Engg Physics -II Record 1st March 2013

ENGINEERING PHYSICS-II LABORATORY MANUAL I. B.TECH, II SEMESTER – ALL BRANCHES

NAME:

REGD. NO: BRANCH:

GAYTRI VIDYA PARISHAD COLLEGE OF ENGINEERING FOR WOMEN MADHURAWADA, VISAKHAPATNAM.

Certificate

Certified record of practical work done by Ms………………………………………………........ of first B.Tech, Second Semester, ……………………… Branch bearing registered number…………………… in the Engineering Physics laboratories of Gayatri Vidya Parishad College of Engineering for Women, Madhurawada, Visakhapatnam during the academic year 2012-13. No. of experiments done and certified:

Lecturer in charge

Date

Examiners:

1.

2.

INDEX

1. Thermistor characteristics (Theory part) 1 Thermistor characteristics (Experimental part) 2 – 3 2. Band gap of semiconductor (Theory part) 4 – 5 Band gap of semiconductor (Experimental part) 5 – 7 3. Resistor – Capacitor time constant (Theory part) 8 – 10 Resistor – Capacitor time constant (Experimental part) 10 – 13 4. Zener diode – V – I characteristics (Theory part) 14 – 17 Zener diode – V – I characteristics (Experimental part) 18 – 19 5. Stewart and Gee Apparatus (Theory part) 20 – 21 Stewart and Gee Apparatus (Experimental part) 22 – 23

APPENDIX 6. BREAD BOARD 24 – 25 7. Circuit symbols of components 25 8. Kirchhoff’s laws 26 9. Resistor colour code 27 10. Least square fit method 28 11. Abbreviations 28 12. Tan θ table for selected values 28

DATA SHEETS

S.NO. DATE NAME OF THE EXPERIMENT PAGE NO. REMARKS

ENGINEERING PHYSICS LABORATORY – II

1 G.V.P. COLLEGE OF ENGINEERING FOR WOMEN

T

T

THERMISTOR THEORY:

The name thermistor comes from thermally

sensitive resistor. They are basically

semiconducting materials and are of two distinct

classes:

1. METAL OXIDES: They are made from fine

powders that are compressed and sintered at high

temperature. MnR2ROR3R (manganese oxide), Ni O

(nickel oxide), Co OR3R (cobalt oxide), CuR2ROR3R

(copper oxide), FeR2ROR3R (iron oxide), TiOR3R

(titanium oxide) UR2ROR3R (uranium oxide) etc, are

the few examples. They are suitable for

temperatures 200-700 K. If the temperature is

higher than this range then AlR2ROR3R, Be O, Mg O,

ZrOR2R YR2ROR3R and DyR2ROR3R (Dy :dysprosium) are

used.

2. SINGLE CRYSTAL SEMICONDUCTORS:

They are usually Germanium and Silicon doped

with 10P

16P to 10P

17P dopant atoms/cmP

3P. Ge

thermistors are suitable for cryogenic range

1-100 K. Si thermistors are suitable for 100-250

K. After 250 K the Silicon thermistors will

become PTC (positive temperature coefficient)

from NTC.

The resistivity and the conductivity of the

thermistor are related to the concentration of

electrons and holes n and p of the semiconductor

though the relation,

( ) ………………... (1)

The concentrations n and p are strongly

dependent on temperature T in Kelvin.

Where ERaR is called activation energy which is

related to the energy band gap of that

semiconductor. Hence, As temperature

increases, the resistance R(T) changes according

to the relation,

( [

]) ……………. (2)

Where RROR is the resistance of the thermistor at

absolute temperature TRoR. Here TRoR is usually the

reference room temperature. B is a characteristic

temperature that lies between 2000K to 5000K.

The temperature coefficient of resistance is

defined as the ratio of fractional change in

resistance (

) to the infinitesimal change in

temperature .

……….. (3)

The typical value of is about 0.05/K. It is

almost 10 times more sensitive compared with

ordinary metals. Thermistors are available from

1KΩ to 1MΩ.

Advantages:

They are low cost, compact and highly

temperature sensitive devices. Hence are more

useful than conventional thermometric devices.

Using eq. (2) at some constant reference

temperature, say TROR= 300K, the resistance will

be

(

)

Where, (

)

To make the expression to look like a linear

relation to determine the values of A and B

constants, take natural logarithm on both sides of

the above expression,

…………………….. (4)

The exponential curve now became linear. If we

plot the variable

, we will get A and

B constants from the intercept and slope of the

straight line.

DESIGN OF EXPERIMENT:

PRINCIPLE: If we measure the resistance R of

thermistor at various temperatures (T), we can

plot the

graph and obtain the

values of A and B.

How to vary the temperature T?

Using an electric heater we can change the

temperature roughly from 30 to 60 .

How to measure the resistance R?

Using Wheatstone’s bridge.

Wheatstone’s bridge principle:

The circuit shown here is a Wheatstone’s bridge

and it consists of four resistors RR1R, RR2R, RR3R and

RR4R, a

galvanometer

(G) and a Battery

(V). Suppose the

resistance RR4R be

unknown. The

voltage applied

to this circuit by

the battery is

only to set up

some current and

its magnitude has no importance, i.e. whether or

2V or 5V it does not matter at all. Wheatstone

bridge gets balanced, i.e. the Galvanometer

shows a zero deflection when,

G

R3 R4

V

R1 R2



T

T

Or

If the resistances RR1R and RR2R are equal, then the

bridge will be balanced, i.e. the null deflection in

Galvanometer, when RR4R = RR3R. If we choose R R3R

as a variable resistor, like a decade resistance

box, the unknown resistance RR4R will be equal to

the resistance maintained in the box.

Measurement of resistance of thermistor:

Here in this experiment we employ a

1KΩ (at room temperature) thermistor. We form

a Wheatstone’s bridge with two fixed value

resistors each of 1KΩ resistance along with a

variable decade resistance box. Two arms of the

bridge are formed by 1KΩ resistors and the other

two arms, one with thermistor and the other with

decade resistance box. The sensitivity of

measurement of resistance will be better when

all the four resistors here are of same

(comparable) magnitude, hence the remaining

R’s are 1KΩ each.

Applications of thermistors:

1. They are used as temperature sensing

elements in microwave ovens, heaters

and also in some electronic

thermometers.

2. Used as sensor in cryogenic liquid

storage flasks.

3. Used as compensator for providing

thermal stability to transistor based

circuits.

4. Used in fire alarms, Infrared detectors as

sensor.

THERMISTOR EXPERIMENT Aim:

1. To study the variation of resistance of a thermistor with temperature.

2. To find the temperature (thermoelectric) coefficient of resistance (α) of the thermistor.

3. To determine A and B coefficients.

Apparatus: Thermistor (1 KΩ), electric heater (max 70P

0P C), 1.5 Volt battery or a D.C. power supply, mercury

or benzene thermometer (0 – 110 ), test tube containing insulating oil (edible oil / castor oil),

resistors (1kΩ - 2 No.s), Galvanometer (30 – 0 – 30), resistance box (1 to 1000Ω range),

connecting wires.

Formulae:

(

)

Procedure:

1. Construct the bridge according to the

circuit diagram (UMaintain at least 1000 Ω

Uresistance in the Resistance box before

connecting the circuit, i.e. remove the 1000Ω

plug key).

2. The 1 KΩ resistors are already connected

on the back panel of the board. Hence no

need to connect them again.

3. If a variable D.C. source is given instead

of a battery, set the voltage to 1.5 or 2 Volt

with the help of a multimeter.

4. The bridge gets balanced (Galvanometer

shows “0” deflection) when the resistance of

thermistor gets equal to that of the resistance

box. Remove the plug keys of resistance box

and find out the null point resistance.

T

G

RB RT

1.5 V

R1=1KΩ R2=1KΩ

Electric heater

Test tube with Coconut oil

Ther

mo

met

er

T

G

1.5 V

R2=1KΩ R1=1KΩ

RB



T

T

5. Start heating the thermistor by turning on the heater switch on the board.

6. Measure the resistance of thermistor for every two degrees centigrade rise in temperature. Note

the readings up to 60P

0P C in steps of 2P

0P C.

7. At each temperature bridge is not balanced initially and it shows some deflection. It can be made

zero by adjusting the resistances in the variable resistance box. Tabulate the readings.

8. Remove the power supply or battery, soon after you complete the experiment. If you forget

doing this, it will cause the galvanometer to deflect more causing damage to its restore spring.

Graph:

A graph is plotted by taking R versus T (K). This graph gives the value of α.

Another graph is plotted between ln R and (1/T(K)). The slope of this graph gives B and its

intercept on y (ln R) axis gives ln A from which A can be calculated. UBut it is not possible to find

out the intercept from the graph.U It can be done with the help of least square fit method as

described in the Appendix.

Use this method to compute both slope (B) and intercept (ln A) of the straight line. Here assume X as

(1/T) and Y as lnR. The intercept C gives the value of ln A and the slope will give B (in K). From the

intercept find out the value of A (in Ω).

Precautions:

1. Temperature of the thermistor should be

less than 70P

0P C.

2. Thermistor must be immersed completely

inside the hot oil bath.

3. Readings of thermometer must be noted

without parallax.

