating platform alone is rotated in the anticlockwise

direction and the spectrum is followed with the telescope. At one stage the spectrum

as a whole will be found to stop. This is the position of minimum deviation.

The telescope is fixed and the tangential screw is worked such that the fixed

edge of the image of the slit (for each coloured band) turns at the vertical crosswire.

The reading for minimum deviation of each band is found on both verniers. Then the

grating is removed and the direct reading of the slit is taken.

10

11

Observation and Calculation: To calculate the L. C. of the vernier of the spectrometer:

Value of the smallest M. S. D.

No. of divisions on the vernier scale = 30

== V.S.Dof No. Total

M.S.D 1 of Value count Least

Order of spectrum n = 1 T.R. = M. S. R. + (C. V. D. × L. C )

Vernier Direct reading R0

M. S. R. C. V. D. T. R.

V1

V2

Spectral

lines Vernier

Reading at minimum deviation

position (R) Mean

D

λ =

N(D/2)Sin 2

MSR C.V.D. T.R.

Angle of min

deviation

D = R∞R0

Yellow

V1

V2

Green

V1

V2

Blue

V1

V2

12

Number of lines on the grating per unit length N = 6 × 105/m

2 Sin (D/2) = nNλ Where N – number of lines / m

N(D/22Sin =λ n - order of spectrum

D – angle of minimum deviation.

Result: Wavelength of yellow line = nm

Wavelength of green line = nm

Wavelength of blue line = nm

13

NEWTON’S RINGS

Aim:

To determine the wavelength of the given monochromic light by Newton’srings

method.

Apparatus:

Travelling microscope, sodium vapour lamp, plano convex lens of large radius of

curvature, optically flat glass plate, reflecting glass plate etc.,

Principle:

Newton’s rings are circular interference fringes in a thin air film between a plane

glass plate and a plano convex lens of large radius of curvature. The diameter (Dn) of

the nth dark ring (n is integer) is given by D2n = 4Rnλ, where R is the radius if

curvature of the plano convex lens and is the wavelength of the monochromatic light.

Since the order n of the dark ring can not be found exactly, the method of differences

of the graphical method is made use of . In this method another dark ring of order m

is also considered. Its diameter Dm is given by D2m = 4Rmλ. Since the difference (m-

n) can be found exactly, the wavelength can be calculated using the relation,

m)-4R(n/)D(D 22mn −=λ

Procedure:

The least count of the vernier of the traveling microscope is found out. The given

plano convex lens of large radius of curvature is placed on a plane glass plate to get

an air film of circular symmetry. This set up is placed below a traveling microscope.

The air film is illuminated normally by reflecting the horizontal beam of sodium light

using an inclined glass plate. The traveling microscope is focused and the newton’s

rings (bright and dark circular interference fringes) are observed. The crosswire is

made tangential to various dark rings on the left side, and then on the right side,

noting down the microscope readings each time. The diameter Dn of these dark rings

are calculated. Mean value of is found out. Knowing the radius of

curvature R of the convex surface of the lens, 1 can be calculated.

)D(D 22mn −

Result:

Wavelength of the given monochromatic light = nm

14

Observations and calculations: 1) To Calculate the L.C of the traveling microscope:

given rotations of Noscalepitch along travelledDistances screw theofPitch =

Number of divisions on the head scale =

L.C = HSD ofNo.

Pitch = cm

2) Radius of curvature of the lens R = cm 3) To find the diameter of the dark rings TR = PSR + (HSD × L.C) n-m=6 Order of the rings n or m

Microscope readings in cms DiameterD=X-Y

(cm) D2

n D2n- D2

m Left side (x) Right side (y) PSR HSD TR PSR HSD TR

16

14

12

10

8

6

Mean Value of (D2

n- D2m) =

4) Wavelength of light, λ = (D2n- D2

m) / 4R (n-m) = cm = cm

15

Ex. No.............. Date: …………….

ZENER DIODE Aim : To draw the V-I characteristic curve of a zener diode and to determine its

breakdown voltage, forward knee voltage and zener resistance.

Apparatus: The apparatus required are variable D.C. power supply, voltmeter,

currentmeter, resistor, a zener diode etc. The zener diode is a semiconductor device

made by the junction of heavily doped p and n type semiconductors.

Working: As soon as junction is formed between a p and n type materials charge

diffusion across the line of contact takes place because of charge concentration

gradients. Electrons from n side diffuse towards p side and holes from p side diffuse

towards n side. This charge displacements results in the development of an electric

field and hence a potencial which at equilibrium opposes further diffusion of charges.

