DECCAN COLLEGE OF ENGINEERING & TECHNOLOGYdeccancollege.ac.in/EEE_LAB_MANUALS/IIIYRCANDM.pdf ·...

DECCAN COLLEGE OF ENGINEERING & TECHNOLOGY

(Nampally, Dar-us-Salam, Hyderabad)

Department of Electrical & Electronics Engineering

CIRCUITS & MEASUREMENT LAB MANUAL

for

BE - EEE & EIE- V Semester

Prepared by

Mrs. Shaziya Sultana, Assoc. Prof.

Ms. Roqayya Aimun, Asst. Prof.

Mr. Md Ahmeduddin Farooqi, Asst.Prof.

Mr. Shaik Mohammed Mukassir, Asst. Prof.

Mr. Mohd. shahabuddin, Lab Tech.

Approved by

Dr. Prof. Sardar Ali

Head of the department (EEE)

B.E. EEE V SEMESTER DCET CIRCUITS & MEASUREMENTS LAB MANUAL

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Name: ________________________________Roll No: ___________________

INDEX

S.No Date Name of the Experiment Page No Sign

1

Verification of KCL & KVL using Mesh and

Nodal Analysis

2

2

Verification of a) Thevenin’s Theorem

b)Norton’s Theorem c)Superposition

Theorem d)Max. Power transfer theorem

5

3

Open Circuit, Short and ABCD parameters

of two port parameters

15

4

Simulation of 2nd order RLC circuit using

PSPICE

21

5

Transient Response of RLC Circuits

25

6

Measurement of low resistance by Kelvin’s

Double Bridge

27

7

Measurement of Active, reactive power

measurement using two wattmeter method

29

8

Calibration of Single Phase Energy meter by

Phantom loading and measurement of power

direct loading

35

9

Measurement of a) Inductance by

Maxwell’s and Andersons Bridge b)

Measurement of Capacitance by DeSauty’s

Bridge

37

10

Use of DC Potentiometer for measurement

of unknown voltage and Impedance

40

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EXPERIMENT NO.1

VERIFICATION OF KIRCHHOFFS LAW (KCL AND KVL) USING MESH AND

NODAL ANALYSIS

AIM: - To verify Kirchhoff’s current law and Kirchhoff’s voltage law for the given

circuit using mesh and nodal analysis.

APPARATUS:-

Sl.No

. Apparatus Range Quantity

1 RPS (regulated power supply) (0-30V) 2

2 Resistance 2K, 2K 1k 6

3 Ammeter (0-30mA)MC 3

4 Voltmeter (0-30V)MC 3

5 Bread Board & Wires -- Required

Statement:

KCL: The algebraic sum of the currents meeting at a node is equal to zero.

KVL: In any closed path / mesh, the algebraic sum of all the voltages is zero.

Precautions:

1. Voltage control knob should be kept at minimum position.

2. Current control knob of RPS should be kept at maximum position.

Procedure for KCL:

1. Give the connections as per the circuit diagram.

2. Set a particular value in RPS.

3. Note down the corresponding ammeter reading

4. Repeat the same for different voltages

Procedure for KVL:


2. Set a particular value in RPS.

3. Note all the voltage reading

4. Repeat the same for different voltages


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Circuit - KCL

Circuit - KVL

KCL - Theoretical Values:

S.No.

Voltage

E

Current

I1=I2 + I3 I1 I2 I3

Volts mA mA mA

1 5

2 10

3 15

4 20

5 25


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KCL - Practical Values:

S.No.

Voltage

E

Current

I1=I2 + I3 I1 I2 I3

Volts mA mA mA

1 5

2 10

3 15

4 20

5 25

KVL – Theoretical Values

KVL E2=V2+V3

V

1 5 5

2 10 10

3 15 15

4 20 20

5 25 25

KVL - Practical Values

KVL E2=V2+V3

V

1 5 5

2 10 10

3 15 15

4 20 20

5 25 25

Model Calculations:

Result:Thus Kirchoff’s voltage load and Kirchoff’s current law verified both theoretically

and practically.