4. Connections should be made properly

without any loose contact.

5. Resistance must be varied quickly in the

resistance box to get the null point within

the 2P

0PC intervals.

6. Battery must be disconnected immediately

after completion of the experiment.

Viva-Voce Questions:

1. Where do you find applications of

thermistor? Name a few of them. They are useful in temperature sensing and

controlling equipments. Ex. Microwave

ovens, Infrared heat sensors, Liquefied gas

temperature sensors in cryogenics.

2. Explain the principle of Wheatstone’s

bridge.

In the bridge circuit, the potential at the two

nodes across which the galvanometer is

connected will be same when the four

resistors RR1R to RR4R satisfy the relation

3. After obtaining the data from this

experiment, you will have the values of A

and B coefficients. Can you determine

the temperature of your body? I will

provide you only a thermistor and a

multimeter. If yes, describe the method.

If No, justify your answer. Yes, it is possible. Suppose that you want

to measure your body temperature. Just

keep it in tight contact with your body

(cover it tightly with skin). Use the

multimeter to measure the resistance of this

thermistor. After few seconds of contact

with body, thermistor attains constant

resistance. With the known A and B

coefficients, we can measure the body

temperature by substituting in

(

)

(

)

T1 T2

T in K

R1

R2

in K-1

Slope = B

ln R



REFERENCES:

1. Physics of semiconductor devices, S. M. Sze, 3 P

rdP ed, John Wiley publications, chapter 14, sensors,

Thermal sensors, p.744-746.

2. The art of Electronics, Paul Horowitz, 2 P

ndP ed, Cambridge university press, chapter 15,

Measurement transducers, Thermistors, p.992-993.

3. Electronic devices and circuit theory, R. Boylestad, 7 P

thP ed, Prentice hall publications, Art. 20.11

Thermistors, p.837-838.

4. Electronic sensor circuits and projects, Forrest Mims – III, Master publishing, p.13, 46-47.

5. Advanced level physics, Nelkon and Parker, 3P

rdP Ed, Wheatstone’s bridge, p.829-834.

BAND GAP OF SEMICONDUCTOR USING PN JUNCTION DIODE

THEORY: PN junction diode is an example for extrinsic

semiconductor. It can be biased in both

forward and reverse directions. The current

that flow through the diode when its junction

is biased with a voltage V will be

(

)

With

.

Where,

V = Applied voltage across junction

IRsR = Reverse saturation current, a constant

dependent on temperature of junction

η = A constant equal to 1 for Ge (high

rated currents) and 2 for Si (low rated

currents)

VRTR = Volt equivalent of temperature

=

, T = Temperature of junction in

Kelvin

A = Area of cross – section of junction

e = Elementary charge = C

DRp(n)R= Diffusion constant for holes

(electrons)

for holes and

for electrons

= Mobility of holes

LRp(n)R = Diffusion length for holes

(electrons)

pRnoR = Equilibrium concentration of holes

(p) in the n – type material

=

nRpoR = Equilibrium concentration of

electrons (n) in p – type material

=

nRiR = Intrinsic carrier concentration (/cmP

3P)

nRiRP

2P =

B = A constant independent of T

ERGR = Energy band gap of semiconductor

(in Joule)

NRA R= Acceptor ion concentration (/cmP

3P)

NRD R= Donor ion concentration (/cmP

3P)

The term IRsR is highly temperature dependent.

The expression for it can be written as

(

)

(

)

(

)

(

)

(

)

(

)(

)

(

)(

)(

)

(

)

Experimentally it was observed that the

mobility term in the bracket varies as .

Hence,

………………………… (1)

is a constant whose magnitude is in nano or

pico ampere.

Under reverse biased condition applied

voltage V will be negative and hence the

expression for current through diode will be,

(

)



Diode will have only the reverse saturation

current flowing through it. The negative sign

indicates that the current is flowing in opposite

direction to that of forward bias. Hence the

current IRDR through diode in reverse bias will

be

(

)…………. (2)

Applying natural logarithms on both sides

implies,

[ (

)]

(

) ……………. (3)

This is the equation of the straight line with

ln(IRDR) as ordinate(y – axis) and 1/T as abscissa

(x – axis). ln(IR0R) is the y intercept of the graph.

If we plot 1/T versus ln(IRDR) graph, its slope

with x – axis gives the value of (–

). By

knowing the Boltzmann constant kRBR we can

evaluate the energy band gap of the

semiconductor, similarly we can estimate the

value of Boltzmann constant if we know the

energy band gap of the given semiconductor.

Applications:

1. We can use this to make a diode

thermometer.


PRINCIPLE: If we measure the reverse

saturation current through the diode by

varying its temperature, we can plot the

graph and obtain slope (–

).

Which diode is suitable for this?

OA79, Germanium diode, used as envelope

detector in amplitude demodulation circuits.

Why this OA 79? Why not any other?

Because reverse current variation is more in

the case of Germanium than with silicon.

Hence for a small temperature range of

variation (30P

0P to 60P

0PC), it is better to choose

Ge diode than any other silicon diodes. If we

want to do this experiment with silicon diodes,

we must have an electric heater capable of

giving temperatures up to 150P

0PC.

How to vary the temperature T?

Using an electric heater we can change the

temperature roughly from 30 to 60 .

How to measure the reverse current?

Using a moving coil micro ammeter.

Biasing the diode:

Use a constant voltage D.C. power supply or a

battery to bias it in reverse direction. The

voltage applied must be very low, 2 Volt. In

case of an ideal diode the reverse current does

not vary with applied reverse voltage. But in

practical diode case, it increases with increase

in reverse voltage. This is due to the increase

of leakage currents across the junction with

applied voltage. At room temperature, the

reverse current may be small and different for

same type of diodes, but it follows the

equation (2). The values of IRoR may vary from

diode to diode.

Description of heater:

The heater contains an electric heating

element attached to a stainless steel container

holding some cold water. A test tube

containing oil is immersed in the water bath.

Oil is an insulator of electricity and hence it

is used for heating the diode. This also

provides uniform heating of diode. The diode

with properly insulated connecting wires is

immersed in the oil bath. Thermometer is also

kept inside the oil bath to measure its

temperature. We cannot directly insert the

diode inside the water bath as tap water

contains lots of minerals dissolved in it and

acts like conductor. This will short circuit the

diode.

Useful data:

From the data sheet of the OA 79 diode:

Material of the diode is Germanium.

Maximum surrounding temperature is

60P

0PC.

Maximum allowed reverse current

through the diode is 60µA.

BAND GAP OF SEMICONDUCTOR EXPERIMENT

Aim: To determine the energy band gap of the

material of the semiconductor by studying the

variation of reverse saturation current through

given PN junction diode with temperature.

Apparatus: OA 79 Ge diode, heater (max 60 P

0P C),

thermometer, test tube containing insulating

oil (edible oil or castor oil), power supply (2V

D.C.), connecting wires, micro ammeter

(0 - 50 µA) and a voltmeter or multimeter.



VD

ID

T

Stainless steel container water bath

Test tube containing oil

A

2 V

+ +

_ _

+

Electric Heater

Formula:

Reverse current through diode is given by

(

)

Where, ERGR is the energy band gap of the

material of the semi conductor diode, T is the

absolute temperature of the diode junction and

kRBR = 1.38 x 10P

-23 PJ/K is Boltzmann constant.

Circuit diagram:

Caution: Set the applied reverse bias voltage

at 2 Volt. Do not increase this value more. Do

not heat the diode beyond 60P

0PC.

Procedure:

1. Build the circuit as shown in the circuit

diagram.

2. Observe the initial temperature of the

thermometer. If it is high (>30P

0P C) then

replace the water in the heater jar with

some cold water and try to reduce the

temperature below 30P

0P C.

3. Apply the reverse voltage (2 Volt) by

adjusting the potentiometer (if a battery is

given, then there is no need of doing this

adjustment).

4. Switch on the heater. Note down the

reverse current in the micro ammeter for

say, every 2P

0PC rise, in temperature of the

diode (if micro ammeter is not available,

you can use a multimeter in D.C. current

mode under 200 µA ranges).

5. Tabulate the readings.

6. Complete the calculations relevant to the

tabular form and get the answer for slope.

7. Plot a graph between lnI and 1/T to obtain

its slope.

8. Calculate the ERGR from both slopes obtained

from graph and table.

Precautions:

1. Readings of thermometer must be noted

without any parallax error.

2. Reverse bias voltage must be regulated at 2

Volt throughout the experiment.

3. Diode should be completely immersed inside

the oil bath.

GRAPH:

Plot a graph by taking the values of ln I vs

1/T. Find out the slope of the curve. Do not

consider the origin of this graph.

Usually we start at 300K and go up to 333K,

hence 1/T varies roughly from to . So start at 2.98

and go up to 3.34 by choosing the scale

On 1/T axis as

Usually IRDR varies from 2 µA to 60 µA. So ln

IRDR varies roughly from to – 13.2. So start at

– 9.7 and go up to – 13.2 by choosing the

scale

On ln I axis as

Slope (ERGR/kRBR) can be calculated from both

straight line data fit as well as from the

graph.

Viva-Voce questions:

1. Distinguish intrinsic and extrinsic

semiconductor.