The potential so developed is called contact or barrier potential. One more effect of

this charge diffusion is the neutralization of charge carriers in the neighborhood of the

junction. This region around the junction where the free charges are depleted is called

depletion region whose width depends upon the doping concentrations. Since zener

diode is a heavily dropped one, the depletion width is very small. When zener diode

16

is forward biased, the applied voltage V opposes the contact potential V0. Hence for

V=0 the net potential across the junction is V0 and no current flows across the

junction. As V is increased slowly, the contact potential decreases and hence some

charges are able to cross the junction resulting in a current flowing from p to n side.

Once V=V0 there is no barrier potential across the junction and hence charge carriers

freely move across the junction resulting in the sharp increase of current. The

external voltage V at this point is called knee voltage or cut-in voltage which is nother

but the measure of contact potential for V>V0 the increase in current is exponential in

nature. When the zener diode is reverse biased the contact potential is reinforced and

hence effectively stops the flow of charges. However, there are always some minority

carriers on n and p sides (generated due to thermal energy available) whose flow

across the junction is aided by the reverse potential.

This results in a small reverse current flowing from n to p side which remains

constant independent of applied voltage at a particular temp. However, on increasing

this –ve potential a stage will be reached wherein the vacant energy levels of the

conduction hand of n-side appear at the same height as those of filled levels in the

valence band of p-side. As per the quantum mechanical considerations, at this stage,

there is a finite probability of electrons crossing the junction which is otherwise a

barrier for their flow. Such a process is called tunneling. The tunneling effect is more

for smaller widths of depletion region, which is the case in zener diodes, because of

their heavy dropping. This property can be made use in zener diodes so as to have

breakdowns at specific voltages.

Procedure: The circuit is built up a shown in the forward bias circuit diagram. A

suitable series resistor Rs is choosed to limit the current through the zener diode well

below the maximum power rating. Voltage (V) of different values are applied across

the diode and the corresponding values of current (I) through it are noted down. The

points are plotted in the first quadrant on a graph sheet taking V along X-axis and I

along Y-axis. Next the circuit is built up as shown in the reverse bias circuit diagram.

Sets of voltage, current readings are plotted in the third quadrant on the same graph

sheet. Reading are taken carefully so that the points are evenly spread on the line in

the graph. More sets of readings should be taken in curved part of the graph. The

straight line portion of the forward bias graph is extrapolated to meet the V-axis and

the forward knee voltage is found. Similarly, the straight line portion of the reverse

biase graph is extrapolated to meet the V-axis and the break down voltage (V) is

found, the zener resistance Rz is calculated.

Result:

Forward knee voltage =

Break down voltage =

17

Zener Resistance =

Observation and Calculation: To Draw the characteristic curve of the zener diode:

FORWARD BIAS REVERSE BIAS

Voltage V (Volt)

Current I (mA)

Voltage V (Volt)

Current I (mA)

Calculations from the graph:

Forward knee voltage =

Break down voltage of the zener diode Vz =

Change in the zener voltage in the break down region ΔV =

Change in the zener current in the break down region ΔI =

Zener resistance Rz = (ΔV /ΔI)

18

Ex. No.:………………………

Date: ………………………….

ENERGY GAP OF A SEMI CONDUCTOR Aim: To determine the forbidden energy gap of smi-conductor.

Apparatus: Constant current source, current meter, voltmeter, heater, water bath,

thermometer, semi-conductor etc.

Principle: Forbidden energy gap of a material is the energy difference between the

upper limit of its valance band and the lower limit of its conduction band.

For the determination of energy gap (Eg) the semi conductor used here is in the form

of diode (p-n crystal). The forward current in such a diode is given by

If = Is ( exp [eV/nkT) – 1 ]

Where V = forward voltage across the junction, e = electronic charge, k = boltzmann

constant, T = absolute temperature, n is a constant and Is = reverse saturation current

which is given by

Is = BT3 exp (Eg/nkT)

Where B is a constant, For a low constant forward current a fair approximation

simplified the above equation as

eV = Eg – nkT

Hence a plot of V verse T gives a straight line graph with the V – intercept equal to

Eg / e at T = 0 K, from which the energy gap of the semiconductor can be obtained

Procedure: The circuit is built up a shown in the circuit diagram. The forwardbiased

Diode is kept at room temperature. A constant forward current If (< 80μA) is passed

through the diode. The room temperature id noted down. Then the diode is immersed

in a hot bath. Voltage across the diode is noted down for different temperatures as the

bath cools down. The points are plotted taking voltage across the diode along the

Y-axis and the temperature of the diode in Kelvin along the X-axis. A straight line

graph is drawn and it is extrapolated to zero Kelvin. The V-intercept of the line at

zero Kelvin is found and the energy gap of the semiconductor is calculated.