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EXPERIMENT NO.2

VERIFICATION OF (A) THEVENIN’S THEOREM (B) NORTON’S THEOREM

(C) SUPERPOSITION THEOREM (D) MAXIMUM POWER TRANSFER THEOREM

PART-1

AIM: - To verify Thevenin’s Theorem.

APPARATUS:-

S.No Apparatus Type Range Quantity

1 Regulated power supply - 0-30 Volts 1

2 Ammeter MC 0-20 mA 1

3 Voltmeter MC 0-20 Volts 1

4 Ohmmeter Digital 0-10 ohms 1

5 Circuit board - - 1

6 Decade resistance box - 0-10KΩ 1

7 Connecting wires - - As required

THEORY:-

THEVENIN’S THEOREM: -

Any linear bilateral network with respect to a pair of terminals may be replaced

by a voltage source Vth, where Vth is open circuit voltage (i.e. Voltage across the terminals

when RL is removed ) in series with resistance equal to Thevenin’s resistance Rth, where Rth

is the internal resistance of the network from terminals A and B with voltage sources

replaced by their internal resistances, if any , and current sources by infinite resistance. The

current flowing through a load Resistance RL connected across any two terminals A and B

of a linear, passive, bilateral network is given by

IL = Vth / (Rth + RL)

CIRCUIT DIAGRAM:

Fig. 1


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Fig. 2

Fig 3 Fig 4

PROCEDURE:-

1. Connect the circuit as shown in the diagram and apply suitable voltage, remove RLand.

note down the open circuit voltage (Vth) across terminals A & B. (Fig.2).

2. Connect the circuit as shown in Fig.3. And note the Thevenin’s Resistance Rth by

means of a multi meter (Ohm meter).

3. Connect the circuit as shown in Fig.1. For a particular value of load resistance RL,

keeping the voltage of RPS at the same value as in step 1, note the value of the current.

Verify the value obtained by applying the Thevenin’s theorem i.e. IL should be equal to

Vth/ (Rth + RL).

4. Repeat step 3, for various values of load resistances and compare with the calculated

values as obtained by applying Thevenin’s theorem.

5. Vary the input voltage and take three sets of readings (step 2. Need not be repeated as

long as the network is not changed).

6. Fig. 4 shows the Thevenin equivalent circuit with load resistor.


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THEORITICAL CALCULATIONS:-

Rth = 𝑅2 +𝑅1𝑅3

𝑅1+𝑅3 =

Vth = 𝑅3 * 𝑉𝑠

𝑅1+𝑅3 =

IL = 𝑉𝑡ℎ

𝑅𝑡ℎ+𝑅𝐿

OBSERVATIONS:-

Vs = 5 V; Vth = ______ volts; Rth = _____ Ω

S. No.

RL (Ω)

IL(mA)

Measured Value

IL = 𝑉𝑡ℎ

𝑅𝑡ℎ+𝑅𝐿 (mA)

(By applying theorem)

RESULT:- Thevenin’s Theorem is verified.


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PART-2

AIM: - To verify Norton’s Theorem

APPARATUS:-





4 Ohmmeter Digital 0-10 ohms 1




THEORY:-

NORTON’S THEOREM:

Any linear bilateral network with respect to a pair of terminals may be replaced by a current

source, whose value is equal to the current passing through it when short circuited, in

parallel with a resistance equal to the Thevenin’s resistance. Then the current through the

load resistance is given by

IL = Isc* 𝑅𝑁

𝑅𝑁+ 𝑅𝐿

CIRCUIT DIAGRAM:-

Fig.1

Fig. 2


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Fig. 3 Fig. 4

PROCEDURE:-

1. Connect the circuit as shown in Fig. 2. and applying suitable voltage through RPS.

Determine the short circuit current. ( Isc )

2. Connect the circuit as shown in Fig.1and note down the load currents for various

values of load resistance (RL) and compare with the theoretical values obtained

using Norton s equivalent circuit. ( Fig. 4)

3. Repeat step 1& 2 for various values of source voltages (Note RN obtained from

Fig. 3 is the same value as the one obtained in Thevenin’s equivalent circuit)

THEORITICAL CALCULATIONS:-

RN = 𝑅2 +𝑅1𝑅3

𝑅1+𝑅3 =

I = 𝑉𝑠

𝑅 =

ISC = 𝐼 ∗𝑅3

𝑅2+𝑅3 =

IL = ISC *

𝑅𝑁

𝑅𝑁+𝑅𝐿


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OBSERVATIONS:

Vs= 5 V; Isc = ______ m A; RN = ______ Ω

S.No

RLΩ

IL(mA)

(Measured Value)

IL = ISC * 𝑅𝑁

𝑅𝑁+𝑅𝐿 (mA)

(By applying theorem)

RESULT: - Norton’s Theorem is verified.