If the semiconductor material consists of no

impurities (dopants), then it will be intrinsic

(pure) semiconductor. If it contains dopants

acceptor type [p-type] – III group elements

or Donor type [n-type] – IV group elements

then it will be an extrinsic semiconductor.

2. What are the band gaps of Silicon and

Germanium?

For silicon; (eV = electron volt)



For Germanium,

T is the temperature of the sample in Kelvin.

At 300K, ERG R= 0.72 eV for Ge; ERGR= 1.1 eV

for Si.

3. How do you test the diode for its polarity

using a multimeter?

There will be a Usymbol of diodeU on the

multimeter’s mode changing dial. Turn the

dial to diode testing mode. Connect the two

leads of the multimeter to the two leads of

the diode. If the multimeter shows infinite

resistance (it shows a “1 ” Or “OL” means

out of range, very large), then it is reverse

biased and the terminal of diode that is

connected to positive (red probe) of

multimeter will be the UcathodeU of the diode

and the other one will obviously be the

anode. Similarly, if the meter shows some

finite resistance like few hundred (150, 540

etc), then it is forward biased, i.e. the

terminal of diode that is connected to positive

(red probe) of multimeter will be the UAnodeU

of the diode and the other one will be the

Cathode. During this process, multimeter

applies some known voltage across its leads

and measures its resistance.

4. If I reveal the material of the diode used,

can you estimate the Boltzmann constant

from this experiment? If yes, describe how

do you do it, if no, say why?

(Think and answer)

5. Why do we observe small current (of the

order of Micro amp) in this experiment?

What are responsible for this small

current?

Because reverse current is due to the

minority carries only. As their number is

very small the current is also small.

6. In which biasing of diode are you doing

this experiment?

Reverse bias.

7. Can you determine the band gap by

changing the bias of the diode? If yes,

describe how you do it. If no, explain

why? (think and answer)

8. If I give you a silicon diode and the same

experimental set up (micro ammeter 0-

50range), can you find out its band gap?

Justify your answer.

No, the reverse current variation is very

small of the order of few nano amperes per

degree centigrade and hence it not possible

to observe the variation in reverse current

with the micro ammeter for a temperature

range of 30-60P

0P C

9. What is the magnitude of reverse current

in silicon at moderate temperatures?

Few tens of nano amperes.

10. Can you make a diode thermometer

using this setup? If yes, say how? If no,

say why?

Yes, once if we know the value of IR0R

(antilog of intercept of lnI vs 1/T graph)

from the experiment, we can measure the

T. Just bring the diode in contact with the

body whose temperature is to be measured

and measure the reverse current (IRDR)

accurately. As we know the IR0R and IRDR we

can determine the T in Kelvin for that body

using the relation (

).

References:

1. Electronic devices and circuits, Millman and Halkias, McGraw hill student edition

p.126-132.

2. Semiconductor device physics and technology, SM Sze, M K Lee, 3P

rdP Ed, John wiley,

P.107.



RESISTOR – CAPACITOR CIRCUIT – TIME CONSTANT

THEORY:

Resistor and capacitor combination circuits

have got great importance in the field of both

electrical and electronics engineering. This is

the fundamental circuit to understand the

working of many complex electronic circuits.

Consider a resistor of resistance R and

a capacitor of capacitance C. They can be

biased with an external D.C. source to start the

process of charging.

Suppose that switch S is closed.

Apply Kirchhoff voltage law (KVL) to the

above circuit of Charging.

Where, the sub scripts R and C denote the

voltages across the resistor and capacitor. If

we assume a current of i(t), a function of time,

then from Ohm’s law,

.

If the instantaneous charge on the plates of the

capacitor is , then

, Where, C

is the capacitance of the capacitor.

Substituting them in above eqn. implies,

;

But, is equal to the rate of change of

charge in the circuit, i.e.

Differentiate this expression with respect to

time t.

Voltage V across battery does not change with

time,

Put a trial solution,

Going back to differential equation,

(Assuming α≠0)

This implies

(

)

Voltage across capacitor will be,

(

)

, when capacitor charges to maximum

value qR0R, the voltage across it will be VO.

Hence,

(

)

Current will be,

(

)

(

);

(

)

Hence,

At t = 0, is , the maximum current

flowing through the circuit. Using,

(

)

Where, iR0R is the current in the circuit at t=0,

iR0RR represents the initial voltage across the

resistor, i.e. V;

( (

))

(

)

(

)

S

V

R

C VC

VR



DISCHARGING OF CAPACITOR: Similarly for discharging of capacitor, KVL

gives

Proceeding in the same manner as above, we

can show that voltage across the capacitor

during discharging will be

(

)

GRAPHS:

APPLICATIONS:

1. In electronic circuits, capacitor is a

crucial element. Its behavior in

electronic circuits can be better

understood from this experiment.

2. We can use this circuit to produce time

delay in D.C. operated circuits.

3. Capacitor – Load resistor combination

is used in filter circuits.

4. To set or reset the Digital IC’s at the

time of start or during their operation.


PRINCIPLE: To study the charging process,

we maintain a constant D.C. voltage across the

serial combination of Resistor and Capacitor

to study how the voltage changes across the

capacitor with time by noting down the

voltage at capacitor in regular intervals of

time. After plotting the graph of voltage vs.

time we can compute the time constant for the

circuit from charging process.

To study the discharging circuit, we first fully

charge the capacitor to the maximum value

and then discharge it through resistor. Once

again the voltage across the capacitor in this

process is to be noted in regular intervals of

time and graph is to be plotted.

Which capacitor is suitable for this?

Any electrolytic capacitor with fairly large

capacitance. (2200 µF, 3300 µF, 4700 µF etc)

Why large capacitance?

Because we want to observe this process by

means of a manually countable time period,

say few tens or hundreds of seconds. If it is a

very small capacitance, then it will be difficult

to observe the variation of voltage with time, it

drops rapidly.

What must be the voltage rating of the

capacitor?

In our lab we often use 12 to 22 Volt D.C.

power supplies. Standard capacitors are

available from 12V, 16V, 25V, 35V etc. So it

is preferred to use at least 25V rating for

capacitor. If it has more voltage rating then it

Voltage across capacitor with time during CHARGING

C A P A C I T O R

Time

τ = Time constant τ = Time constant Voltage across capacitor and Resistor with time

during DISCHARGING

S

V

R

C VC

VR

TIME

VO

LTA

GE

V

O

V

t

VC(t)

VR(t)

VC(t) + VR(t) = V at any ‘t’

Capacitor

Resistor

CHARGING PROCESS Vs. TIME



can also be used safely. But a 12V or 16 V

rating for capacitor may not be safe always.

Which value of resistor we have to choose?

As we wish to study this process slowly, it is

better to use a resistor R that gives an RC

product of approximately 100 to 400 seconds.

If you are using a 3300 µF, 25V rating

capacitor, it is better to use at least 50KΩ

resistor which gives

.

If we use less value of resistor than this, it will

charge or discharge very quickly and it

becomes difficult to note down the readings.

What should be the minimum wattage

(power rating) for resistor?

In the above example, if we use an 18 volt

supply, then the maximum current that flows

in the circuit will be

. So,

Hence any wattage carbon resistor is suitable

(1/8P

thP Watt, 1/4P

thP Watt or even ½ Watt is OK)

How to measure the Voltage?

Using a multimeter in D.C. voltage mode.

Biasing the capacitor:

As we are using electrolytic capacitor beware

of the polarity. The positive of capacitor must

be connected towards the high potential

(positive) of the D.C. source.

R – C CIRCUIT – TIME CONSTANT EXPERIMENT

Aim: 1. To study the charging and discharging

processes of Resistor and Capacitor

series (R-C) circuit.

2. To determine the time constant of the

circuit from the charging and

discharging curves.

Apparatus:

Resistors, electrolytic capacitors, D.C.

power supply, Multimeter, bread board,

connecting wires and stop watch.

Formulae:

Across capacitor,

[

]……. While charging

[

]……….. While discharging

Circuit diagram:

CHARGING PROCESS

DISCHARGING PROCESS

Procedure:

Set the multimeter in 20 Volt D.C. voltage

mode

Charging process:

1. Connect the circuit on the bread board as

shown in the above figure (charging).

2. Calculate the theoretical value of the time

constant using the above formula.

3. Switch on the circuit. Join the nodes A and

B to the multimeter leads. Join the two

leads and Uhold them togetherU.

4. Switch on the stop watch and separate the

probes of multimeter simultaneously. Start

counting of time.

5. Note the initial reading of voltage across

capacitor as zero volts.

6. While joining the ends of the capacitor with

a wire, it gets discharged and the voltage

across it becomes zero. As the multimeter

S

V

R

C VC

VR

A

B

A: connect this point to +ve (RED) probe of

multimeter

B: connect this point to – ve (BLACK) probe

of multimeter

S

V

R

C VC

VR

A

B

A: connect this point to +ve (RED) probe of

multimeter

B: connect this point to – ve (BLACK) probe

of multimeter



probes are connected to the ends of the

capacitor, joining the leads of the

multimeter discharges the capacitor to zero

volts. You must hold the two leads of

multimeter together Uuntil Uyou switch on the

stop watch.