Result: The energy gap of the given semiconductor = eV

19

Observations and Calculations: Semiconductor used: Constant Forward current through the diode If = To find the voltage across the junction at various temperature:

Temperature in 0C (T)

Temperature in K Junction Voltage (V)

V – intercept of the straight line at zero Kelvin = Eg / e = V- (dV/dT) × T

20

∴ Energy gap of the given semi conductor Eg =

Ex. No.: …………………………….

Date:…………………………………..

RECTIFIERS AND FILTERS Aim: To find the ripple factors in a) Half wave rectifier, b) Full wave rectifier c) Full

wave rectifier with capacitance (C) input filter, d) Fullwave rectifier with inductance

and capacitance (LC) input filter, e) full wave rectifier with π - section filter (CLC

filter)

Apparatus: A suitable step down transformer, diodes, capacitors, inductors,

resistors, milliammeter, ac. And dc voltmeters etc.

Theory: A rectifier is a device which converts an alternating current into

undirectional pulsating current. Diodes are used to construct a rectifier. Filter circuit

may consists of inductor and capacitors. An inductor in series offers impedence for

the flow of ac but does not resist dc. A capacitor in parallel blocks dc but bypasses ac

component of the current.

The object of a rectifier is to convert the a.c into d.c. A measure of the purity of d.c

output is the ripple factor r which is defined as the ratio of two currents (or voltages)

components.

i.e, r = component dc

componentacofvaluerms)oreffective(

= dc

r

dc

r

V)rms(V

I)rms(I

=

Where Ir and Vr are the ripple current and voltage of the output.

Now Irms2 = Idc

2 + (Ir)2rms where I rms is the rms value of the total half wave rectified

output current ∴ 2dc

2rmsrmsr II)(I −=

1)II

(I

III)(I

r 2

dc

rms

dc

2dcrms

dc

r −=−

== rms

21

It can be shown that, πm

dcmrmsI

I and 2/II == with these substitutions,

1.21 1 - 4

1/I

2/Ir 2

2

m

m ==−⎟⎟⎠

⎞⎜⎜⎝

⎛=

ππ

Similarly the ripple factor due to full wave rectifier can be shown to be

r = 0.48 1 - 8

2

=π

The ripple factor in case C - filter r = fCR34

1

Procedure:

a) The circuit for half wave rectifier is built up. When the alternasting current in

the secondary of the transformer is passed through the diode the negative half

cycle of the A.C. is cut off, the positive cycle comes out as the direct current.

The pulsating D.c. from the half wave rectifier is passed through a load

resistor (RL) and the current (I) is measured through a milliameter (mA). The

direct voltage (VDC) across RL is measured using a D.C. voltmeter. The A.C.

component (VAC) of this pulsating voltage across RL is measured using a

capacitor and an A.C. voltmeter in series. The ripple factor (r = VAC / VDC) is

calculated. The ripple factors are found for the pulsating D.C. current through

different load resistors and a graph of ripple factor versus load resistance is

drawn.

b) The circuit for full wave rectifier is built up. Both the half cycle of the

alternating current in the secondary of the transformer get converted into

pulsating direct current when passed through the two diodes. The ripple factor

for the pulsating D.C. through the load resistor RL is found out. A graph of

ripple factor versus load resistance is drawn.

22

c) The circuit for full wave rectifier with capacitance input filter is built up. The

pulsating D.C. gets rid of a portion of its A. C. component when filtered

through the capacitor. The ripple factor for the filtered current through the

load resister RL is found out. A graph of ripple factor verses load resistance is

drawn.

d) The circuit for F. W. rectifier with π is inductance and capacitance input filter

is built up. The ripple factor for the filtered current through the load resistor

RL is found out. A graph of ripple factor verses load resistance is drawn.

e) The circuit for F.W. rectifier with section filter (C-L-C filter) is built up. The

ripple factor for the filtered current through the load resistor RL is found out.

A graph of ripple factor verses load resistance is drawn.

The ripple factor of the output current in the various cases are compare.