PART 3

AIM: - To verify superposition theorem.

APPARATUS:-






CIRCUITS DIAGRAM:

Fig 1


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Fig 2.

Fig 3

THEOREM:-

In a bilateral network consisting of a number of sources, the response in any

branch is equal to sum of responses due to individual sources taken one at a time with all

other sources reduced to zero. When a network consists of several sources, this theorem

helps us to find the current in any branch easily, considering only one source at a time.

PROCEDURE:-

1. Connect the circuit as shown in fig.1

2. Adjust the voltage of the RPS-1to 5V and that of RPS-2 to 10V. Note the current.

3. Disconnect RPS-2 and short the terminals. With source voltage (1) at 5V read the

Ammeter reading. (Fig, 2).

4. Disconnect RPS-1and short the terminals. With the source (2) Voltage at 10V read

the current

from the ammeter. (12) (Fig 3).

5. Verify the equation I = I1 + 12.

6. Repeat steps 2 to 5 for different voltages.


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OBSERVATIONS:

S.No V1 (volts)

V2 (volts) I (mA) I1 (mA) I2 (mA) I= I1 + I2

(mA)

RESULT: - Superposition theorem is verified.

PART-4

AIM: - To verify Maximum power transfer Theorem.

APPARATUS:-








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CIRCUIT DIAGRAM & EXPECTED GRAPH:

Fig. 1 Fig .2

THEOREM:-

A Resistance load absorb Maximum power from a network when its resistance

equals to the resistance of the network as viewed from the output terminals with all the

current and voltage sources removed leaving behind their internal resistance if any.

PROCEDURE:-

1. Connect the circuits as shown in the Fig. 1

2. Vary the load resistance RL from values lower than Ri and measure the current 1L

3. Calculate the power output in each case (P=1L2 RL )

4. Tabulate the reading of RL, IL and power P

5. Plot the curve RL v/s P (Refer fig. 2)

6. From the curve, observe that Maximum power occurs when RL= Ri.


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OBSERVATIONS:-

Ri = ______Ω .

S.No RL (Ω) IL (mA) P= IL2 RL(mW)

RESULT: -Maximum power transfer theorem is verified.


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EXPERIMENT NO. 3

OPEN-CIRCUIT, SHORT-CIRCUIT AND ABCD PARAMETERS OF TWO PORT

NETWORK

AIM: - To determine Z, Y, ABCD & h parameters for a two port network.

APPARATUS:-







THEORY:-

A Two port network (Fig. 1(a) & 1(b)) can be represented by

a. Open circuit impedance parameters (Z) or

b. Short circuit admittance parameters (Y) or

c. ABCD parameters or

d. Hybrid parameters.

Fig. 1(a) Fig. 1(b)

Then various input-output relationships between the voltages and currents may be

described by the following matrix equations.

a) [𝑉1

𝑉2]= [

𝑍11 𝑍12

𝑍21 𝑍22] [

𝐼1

𝐼2] b) [

𝐼1

𝐼2] = [

𝑌11 𝑌12

𝑌21 𝑌22] [

𝑉1

𝑉2]


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c) [𝑉1

𝐼2] = [

𝐴 𝐵𝐶 𝐷

] [𝑉2

−𝐼2] d) [

𝑉1

𝐼2] =[

ℎ11 ℎ12

ℎ21 ℎ22] [

𝐼1

𝑉2]

Any set of above four types of parameters may be used to describe the network as for as

it is as behavior at the external terminals are concerned.

DETERMINATION OF Z - PARAMETERS:

CIRCUIT DIAGRAM:

When input port is open circuited (I1 = 0)

Fig.2 (a)

S.No V1 Volts V2 Volts I1 mA I2 mA

1 5 V 0

2 10 V 0

When output port is open circuited (I2 = 0)


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Fig.2 (b)


1 5V 0

2 10V 0

Note: - In open circuit current will be zero.