7. Note down the voltages in regular intervals

of time (say 10 or 20 sec) and tabulate

them. it can be decided on the basis of

time constant, if time constant is about 220

sec, then we can go in steps of 20 sec; if it

is about 100 sec or less, we can go in steps

of 5 or 10 sec.

8. Take the readings until the capacitor

charges to maximum voltage (of power

supply).

Set the multimeter in 20 Volt D.C. voltage

mode

Discharging process:

1. Replace the resistor in the charging circuit

with another high value resistor.

2. Disconnect the wire joined to positive of

power supply from the resistor.

3. Join this wire to the ground. (If there is any

charge that is left on the positive plate of

the capacitor that will be discharged

through the resistor).

4. Join the positive probe of multimeter

(attached to the positive of capacitor) with

positive of the power supply and Uhold itU.

(As we want to study the discharge process,

the capacitor must have sufficient charge.

So charge it directly by joining the positive

lead of capacitor to the positive of power

supply).

5. Note down the voltage on the capacitor at

this “zero” time.

6. Switch on the stop watch and

simultaneously UremoveU the positive probe

of multimeter from the positive of power

supply. (this will allow the capacitor to

decay through resistor)

7. Note down the values of the voltage across

capacitor in the same intervals of time as

above until some minimum value of

voltage appear across it. (Say about two

volts)

Graph: Plot a graph by taking the voltage across capacitor versus time both for charging and

discharging cases.

Choose the time axis scale as 1 division = 20 sec and the voltage axis scale as 1division = 1 volt. Use

separate graph sheets to plot these graphs.

From each graph calculate the time constant of the circuit. On charging graph, the time taken

for the capacitor to charge to 63% of the maximum value is its time constant. Similarly on

discharging graph, time taken by the capacitor to discharge to 37% of its maximum value is its time

constant.

Precautions:

1. Do not short the ends of the power supply. This will damage your power supply.

2. Connections on the breadboard must be tight. Avoid loose contacts.

3. Start counting of time immediately after closing the switch wire while charging as well as

discharging the capacitor.

4. While charging the capacitor wait for sufficiently long time to reach the saturation value. Do not

stop the process at the middle.

Viva – voce questions:

1. Will you get a different answer to the

time constant of RC circuit if we replace the

power supply from say 12 Volt to 18 Volt?


As the time constant does not depend on the

voltage of the power supply, the answer

remains same as RC.

2. While discharging the capacitor, suppose

that I forgot to switch on the stop watch.

Some time lapsed. Then I have started

taking readings of voltage across capacitor

versus time. Will it give me correct answer

for τ? Justify.

Yes. We will get correct answer. Where ever

we start counting of time, there the voltage

across capacitor will be the new maximum

voltage V. From there the voltage starts falling

exponentially. Measure the time elapsed

between the instant at which voltage is V and

the instant where the voltage became 0.37 V.



It gives the time constant.

3. During discharging of capacitor if the

power supply is turned off, will you get

correct answer to the time constant? Justify

your answer.

For discharging process we do not need any

power supply. Hence nothing happens. (Power

supply is initially required to charge the

capacitor. Once after charging the capacitor, it

is not required)

4. Can you find out the value of an

unknown resistor/capacitor (either C or R

will be given to you, but not both) from this

experiment? If yes, describe how you get it.

If No, say why it is not possible?

Yes. Build the charging or discharging circuit

with the given components. Study the voltage

variation in small intervals of time. (Because

we initially do not know whether to take 5 sec

time intervals or 10, 20 seconds). If the

voltage falls or increases rapidly, then take the

smallest time interval possible. If the voltage

is not varying much then accordingly you can

decide whether to take 10 sec, 20 sec or even

30 sec time intervals. Measure the time

constant using the voltage – time graph. This

gives R.C product value. As one of them is

known, other can be estimated.

5. I have started studying the discharging

of a capacitor (R=56KΩ and C= 3300 F,

Voltage source is 12V). My aim is only to

find out its time constant. I have done the

experiment and noted the voltage versus

time up to 900 seconds. Is it an efficient way

of doing the experiment?

RC= 184.8 sec, hence we can stop at roughly

around 300 sec range to know the time

constant experimentally from graph. So it is

waste of time to take the readings up to 900

sec. If the variation in voltage reduces, say

during one or two minutes time if the voltage

drops by 1 volt, then we can stop.

6. Find out the voltage VROR across the

resistor after a very long time. What will be

the voltage across C after very long time?

After long time (say few tens of minutes), the

voltage across the capacitor will be equal to

the voltage of the D.C. voltage source. If we

measure the voltage VRRR across R, after long

time it will be zero. (Use charging equation)

7. In certain logic integrated circuits (IC’s),

it is necessary to SET or RESET the output

of the circuit. It is something like the reset

button of your digital stopwatch which

makes the output time Zero. It is required

to send a high voltage (something like 12V)

pulse for a short duration of time and later

it should go down to zero (0 Volt). Can

you produce it by using this circuit? If Yes,

where to take the output? If yes, suggest

where to take the output voltage if I need a

low voltage (0 Volt) initially that should go

quickly to a high voltage (12Volt).

(Think! And answer!)

8. If the answer to above question is Yes,

what value of resistance would you suggest

in achieving this action, Smaller or larger?


We should take large value of resistor and

small value of capacitor. For a given RC,

initially the voltage appears entirely across R

at time t = 0. If R is small, then this will

produce an unwanted spike (sudden extraction

of current from the power supply). This is

undesirable. Hence if we take large R and

small C, these spikes would not exist.

9. Transistors are devices which can be used

as electronic switches. You will learn about

the action of transistors in later courses. For

the time being suppose that the Base of a

transistor is a control (something like tap head

which controls the water flow) which can turn

On or Off the transistor depending on the

voltage applied at Base. Suppose that I want to

watch a programme on a television after some

known time delay, say after 10 minutes

(10 60=600 sec). My transistor can work as a

switch that can turn the T.V. On or Off

depending on the voltage applied at its Base.

Can you design an RC network that gives me a

voltage of 10 volt after 600 sec? You can

choose the resistor of your choice, but

capacitor is 3300 F and Voltage source is

15Volt. Decide where to take the output of this

RC circuit. (Think and answer)

10. During discharging of capacitor if we

plot , where, V is the voltage

across capacitor at time t, what will be the

shape of the graph? If we take the slope of

the graph at any point what does it give?

V VC

VR



It will be a straight line with negative slope

During discharging process,

(

)

V = voltage of power supply

(

)

[

] [ (

)]

[

] [

]

Y = m X

Hence if we plot [

] vs. time t

during discharging process, we will get a

straight line passing through origin with

slope -1/RC.

11. During charging, if we plot

(

) vs. time t, what will be the

shape of the graph? (V(t)=voltage across C,

V = voltage of D.C. source)

It will be a straight line passing through origin

with slope (-1/RC). For charging process,

(

)

V = voltage of power supply

(

)

(

)

(

)

(

)

Y = m X

References:

1. Fundamentals of physics, Robert Resnick, David Halliday, Walker, 7P

thP edition, Art. 28.4, RC

circuits, p.882-887.

2. University Physics, Young, Art. 26.4, RC circuits, p.896-900.



ZENER DIODE VOLT – AMPERE CHARACTERISTICS

THEORY:

Semiconductors are basically of two types.

Intrinsic semiconductors: These are in their

purest form, without any impurities (Dopants).

Extrinsic semiconductors: These are

impurity added (Doped) intrinsic

semiconductors. Doping is a process of adding

impurity atoms to the pure semiconductors.

The reason for this doping is only to increase

the conductivity of the semiconductors. By

adding Group III elements Boron, Aluminum,

Gallium, Indium (Trivalent impurity) to the

pure semiconductors, it becomes P – type. By

adding Group V elements Nitrogen,

phosphorus, Arsenic, Antimony, Bismuth

(pentavalent impurity) it becomes N – type. P

– type has excess of holes as majority carriers

and N – type has excess of electrons as

majority carriers.

Diode is a semiconductor based electronic

component. It is formed by joining a p – type

section of semiconductor with n – type

section. It has anode (p – type) and cathode

(n – type). It is a polar device, i.e. its operation

will depend on the direction of connection

(biasing).

The above symbol represents an ordinary

P – N junction diode. A denotes the positive

(high potential end) Anode and K denotes the

negative (low potential end) of the diode.

Diode acts like a mechanical check valve,

that conducts (allows flow of liquid) only

when the Anode is at relatively high potential

with respect to the cathode. Suppose that A is

at 10 Volt potential and K is at 9.3 Volt

potential. Then the diode will conduct (closed

switch or Forward Bias) a current from anode

to cathode in the direction of arrow shown in

diode symbol. If the potentials are reversed,

i.e. A at 9.3V and K at 10V, it does not

conduct, acts like infinite resistance (open

switch or Reverse bias).

Forward Bias: Anode of the diode will be at a

relatively high potential than that of cathode.

Reverse bias: Cathode of the diode will be at

a relatively high potential than that of Anode.

Zener and Avalanche diodes are

heavily doped p-n junction

diodes. It is their Ucircuit symbolU.

The doping levels (amounts of added

impurities) are considerably different from

those normally found in a rectifier (PN) diode.