Inference:

Observation and Calculation:

23

Halfwave rectifier:

HALF WAVE RECTIFIER

Resistance Ω

Current mA

Output voltage

Vac

Output Voltage

Vdc

Ripple factor

Observed Vac/Vder =

Theoretical

1.21

Full wave rectifier:

Resistance

Ω Current

mA Output voltage

Aac

Output Voltage

Adc

Ripple factor

Observed Vac/Vder =

Theoretical

0.48 Full wave rectifier with capacitance input filter:

24

Resistance Ω

Current mA

Output voltage

Vac

Output Voltage

Vdc

Ripple factor

Observed Vac/Vder =

Theoretical 1/4√3 fCR

Full wave Rectifier with capacitance and Inductance input Filter:

Resistance

Ω Current

mA Output voltage

Vac

Output Voltage

Vdc

Ripple factor Observed

Vac/Vder =

Full wave Rectifier with C-L-C input filter

Resistance

Ω Current

mA Output voltage

Vac

Output Voltage

Vdc

Ripple factor Observed

Vac/Vder =

25

Ex. No.:………………………..

Date: ……………………………..

HALL EFFECT Aim: To determine Hall coefficient of the given semi conductor and hence its charge

carrier density.

Apparatus: Electro magnet, Hall probe, variable D. C. power supply, milliammeter,

milivoltmeter.

Principle: Consider a rectangular semiconductor specimen whose sides are paellel to

rectangular coordinate axes as shown in the fig. Let a current Ix ( assumed to be due

to +ve charge) flow along its length and a magnetic field Bz is applied parallel to its

thickness. When charges flow in the presence of a magnetic field, they experience a

force F = ev × B = evx Bz where Vx is the velocity of flow of charges. In the above

situation this force is along –ve y direction. As a result the charges are pushed

towards left, thereby creating an electric field Ey, called Hall field in the +ve y

direction. Development of this field opposes further migration of charges. Thus at

equilibrium, the leftward magnetic force equals the rightward electric field force i.e,

evx Bz = = eEy or )1.......(..........BE

vz

yx =

If the charges take a time dt to cross the length 1, then the current dt

neAl dtdq Ix ==

Where n is the carrier concentration in the specimen But ,dtv 1 x= velocity of the

carriers.

or )2.......(..........neA

I v xx =

From (1) and (2) neAI

BE x

z

y =

=newt

Ix

or Ey w = netBI zx

26

but Ex w = VH, the Hall voltage across the specimen

∴ tnet

VHBIRBI zxHzx == where RH = 1/ne called Hall coefficient.

Procedure: The circuit is built up as shown in the circuit diagram. Current (I) is

passed through the hall specimen. The millivoltmeter is adjusted to show zero hall

voltage when the hall probe is away from the magnetic field .

The electromagnet is switched on and the magnetic induction (B) is adjusted to the

desire value by adjusting the current. The Hall voltage (V) is noted. The experiment

is repeated for different values of the magnetic induction.

The points are plotted on a graph sheet with B along X-axis and V along Y-axis. A

straight line graph is drawn. Slope of the graph is calculated. RH and n are

calculated.

Result:

Hall coefficient of the given semi conductor,

Charge carrier density of the given semi conductor,

27

Observation and Calculation Material of the Hall specimen : Indium Arsenide

Thickness of the Specimen : t = 0.14 × 10-3m

Current in the Probe : I =

Charge of the electron : e = 1.6 × 10-19 Coul

To find the Hall voltage :

Magnet Current

(mA)

Magnetic Induction, B

(Tesla

Hall Voltage (V)

(mV)

Slope of the straight line (From the graph) = BV

ΔΔ

Hall Coefficient of the Specimen RH = (T/I) × Slope

= m3 / coul

Number of charge carriers per unit volume of the Specimen n = 1/eRH / m3

28

Ex. No………………..

Date:……………………

TRANSISTOR CHARACTERISTICS

Aim: To draw the input characteristics of the given npn transistor in the common

emitter mode and to determine its knee voltage, input resistance, output resistance and

current gain.

Apparatus: a npn transistor (SL – 100) variable DC power supply for input power (0-5

V), variable DC power supply for output power (0-20V), DC micrometer for input

current (0-1000 μA), DC micrometer for output current (0 – 1000mA), two DC

voltmeters (0 – 20V), connecting wires.

Circuit diagram for common emitter mode of an npn transistor

TRANSISTOR

E – emitter IB - input current

B – base LC – output current

C – Collector VBE - input voltage

LT – input power supply VCE – output voltage

HT – output power supply

Procedure: The circuit is built with the given transistor in the common emitter

mode, as shown in the circuit diagram.

29

Input characteristics: Keeping the output voltage VCE – constant (say, 1 volt), sets of

reading of input voltage (VBE) and input current (IB) are taken, and the points are

plotted on a graph sheet. The input curve is drawn. The straight line portion of the

curve is extra polated to the voltage axis to find the knee voltage (Vo). The input

resistance [R1 = )(I

V

B

BE

ΔΔ is calculated from the straight line portion of the curve.