PROCEDURE:-

1. Connect the circuit as shown in Fig. 2(a)

2. For different values of input voltages (V2), obtain the values V1, I2 with port 2 open

circuited. (I2 = 0)

3. Connect the circuit as shown in Fig. 2(b)

4. For different values of input voltages (V1), obtain the values V2, I1 with port 1 open

circuited. (I1 = 0)

CALCULATIONS:

Calculate the Z - parameters using the following relations.

Z11 = 𝑉1

𝐼1 when I2 = 0 Driving point impedance at port 1.

Z21 = 𝑉2

𝐼1 when I2 = 0 Transfer impedance

Z12 = 𝑉1

𝐼2 when I1= 0 Transfer impedance

Z22 = 𝑉2

𝐼2 when I1= 0 Driving point impedance port 2.

DETERMINATION OF Y – PARAMETERS:

CIRCUIT DIAGRAM:

When output port is short circuited (V2 = 0)


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Fig.3 (a)


1 5 V 0

2 10V 0

When input port is short circuited (V1 = 0)

Fig.3 (b)


1 0 5 V

2 0 10 V

Note: - In short circuit current will be zero.

PROCEDURE:

1. Connect the circuit as shown in Fig. 3(a)


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2. For different values of input voltages (V1), obtain the values I1, I2 with port 2 short

circuited. (V2 = 0)

3. Connect the circuit as shown in Fig. 3(b)

4. For different values of input voltages (V2), obtain the values I1, I2 with port 1 short

circuited. (V1 = 0)

CALCULATIONS:-

Caluculate Y- Parameters using the following relations.

Y11 = 𝐼1𝑉1

when V2 = 0 Short circuits during point admittance at

port 1.

Y21 = 𝐼2𝑉1

when V2 = 0 Transfer admittance.

Y12 = 𝐼1

𝑉2 when V1 = 0 Transfer admittance.

Y22 = 𝐼2

𝑉2 when V1 = 0 Driving point admittance at port 2.

CALCULATION OF ABCD PARAMETERS:

Obtain the ABCD parameters by using the following relation from the readings obtained

in

Z- parameters & Y-parameters

A = 𝑉1

𝑉2 when I2 = 0; B =

𝑉1

−𝐼2 when V2 = 0

C = 𝐼1

𝑉2 when I2 = 0; D =

𝐼1

−𝐼2 when V2 = 0

CALCULATIONS OF h – PARAMETERS:

Calculate the hybrid (h) parameters using the following relations from the readings

obtained in

Z- parameters& Y-parameters

h11 = 𝑉1

𝐼1 when V2 = 0; h12 =

𝑉1

𝑉2 when I1 = 0


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h21 = 𝐼2

𝐼1 when V2 = 0; h22 =

𝐼2

𝑉2 when I1 = 0

INFERENCE:

Verify the following relations for given passive, bilateral network for reciprocity.

Z12 = Z21; Y12 = Y21; h12 = -h21; AD – BC = 1.

RESULT: - Two port network parameters of the given network have been found.


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EXPERIMENT NO. 4

SIMULATION OF SECOND ORDER RLC CIRCUIT USING PSPICE

AIM: - The objective is to study the operation and characteristics of R-L-C series circuit for a

different input signals as stated in the problem.

THEORY: -

Applying KVL to the circuit we get

Vi (t) = i(t) R + L ∂i / ∂t + l/C∫ i ∂t--------(a)

Vo(t) = 1 / C ∫i∂t--------------------- (b)

Taking Laplace of equation a & b

T(s) = Vo(s) / Vi(s) = 1/ (S2 + (R/L)S + l/LC)

In case of series RLC circuit the damping factor is given by In the case of the series RLC

circuit, the

damping factor is given by,

For different values of damping ratio ζ we get the following plot


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The response is over damped for ζ >1

The response is under damped for ζ <1

The response is critically damped for ζ =1

Problem: - The R-L-C circuit R= 8 Ω, L=50UH and C=10UF use PSPICE to calculate and plot

the transient response from 0 to 400us.The capacitor voltages are the output which is to be

plotted. Simulate this for STEP, SINUSOIDAL inputs and input voltage magnitude is 10 volts

for Sinusoidal & 1 volts for Step.