This diode preferably used in REVERSE

BIAS.

A rectifier diode cannot be used in the

breakdown region as it makes permanent

damage to the junction. However, zener and

avalanche diodes are designed to use in the

breakdown region. These diodes are used for

voltage reference and voltage regulator

circuits. There are two mechanisms that cause

a reverse-biased p-n junction to break down:

the UZener effectU and Uavalanche breakdownU.

Either of the two may occur independently, or

they may both occur simultaneously. Diode

junctions that break down below 5 V are

caused by the UZener effectU. Junctions that

experience break down above 5 V are caused

by Uavalanche breakdownU. Junctions that

break down around 5 V are usually caused by

a combination of the two effects.

A zener diode is produced by moderately

doping the p-type semiconductor and heavily

doping the n-type material (see Fig below).

Observe that the depletion region extends

more deeply into the p-type region.

Under the influence of a high-intensity electric

field, large numbers of bound electrons within

the depletion region will break their covalent

bonds to become free. This is ionization by an

Depletion region

Heavily doped

N – Side

Moderately doped P – Side

Denotes atoms/ions

A REVERSE BIASED ZENER DIODE

Bubbles ( ) denote holes and black dots ( ) denote electrons



electric field. When ionization occurs, the

increase in the number of free electrons in the

depletion region converts it from being

practically an insulator, to being a conductor.

As a result, a large reverse current may flow

through the junction. The actual electric field

intensity required for the Zener effect to occur

is approximately 3 X 10P

7P Volt/meter. From

basic circuit theory we recall that the electric

field intensity E is given by

V = E d

where

E = electric field intensity (volts per meter)

V = potential difference (volts)

d = distance (meters)

In terms of the p-n junction depicted in above

Fig. we note that the applied reverse voltage is

V and the depletion region width is the

distance d. The narrower the depletion region,

the smaller the required reverse bias to cause

Zener breakdown. A small reverse bias can

produce a sufficiently strong electric field in a

narrow depletion region. By controlling the

doping levels, manufacturers can control the

magnitudes of the reverse biases required for

Zener breakdown to occur. Only certain

standard zener diode voltages are available.

These range from 2.4 to 5.1 V. With lightly

doped p-type material, the depletion region

may be too wide for the electric field intensity

to become sufficient for Zener breakdown to

occur. In these cases, the breakdown of the

reverse-biased junction is caused by avalanche

breakdown (see Fig below).

The depletion region is wider because it

extends more deeply into the p region.

Reverse saturation current is a current flow

across a reverse-biased p-n junction due to

minority carriers. Even though the electric

field strength is not large enough to ionize the

atoms in the depletion region, it may

accelerate the minority carriers sufficiently to

allow them to cause ionization by collision.

The specifics may be outlined as follows:

1. The depletion region is too wide to allow

an electric field intensity of at least 3 X10P

7P

V/m.

2. The minority carriers are accelerated by the

applied electric field.

3. The minority carriers gain kinetic energy.

4. The minority carriers collide with atoms in

the depletion region.

5. The valence electrons of the atoms receive

enough energy from the collisions to

become free (conduction band) electrons.

6. As a result, the number of free electrons in

the depletion region increases to support a

large reverse current. This avalanche of

carriers is also termed as “carrier

multiplication" since one minority carrier

may ultimately cause many free electrons.

The V- I characteristic curve for a zener diode

will be similar to rectifier diode in forward

bias condition. Its behavior in reverse bias is

different from rectifier diode.

Important points from V – I characteristics:

1. Cut – in Voltage (VRγR): During forward

bias of the diode, if we slowly vary the

voltage across the diode, there will be no

observable current up to a characteristic

voltage known as Cut – In or Break – in

voltage or Knee voltage. The minimum

forward voltage to be applied to the diode

to make it just conducting is called its Cut –

in voltage. For Silicon diodes, this cut – in

voltage will be approximately 0.6 to 0.7

Depletion region

Heavily doped

N – Side

Moderately doped P – Side

The black dotted electrons on the P-side are minority carriers that are “Feeling” forward bias and travelling with high speed, colliding with ions of depletion region causing them to release electrons. Their number increases drastically and an avalanche (flood) of electrons are released (Avalanche breakdown)

MECHANISM OF AVALANCHE

BREAKDOWN

MECHANISM OF AVALANCHE BREAKDOWN



Volt. For Germanium diodes it will be

approximately 0.2 to 0.3 Volt.

2. Break – down voltage (VRZR): During

reverse biasing of diode, initially there will

be no current through the diode.

(Exception: if we use a micro ammeter, we

can observe some small current, a milli –

ammeter does not show any current ) As we

increase the magnitude of reverse voltage,

there will be a characteristic voltage for the

diode at which it starts conducting

infinitely. Sudden raise of current will be

observed at this point leaving the voltage

across diode almost constant. This voltage

is called the Break – down voltage. For

voltages less than 5V zener break down is

dominant and for voltages greater than 5V,

Avalanche breakdown is dominant.

3. Dynamic Resistance (RRFR and RRZR): During

forward or reverse biasing of diode there

are points at which the current through

diode increase rapidly. At these points the

variation of current with voltage is non –

linear, reflecting that these devices are non

– Ohmic. For Ohmic devices, that obey

Ohm’s law, the resistance does not change

with applied voltage and hence they have

some fixed value of resistance. But here in

the case of diode, the resistance changes

with applied voltage. So we define the ratio

of differential change in Voltage across the

diode with the corresponding differential

change in current through it as the

UDynamic ResistanceU.

4. Material of the diode: Depending on

the cut – in and break – down voltages as

described above, we can decide the make of

the diode.

APPLICATIONS:

1. As voltage regulators for both line

regulation and load regulation in D.C.

power supplies.

2. Used in generating reference voltages

for transistor based and integrated

circuits.


PRINCIPLE: To study the V – I

characteristics of the zener diode, we must

measure the current through the diode by

applying various voltages to the diode in both

forward and reverse biases. This can be done

with a variable voltage D.C. source and a

milli – ammeter.

What is the D.C. source?

A variable D.C. power supply with zero

minimum voltage to at least 15 to 20 V

maximum voltage. Its power rating must be

sufficient to draw at least 100 mA current at

these voltages. In our lab we are going to use a

0 – 20 V variable D.C. source with 1Ampere

maximum current.

How to choose the diode?

The zener break – down voltage should not

exceed the maximum voltage supplied by the

D.C. source. As a rule of thumb, the difference

between maximum voltage of the source and

the break – down voltage of the diode must be

greater than at least 5V. If the D.C. source has

maximum voltage of 15 Volt, we can use

zener diodes of break – down voltages up to

10V. The power rating of the diode is

specified by the manufacturer. If we want

mA

RS

REVERSE BIAS V VD

mA

RS

FORWARD BIAS V VD

VR

VR



more current through the diode, we must use

high power rated diodes. In our lab we use

either half watt or one watt rated zener

diodes. Their voltage ratings usually vary from

5V to 13V.

How to recognize its polarity?

There will be a ring (band) on the cathode side

it will be the negative of diode and obviously

the other one will be positive of diode. If the

band is not visible, you can test it with a

multi-meter.

How to test a diode with a multi-meter?

There will be a diode symbol on the

multi-meter dial knob. Turn it to the diode

testing mode. Join the positive (red probe) of

multi-meter to one end of the diode and the

negative (black probe) to the other end of

diode. If the meter shows a low resistance of

say few hundred, it means that the diode is

forward biased, i.e. the leg of diode connected

to positive (red probe) is it’s positive and vice

– versa. If the multi-meter shows an infinite

resistance, it means that it is in reverse bias,

i.e. the leg of diode connected to the positive

(red probe) of multimeter is its cathode

(negative) and vice – versa.

How to check whether a diode is working or

spoiled?

To check whether the diode is working or

spoiled use the multimeter test as described

above. If the diode shows very low resistance

in both directions, it is spoiled. If it shows

high resistance only in one direction, it is in

good condition.

What is the function of series resistance

RRSR?

RRSR is used for limiting (controlling) the

current through diode. The value of this

resistor can be decided by the power rating of

the diode.

How to measure the current?

In our lab we have milli – ammeters of 0 – 50

and 0-100 range. We can also use the digital

multimeter (DMM) in current measuring

mode.

Fixing the values of components:

Apply KVL to the forward bias circuit.

During forward bias VRDR =0.7 V approximately

for silicon diode. If the power rating of Zener

is P, maximum current it can hold without

being destroyed is iRmaxR, then,

Or

This will tell us the maximum current the

diode can withstand when a voltage of VRDR is

applied to it. The resistor must be capable of

controlling the current to this threshold value.

As a rule of thumb, we restrict our self

to a threshold current value which is much

lower than the value predicted by the above

expression for iRmaxR. If the predicted value is

say 90 mA, then we restrict to ¼ of this value,

say 20 to 25 mA. Take this value as iRmaxR.

This is to ensure the durability of the diode. If

the applied maximum voltage by the D.C.

source is say 20 V, then

(In forward bias)

Suppose that the zener is a half watt rated.

Then,

. Hence it

can withstand 700 mA. But our

milli – ammeter has only 50 or 100 mA range,

it is better to restrict up to 30 mA in forward

bias. So, IRmaxR is 0.03Amp. Hence,

or

.