Out put and Transfer Characteristics: Keeping the input current IB constant,

(say, IB = 40μA), sets of readings of output voltage (VCE) and output current (IC) are

taken, and the points are plotted on a graph sheet. The output curve is drawn for this

constant value of the input current. The sets of readings (VCE, IC) are also taken for

another constant value of the input current (say, IB = 80μA). The output curve is also

drawn for this constant value of the input current. The output resistance ⎥⎦

⎤⎢⎣

⎡ΔΔ

C

CE

IV

is

calculated from the straight line portion of one of the output curves (say of 80μA) in

put current.

Values of output current (IC1 and IC2) are found form the graph of the output

curves corresponding to the values of input current (IB1 and IB2) at a constant value of

the output voltage (usually, VCE= 0).

The current gain IIII

II

b1b2

c1c2

b

c

−−

=ΔΔ

=β

Observations and Calculations

Input Characteristics Output and Transfer Characteristics

Output Voltage} volt 1 VCE = Input Curent, IB

(μA)

I B1 = 40μA

I B2 = 80μA

Input Voltage, VBE

Volt

Input Curent, IB

(μA)

Input Voltage, VCE

Volt

Output Current IC1 – (mA) IC2- (mA

0.0

0.2

0.4

0.5

0.6

0.7

0.8

0.9

0.0

0.1

0.2

0.3

0.5

0.7

1.0

2.0

5.0

10.0

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Calculation of the input resistance from the input curve at the output voltage of

1 volt:

=ΔΔ

= I

V Rb

BE1

Calculation of the output resistance from the output curve at the input current of 80μA

=ΔΔ

= I

V Rc

CE1

Calculation of the current gain from the output curves at the output voltage of

1 volt:

B1B2

C1C2

B

C

IIII

II

−−

=ΔΔ

=β

Result; Knee Voltage =

Input resistance =

Output resistance =

Current gain =

31

PLANCK’S CONSTANT

Aim: To determine the Planck’s constant and the work function of the material of the

photo cathode in the given photo-emissive cell.

Apparatus: Photo-emissive cell, a white light source, optical filters, a micro-

ammeter, a voltmeter, connecting wires.

Circuit diagram: DCM

32

Principle: When light of a particular frequency falls on a photo-cathode, photo

electrons are ejected. The kinetic energy (Kmax) of the most energetic photo electron

depends on the frequency (ν) of the incident light. These electrons can be retarded by

the application of a retarding potential and the electrons can be stopped completely by

increasing the retarding potential to a value called stopping potential (Vo). Then no

current (Ip) flows in the external circuit. In the experiment the stopping potentials are

measured for lights of different frequencies. White light source and optical filters are

used to get the light of a particular frequency. Einstein’s photo electric equation is

Kmax =hν-hνo, where h is the Plank’s constant and νo, is the threshold frequency. In

the experiment Kmax =eVo where e is the electronic charge. Hence the equation takes

the form eVo =h ν – h νo

A plot of Vo versus ν gives a straight line graph ;with a slope equal to h/e and ν -

intercept νo. The work function of the photo-cathode is given by ϕ = h νo.

Procedure: The circuit is built up as shown in the circuit diagram. An optical filter is

placed in the patch of the light from a white light source. The wavelength of the light

is noted down from the filter and the frequency is calculated.

The photo cathode is illuminated using this light. A retarding potential is

applied and its value is increased so as to make the photo-electric current zero. This

stopping potential is noted down. Similarly the stopping potentials are found for lights

of different frequencies using other filters. A straight line graph of stopping potential

versus frequency of the light is drawn. The slope is found and the Plan k’s constant is

calculated. Also, the threshold frequency is found and the work function of the photo

cathode is calculated.

Observations and calculations:

To find the stopping potential for lights of different frequencies:

Optical filter Frequency

λ×

=sm103V

8 /

(Hz)

Stopping potential

Vo (Volt) Colour Wavelength

(λ)(m)

From the graph, slope = h/e =

∴ Plank’s costant, h = (slope) (e)

= ( )(1.602 x 10-19 coul)

h = …………………………... Js

Threshold frequency, νo =…………………………..Hz

∴Work function, ϕ = h νo = eVJ1061

HzJs1062619

34

/.(().(

−

−

××

ϕ = eV

Result: Planck’s constant =

Work function of the photo-cathode in the photo-emissive cell = eV

33

34