The nearest standard resistance value is 680Ω.

The power rating of the resistor can be

calculated using .

Suppose that the maximum current goes up to

30 mA in the resistor, then,

Nearest standard wattage is 1 Watt. If we use a

1KΩ resistor in place of 680Ω, the current

drops and even a 1KΩ half watt resistor can

withstand the maximum current. So, when we

wish to reduce the resistance we must increase

its power rating and vice versa.

For reverse bias replace VRDR with the break

down voltage of the zener diode, say 5.6V, ½

watt rating, then,

.

So, restrict only to 25 mA.

or

, nearest standard value

is 680Ω. So it is better to use 680Ω or more in

both forward and reverse biasing of the circuit.



ZENER DIODE V – I CHARACTERISTICS EXPERIMENT

Aim: 1. To study the volt – ampere

characteristics of the given zener

diode.

2. To determine the Cut – in, Break –

down and dynamic resistances of the

diode from the characteristic curves.

Apparatus: Zener diode (½W), Resistors (1 KΩ, ½W),

Variable voltage D.C. power supply,

milli–ammeter (0 – 50 or 100), Multimeter,

bread board, connecting wires.

Procedure:

FORWARD BIAS:

Circuit:

1. Construct the circuit on bread board

according to the circuit diagram for

forward bias. Zener diode has a black

band on it. It shows the cathode of diode.

2. Vary the potentiometer (knob on the

power supply) and apply various voltages

to the diode in steps of U0.1 VoltU. Note the

current in milli ampere as shown by the

ammeter.

3. Initially, there will be no current through

the diode up to a characteristic voltage,

known as Cut-In voltage. Note values of

current until this characteristic voltage as

zero. Observe carefully for this voltage

and note it down.

4. From here onwards note down the

voltage that you observe across the

diode as function of current through

diode in steps of 2 mA by varying the

potentiometer.

REVERSE BIAS:

Circuit:

1. Connect the circuit in reverse bias as

shown in the circuit diagram, i.e. just

reverse the ends of the diode in the

forward bias circuit.

2. Vary the potentiometer (knob on the

power supply) and apply various voltages

to the diode in steps of U1 voltU starting from

zero.

3. Note the value of current in milli ampere

as shown by the ammeter (initially you

wouldn’t get any current, note them as

zero).

4. At a characteristic voltage known as

UBreak downU voltage, you will get a

sudden raise in the current through the

diode. Observe this carefully and note

down the value.

5. From here onwards note down the

voltage that you observe across the

diode as function of current through

diode in steps of 2 mA by varying the

potentiometer.

Graph: Plot a graph by taking the current through diode versus voltage across diode both for

forward and reverse biases. Split the graph into four quadrants.

Choose the scale on voltage axis (horizontal) as 1 division = 0.1Volt on the positive side and 1

division = 1 volt on the negative side.

Choose the scale on current axis (vertical) as 1division = 1 mA on both positive and negative sides.

From each curve on first and third quadrants, calculate the slope of the graph near cut – in and

break – down points. These slopes will give the dynamic conductances of diode. Inverse of

conductance gives the dynamic resistance of the diode.

mA

RS

REVERSE BIAS V VD

mA

RS

FORWARD BIAS V VD



Precautions:

1. Do not short the ends of the power supply. This will damage your power supply.

2. Connections on the breadboard must be tight. Avoid loose contacts.

3. Check the polarity of diode carefully.

4. Do not connect the diode without current limiting resistor. This will Uburn outU the diode in any

bias.

Viva – voce questions:

1. What is the basic application of a zener

diode?

It is used as a voltage regulator.

2. I have a silicon made zener diode with

VRZR=5.2V connected in reverse bias with

a series resistor of 100Ω and a variable

D.C. source of 0-20V. Estimate the

maximum current flowing in the circuit.

Determine the current in the circuit if

the diode direction is reversed. Suggest

the minimum power ratings for both

zener diode and resistor in both

connections.

In reverse bias,

For diode,

For resistor,

.

In forward bias, for Silicon VRZ R= 0.7 V

For diode,

For resistor,

.

3. Design a voltage regulating circuit

which drives a cell phone charging unit

with required output at 5.6 Volt, 300mA

with input voltage of 10 Volt D.C.

IRmaxR for the zener is 300mA, i.e. 0.3A.

Zener voltage rating is 5.6V, for diode,

For resistor,

Voltage drop across it will be 10–5.6= 4.4V

; This circuit will

work with a load (cell phone) of resistance

greater than 18.66 Ω. If the load resistance is

further reduced, the circuit will not work.

4. What do you mean by dynamic

resistance?

It is the resistance offered by the diode due

to the changes occurred in input voltage.

Static resistance of a diode refers to a fixed

resistance at a fixed voltage. But dynamic

resistance is some kind of average

resistance offered by the diode when the

input voltage changes between two closely

separated voltage levels.

5. Which bias would you suggest for

operating the zener diode to exploit to

maximum extent?

Reverse bias only.

6. Can we use an ordinary PN junction

diode to regulate the voltage instead of a

Zener diode? Justify your answer.

Yes, Junction diode offers a forward drop

of about 0.7 Volt (for silicon). Hence by

using a combination of forward biased

diodes we can achieve voltage regulation

even in forward bias. A serial combination

of two forward biased silicon diodes will

provide a forward drop of 1.4V.

7. What is the basic difference between

Zener break down and avalanche

breakdown?

Zener break down is due to the breaking of

bonds in the depletion region because of

applied external reverse voltage.

Avalanche breakdown is due to the rupture

of bonds in depletion region by the

collisions of minority carriers that are

accelerated by the applied reverse voltage.

As the temperature increases, the minority

carrier concentration also increases, giving

more chance for avalanche breakdown.

RS

10V 5.6



References:

1. Electronic devices and circuits – Discrete and integrated, Stephen Fleeman, Prentice hall, Art.

2-8, zener and avalanche diodes, p.32-36 (taken verbatim).

2. Electronic devices, 9P

thP Ed, Thomas L Floyd, Prentice hall, unit-3, special purpose diodes,

p.113-126.

3. Electronic devices and circuit theory, R. Boylestad, 7 P

thP ed, Prentice hall publications, Art,

semiconductor diode p.10.

STEWART AND GEE APPARATUS

MAGNETIC FIELD ALONG THE AXIS OF CIRCULAR CURRENT CONDUCTOR

THEORY:

Biot – Savart’s Law:

Consider a current carrying conductor (of

arbitrary orientation) as shown in figure. It

carries a current of I. The magnetic field at

a point P at distance from an element of

the conductor will be given by

| |

|

|

| |

Here θ is the angle between the radius vector r

and the length element ds.

, is the free

space permeability constant.

Direction of magnetic field is in the direction

of the cross product of ds and r, given by right

hand screw rule.

Magnetic Field on the Axis of a Circular

Current Loop:

Consider a circular wire loop of radius R

located in the yz plane and carrying a steady

current I, as shown in Figure. We are going to

calculate the magnetic field at an axial point P

at a distance x from the center of the loop.

Consider element of the wire. Using Biot

savart’s law, the field at P due to this will

be

The angle between the ds and r is 90P

0P. So,

And its direction is indicated in the figure.

Also from the figure the angle between vector

r and the y – axis (smaller angle side) is . So,

makes an angle with the x – direction.

Its components along X and Y – directions are

and respectively. When we consider

the entire elements of the loop, their y –

components will cancel with each other

due to the circular symmetry of the coil and

only the x – components survive. So, the total

field at P due to all elements will be,

∮ ∮

Throughout the loop the values of θ and r

remains unchanged and hence can be taken

outside the integral.

∮

∮ is the circumference of the coil.

From the figure,

√

Therefore,



(√ )

√

If the coil contains n number of turns, then the

field gets multiplied by that factor.

The direction of this is always either

parallel or anti – parallel to the axis of the coil.

The field B at the centre of the coil can be

obtained by putting x = 0,

At ,

( )

√

Hence, the field B falls to

√ times of its

maximum value BRoR at the center. We can

use this point to calculate the radius of the

coil, without measuring it physically with a

scale, from the experiment.


PRINCIPLE:

The variation in B along the axis of the

circular coil can be studied experimentally

with the help of a Tangent Galvanometer.

How to measure B?

The coil will produce a magnetic field . There is a huge EARTH magnet that will

produce another field , known as the

horizontal component of Earth’s magnetic

field. The plane containing the axis of the

hypothetical Earth bar magnet is called the

MAGNETIC MERIDIAN.

If we place the plane of the coil in the

magnetic meridian, then there will be two

mutually perpendicular magnetic fields, one in

the North – South direction (Earth) and the

other in the East – West direction (coil). If we

use a magnetic compass near the coil (which is

already set in magnetic meridian), it will

experience a torque due to the action of the

two magnetic fields and will settle ultimately

in the resultant direction of the two fields.

H = 0.38 Oersted or 0.38 X 10 P

- 4P Tesla

By measuring θ we can estimate the

experimental value of using the above

relation.

What is the coil?

A circular frame holding the coil of variable

number of turns is mounted vertically on a

platform. The platform can be adjusted to

make it horizontal with the help of two

leveling screws. The set up has 2 turns, 50

turns and 500 turns of coil for experimenting.

We use only the 50 turn coil.

How to set up the current in the coil?

Using a fixed voltage D.C. source.

How to measure the current?

Using an ammeter of 0 – 3 Amp range.

How to vary the current the circuit?

By using a 20 Ω Rheostat.

Why to adjust the current?

As we measure the magnetic field as a

function of angle, it is necessary to restrict our

self to some fixed range (30P

0P-60P

0P). Hence it is

required to adjust the current to get the desired

value of deflection θ.

Why to restrict only to 30P

0P-60P

0P range?

When using the instrument it is important to

adjust matters so that the deflection is never

outside the range 25° to 65° and preferably it

should be between 30° and 60°. This is

because the value of θ is to be used in the form

tan θ and an effect which can be called 'error

magnification' arises. The matter will be made

clear by considering the following examples:

Suppose the deflection can only be

observed with an accuracy of half a degree.

Let us consider how this possible error will

affect the values of the tangents of deflections

10°. tan 10° 30' = 0.1853 and tan 9° 30' =

0.1673 thus tan 10° 30' - tan 9° 30' = 0.0180.

Now tan 10° 00' = 0.1763.Thus an observation

of θ = 10° ± 0.5° leads to a statement that tan θ

= 0.1763 ± 0.0090. This represents a possible

error of over 5% in tan θ.

N



STEWART AND GEE APPARATUS EXPERIMENT

AIM:

To study the variation in magnetic field with

distance along the axis of circular current

carrying conductor.

APPARATUS:

Stewart and Gee type galvanometer, battery

(D.C. Source 2 Volt - 1Amp), commutator,

rheostat, Ammeter and connecting wires.

CIRCUIT DIAGRAM:

FORMULA:

Where

R0R = 4 X 10P

-7P Henry/meter

n = No. of turn in the coil

i = Current flowing through the circuit

x = Distance of the magnetic compass

from the center of the coil

a = Radius of the coil.

If x and a are expressed in centimeter, then the

resultant expression will be

In gauss, the same formula will be,

DESCRIPTION OF EQUIPMENT:

It consists of a circular coil in a vertical plane

fixed to a horizontal frame at its middle point.

The ends of the coil are connected to binding

screws. A magnetic compass is arranged such

that it can slide along the horizontal scale

passing through the center of the coil and is

perpendicular to the plane of the coil. The

magnetic compass consists of a small magnet

and an aluminum pointer is fixed

perpendicular to the small magnet situated at

the center of the compass. The circular scale in

the magnetic compass is divided into four

quadrants to read the angles from 0 to 90

and 90P

0P to 0P

0P. A plane mirror is fixed below

the pointer such that the deflections can be

observed without parallax.

PROCEDURE:

1. The circuit should be connected as shown

in the diagram.

2. Remove the power connection applied to

the circuit.

3. Place the compass exactly at the centre of

the coil.

4. Adjust the arms of the magnetometer until

the pointer of compass becomes parallel to

it. Rotate the compass until the pointer

reads 0P

0P -0P

0P.

5. Suppose that the coil is placed in magnetic

meridian and switch on the power to

circuit. It will show some deflection.

Carefully adjust the rheostat and bring the

deflection to 60P

0P -60P

0P.

6. Interchange the plug keys of the

commutator and reverse the current

direction in the coil. Note down the

deflections of compass.

7. If your coil is exactly in magnetic meridian,

then the readings of compass should not

differ by more than 5°P

Pfrom their previous

values, before interchanging the

commutator. If this is not satisfied, once

again turn off the power and make the

pointer parallel to the magnetometer and

repeat this until you get all four deflections

within 5P

0P variation.

8. Move the compass to 10 cm distance on

both east and west directions on the

magnetometer and obtain the deflections

with both directions of current.

9. If all the eight deflections that you have

obtained in above case lie within 5P

0P, you

can start taking deflections at various

positions. UNow the instrument should not

be disturbed while moving the compass U.

Otherwise repeat the adjustment by

disconnecting the power.

A

C

S.G. coil

Rh (20Ω) 2 VOLT D.C.

0 to 3 Amp



Tanθ

Position of compass

East 0 West

Tanθ

East 2R West

√

10. Start at 0 cm position and obtain four

deflections. Vary the position to 2 cm either

East or West and obtain four more

readings. Tabulate them.

11. Proceed in the same way at 2, 4, 6…. cm

on both East and West until the deflection

falls less than 20P

0P. Tabulate the readings.

PRECAUTIONS:

1. The Stewart and Gee apparatus should

not be disturbed after the adjustments.

2. Observations are noted down without

parallax.

3. The ammeter and rheostat should be

kept far away from the deflection

magnetometer

Graph:

A graph is plotted taking distance of the compass from the

center of the coil along X-axis and tan along Y-axis. The

shape of the curve is as shown in the figure and is symmetric

about Y-axis. The magnetic field is found to be maximum at

the center of the coil. The radius of the coil ‘a’ is determined by

measuring its circumference. The current flowing through the

circuit ‘i’ and the number of turns in the coil ‘n’ are noted. The

value of magnetic induction is calculated from the above

formula and is compared with the experimental formula B = H

tan θ.

Viva-Voce questions:

1. What are the magnetic forces acting on

the compass when it is mounted on the

axis of the coil? Mention their directions.

The forces are, due to Earth’s magnetic

field along the geographic north direction

and due to coil along either east or west

direction.

2. What is the direction of the magnetic

field produced by the coil?

Along East or West, i.e. perpendicular to

the plane of the coil.

3. Why do we adjust the maximum

deflection at 60° ?

To restrict the error in the measurement of

θ and hence in the tan θ to less than 5%, we

always adjust the maximum deflection to

60°.

4. State Biot-Savart’s law.

Refer to text.

5. Define magnetic meridian.

It is the plane containing the axis of the

earth’s hypothetical bar magnet.

6. Why the ammeter should be placed far

away from the coil?

If it is sufficiently close to the coil, its horse

shoe magnet will influence the resultant

deflection of the compass which is an

undesirable effect.

7. What is the function of rheostat in this

experiment? To vary the current in the circuit and to

bring the deflection to desired value.

8. Can you determine the radius of the coil

without measuring it with a scale?

Yes, consider the tan θ vs. position graph.

Maximum value of tan θ is obtained at the

centre. Calculate the value of

√ .

Draw a horizontal line intersecting the tan θ

axis at this value. The line intersects the

graph (curve) at two different points. The

graphical distance between these two points

will give the diameter of the coil and half

of it will give the required radius of the

coil.

REFERENCES:

1. Advanced level physics, Nelkon and parker, magnetic fields due to conductors, p.935 2. Fundamentals of physics, Resnick, Halliday, Walker, 7P

thP ed, Example 30.3, p.942 (for fig).

APPENDIX ENGINEERING PHYSICS LABORATORY – II


BREAD BOARD: The figure shows sets of five holed boxes. Each hole in a five hole box has METAL CONTACT with the remaining four holes in that

box.

HORIZONTAL BUSES:

The series of holes on the top and bottom parts of the bread board are called horizontal buses. For indexing purpose they were named as A, B, C, D, E, F, G

and H in the figure. UIN PRACTICAL BREAD BOARD YOU WILL NOT FIND ANY SUCH NAMING. U

A bus: The five hole pairs are joined to each other by a metal strip on the back side of bread board. If you insert a battery positive lead in any of the holes in A

bus, the other holes will also have the same potential. Similarly the buses B, C, D, E, F, G and H also have the same hole connections. The above said eight

horizontal buses are independent of each other, i.e. A and B do not have any connection, similarly A and E ; B and F etc, are not connected.

USUALLY THE A BUS IS RESERVED FOR POSITIVE OF THE D.C. SUPPLY. SIMILARLY C BUS IS RESERVED FOR GROUND (NEGATIVE OF

D.C. SUPPLY)

A

B

A

B

C C

D D

E

F

E

F

G

H H

G

1 2 3 4 5 6

7…………………………………………………………………………………………………………………………………………………………………….56 57 58 59 60

……………………………………………………………………….

661 62 63 64 65 66 67………………………………………………………………………………………………………………………………………………………………………………. 120

……………………………………………………………………….

VER

TIC

AL

BU

SES V

ERTIC

AL B

USES



BATTERY/

D.C.

SOURCE

VARIABLE

VOLTAGE

D.C. SOURCE GROUND ZERO POTENTIAL

LIGHT EMITTING

DIODE (LED)

INDUCTOR

RHEOSTAT

Temperature

Sensitive Resistor

VERTICAL BUSES:

The five holed buses numbered as 1, 2,…29,30…58,59,60,….120 in the fig. are called VERTICAL

BUSES. There is a metal strip on the back side of five holes in each vertical bus. Hence there is no

connection between 1 and 2 buses. This is same for all other vertical buses. Hence if we insert any

component lead in a vertical bus, the remaining four holes will come in contact with the component.

There are two rows of such vertical buses in the middle of the bread board in between the horizontal

buses. Vertical buses are used for inserting the components like resistors, capacitors and IC’s.

A bus is reserved for +ve of the power supply. C bus is reserved for -ve of the power supply,

this is also known as ground bus. If the circuit is complex and has many more power

supplies, say, a circuit may run with 18 V, 12 V and 9V power supplies with common ground

(-ve), we can use the B, E, F, D, G, H buses for those power points. Sometimes many

connections are made with a single power point. In that case we can join the A and E buses

with a (jumper) wire to use the entire top line as power bus +V RCCR. Similarly we can join C

and G buses for having a long ground bus. If the circuit is much more complex, then we join

two or more bread boards together to provide more space for the extra components. But the

rule of making a circuit is that its layout must be very clear and understandable to any other

person and at the same time it should use minimum space on the

bread board. COMPONENTS AND THEIR CIRCUIT SYMBOLS:

ZENER

DIODE

CAPACITOR (NON-ELECTROLYTIC)

NO POLARITY,

CAN BE USED

IN BOTH WAYS

CAPACITOR (ELECTROLYTIC)

HAS POLARITY

AMMETER

A +

_

_ +

MICRO AND MILLI -

AMMETERS

µA mA + + _ _

GALVANOMETER

G

PN JUNCTION DIODE

RESISTOR

(FIXED RESISTANCE)

POTENTIOMETER

(VARIABLE

RESISTANCE)



i1

i2

i3

B

D

10V

C

i

A

KIRCHHOFF’S LAWS (KCL AND KVL):

1. CURRENT RULE OR JUNCTION RULE (KCL): The

algebraic sum of all currents meeting at any junction (node) of a

circuit is zero. The convention of current direction is that the

current is positive if it moves towards the given node or junction

and it will be negative, if it moves away from the junction. Here iR1R

is positive as the current is approaching the node and the other

currents iR2R, iR3 Rare negative as they move away from the node.

2. VOLTAGE RULE OR LOOP RULE (KVL): The algebraic sum

of the voltage drops in any closed loop of the given

circuit is zero. It means, VRADR+VRBAR+VRCBR+VRDC R= 0.

VRADR means the potential at point A with respect to the

point D. So, VRADR= +10. Similarly V RDAR= –10.

Convention: Assume an arbitrary direction in the given

loop, i.e. say ABCD. If you are travelling from A to

B, the potential drop will be V RABR, equal to – VRDR, the

voltage drop across the diode in forward bias. This is

because the voltage at B is less than the voltage at A by a value equal to the forward cut – in

voltage of the diode (VRDR). Similarly from B to C, VRBCR=+ i RRLR (by using Ohm’s law). If you are

travelling from C to B, then it will be – i RRLR. Similarly, VRCDR= +VRCR, the voltage across the

capacitor. If the capacitor is charged, then the positive plate will be at high potential than the

negative plate by the value of applied voltage. Hence, the equation will be, +10 – VRD R– i RRLR+VRC

R= 0. If we travel from D to A along DCBA path, then the equation will be, –VRC R+ i RRLR+R RVRDR –10

= 0. Hence both equations are one and the same.

COLOUR CODES FOR CARBON RESISTORS



REFERENCE BOOKS:

1. ELECTRONIC DEVICES 9P

thP Ed; Thomas L. Floyd; Unit -2, Diodes and applications; Prentice

Hall publications. 2. ELECTRONIC DEVICES AND CIRCUITS; Jacob millman and Christos Halkias. Mc. Graw-

hill publications.

BROWN 1

BLACK 0

RED 2

Error: Gold ± 5%

Black - 0 Brown - 1 Red - 2 Orange - 3 Yellow - 4 Green - 5 Blue - 6 Violet - 7 Grey - 8 White - 9

Tolerance: (Error in the mentioned value of resistance) No colour : ± 20% Gold colour : ± 5% Silver colour : ± 10%

The first two colour bands represent the first two digits

Third colour band indicates the number of ZEROs.

Resistance of above resistor will be 10 with two zeros, i.e. 1000 Ω. Gold band indicates 5% error. i.e. ± 50Ω. Resistance will be (1000±50) Ω. If you measure the resistance you will find it lying between 950Ω and 1050Ω

B B R O Y of Great Britain has Very Good Wife



LEAST SQUARE FIT

(FITTING THE DATA TO A STRAIGHT LINE)

To fit the given data to a straight line the following process is to be adopted.

Define a parameter called Residue

∑

The standard deviation S of the data point (xRiR, yRiR) from its average value ( , ) will be

∑

To minimize the deviation with respect to the constants m and c to have a best fit,

After solving the equations we get

∑ ∑ ∑

and

∑ ∑ ∑

After solving for m and c gives

And

Where, refers to the average values of all xRi Rand yRiR respectively.

If the given function is a polynomial of the form y = x P

mP, then use natural logarithm to transform it in

to a linear equation containing logarithmic variables and proceed in the same manner as described

above.

θ error in θ

tan (θ) tan

(θ+0.5) tan

(θ- 0.5) % error in

tan θ

10 ±0.5 0.176327 0.185339 0.167343 5.103143

15 ±0.5 0.267949 0.277325 0.258618 3.490766

20 ±0.5 0.36397 0.373885 0.354119 2.715347

25 ±0.5 0.466308 0.476976 0.455726 2.278461

30 ±0.5 0.57735 0.589045 0.565773 2.015435

35 ±0.5 0.700208 0.713293 0.687281 1.857457

40 ±0.5 0.8391 0.854081 0.824336 1.772394

45 ±0.5 1 1.017607 0.982697 1.745506

50 ±0.5 1.191754 1.213097 1.17085 1.77249

55 ±0.5 1.428148 1.455009 1.401948 1.857676

60 ±0.5 1.732051 1.767494 1.697663 2.015844

65 ±0.5 2.144507 2.1943 2.096544 2.279222

70 ±0.5 2.747477 2.823913 2.674621 2.716881

75 ±0.5 3.732051 3.866713 3.605884 3.494454

80 ±0.5 5.671282 5.975764 5.395517 5.115662

∑

∑

ENGINEERING PHYSICS – II LAB ROLL NO:

G.V.P. COLLEGE OF ENGINEERING FOR WOMEN

Expt. No…………… Date: ……………….. BAND GAP OF EXTRINSIC SEMI CONDUCTOR USING PN JUNCTION DIODE

DATA SHEET Temperature In °C (TC)

T (Kelvin) = TC + 273

Current (I) µA

= ln(I)= ( )2

Total number of observations of made

N = Average

= Average

=

=

=



Expt. No…………… Date: ……………….. THERMISTOR CHARACTERISTICS

DATA SHEET Temperature

in 0 C Resistance

in Ω Temperature in K

Xi= 1/T (K-1)

Yi= ln R

Total number of observations of made N =

Average = Average

From TABLE:

B =

A = From GRAPH:



Expt. No…………… Date: ……………….. RC CIRCUIT – TIME CONSTANT

DATA SHEET CHARGING PROCESS Resistance R = Capacitance C =

RC (Theoretical) = Voltage of D.C. source V =

Time in sec

VOLTAGE ACROSS

CAPACITOR VC (in volt)

0

Time in sec

VOLTAGE ACROSS


FROM GRAPH:

TIME INTERVAL:

Slope of the graph:

Value from graph =



Expt. No…………… Date: ……………….. RC CIRCUIT – TIME CONSTANT

DATA SHEET DISCHARGING PROCESS Resistance R = Capacitance C =

RC (Theoretical) = Voltage of D.C. source V =

Time in sec

VOLTAGE ACROSS


0

Time in sec

VOLTAGE ACROSS


FROM GRAPH:

TIME INTERVAL:

Slope of the graph:

Value from graph =



Expt. No…………… Date: ……………….. ZENER DIODE DATA SHEET

FORWARD BIAS Current limiting resistor RS=

REVERSE BIAS Current limiting resistor RS=

Voltage (in volt) across

Am

met

er

Rea

ding

(SU

PPLY

)

ZEN

ER

DIO

DE

RES

ISTO

R

V VD VR ID (mA)

Voltage (in volt) across

Am

met

er

Rea

ding

(SU

PPLY

)

ZEN

ER

DIO

DE

RES

ISTO

R

V VD VR ID (mA)

FROM GRAPH: FORWARD BIAS CHARACTERISTICS: CUT – IN VOLTAGE (Vγ) : SLOPE OF V – I GRAPH IN FORWARD

BIAS FORWARD DYNAMIC RESISTANCE

Material of diode may be……………..

REVERSE BIAS CHARACTERISTICS: BREAK – DOWN VOLTAGE OR ZENER VOLTAGE (VZ): SLOPE OF V – I GRAPH IN BREAK –

DOWN REGION ZENER RESISTANCE IN BREAK – DOWN

REGION



Expt. No…………… Date: ……………….. STEWART AND GEE APPARATUS

DATA SHEET Current through the coil i = ……….. Ampere Horizontal component of earth’s field H = 0.38 Oersted Circumference of the coil = radius (a) =

Radius of the coil from the Graph =

Sl.

No Distance

x

Deflection magnetometer readings

Θ = tan θ

Bexp=

H tan θ BTh East West

Θ1 Θ2 Θ3 Θ4 ΘE Tan θE Θ5 Θ6 Θ7 Θ8 Θw Tan θW

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Engg Physics -II Record 1st March 2013

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