SOFTWARE REQUIRED: - PSPICE

CIRCUIT DIAGRAM: -

With Step input With Sinusoidal input


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Program:

*RLC SERIES CIRCUIT WITH STEP INPUT*

VS 1 0 PWL(0 0 1NS 1V 1MS 1V)

.PARAM VAL=1

R 1 2 {VAL}

L 2 3 50UH

C 3 0 10UF

.STEP PARAM VAL LIST 1 2 8

.TRAN 1US 400US

.PROBE

.END

Note: -Decreasing resistance leads to oscillations


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*RLC SERIES CIRCUIT WITH SINUSOIDAL INPUT*

VIN 1 0 SIN(0 10V 5KHZ)

.PARAM VAL =1

R 1 2 {VAL}

L 2 3 50UH

C 3 0 10UF

.STEP PARAM VAL LIST 1 20 300

.TRAN 1US 400US

.PROBE

.END

PROCEDURE:

1. Choose the PSPICE schematic from the start menu.

2. Click on the Run Text Edit icon

3. Type the program and save it.

4. Go to PSpiceAD window and open the saved file. The file will be simulated & upon

successful simulation a window pops up saying “simulation completed successfully”.

Click OK.

5. If there exists errors make necessary corrections in program and run again.

6. Again in the PSpiceAD window go to File→ Run probe. (As Microsim probe window

pops up)

7. Click on Add trace and observe input waveform across V1 and output wave form across

capacitor (V1(C)) and I(C).

RESULT: Transient response of RLC Network has been obtained.


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EXPERIMENT NO. 5

TRANSIENT RESPONSE OF RLC CIRCUIT

AIM: To observe the time domain specification of second order system when subjected to

sudden disturbance of Input.

APARATUS: Signal generator, bread board, CRO, probes, RLC components, connecting

wires, resistors, capacitors, Inductance box, decade resistance box, decade capacitance box.

THEORY:

Peak Time (Tp): Time required for the response to reach the peak of time response or the peak

over shoot.

Rise Time:

It is the time required for the response to rise from 10% to 90% of the final value for the over

damped system and 0 to 100% of the final value for under damped system.

Delay Time:

It is the time required for the response to lead 50% of the final value in final attempt.

Peak Over Shoot:

It indicates the normalized difference between time response peak and the steady output peak

percent overshoot % Mp= C(tp)-C(α)/ C(tp) x100.

Settling Time:

Time Required for the response to reach and stay with in a specified tolerance band usually

2% to 5% of its final value.

CIRCUIT DIAGRAM :


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PROCEDURE:

1.Connect the circuit as per the circuit diagram shown

2.Give square wave or step wave input to the circuit.

3. Vary the inductance till the proper damped sinusoid is observed.

4.Observe the time response specifications on CRO (Voltage Waveform).

5. Repeat the same procedure for Sinusoidal input.

RESULT

Time domain specifications are verified for RLC Series Circuit.


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EXPERIMENT NO. 6

MEASUREMENT OF LOW RESISTANCE BY KELVIN’S DOUBLE

BRIDGE

AIM: - To determine resistance of a given wire using Kelvin’s double bridge.

APPARATUS:-


1 kelvin’s double bridge kit - - 1

2 Unknown Resistance - - 1


THEORY:-

In the figure shown below X = Resistor under test

S = Standard resistor

P, Q, p, q = Known inductive resistances (and one pair P and p or Q or q) is variable.

A current, preferably the rated current of resistor under test is passed through the

two resistors X and S from a low voltage, high current battery. A regulating rheostat and

an ammeter are connected for convenience only. A sensitive galvanometer G is connected

across the dividing points of PQ and pq. The P/Q ratio is kept same as p/q, these ratios are

being varied until the galvanometer reads zero. And hence the bridge is balanced and value

of unknown resistance is determined.

CIRCUIT DIAGRAM:-

PROCEDURE:-


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1. Connect one terminal of resistance to + C & the other terminal to – C.

2. Connect + C to + P & - C to – P with the leads provided.

3. Now choose a suitable range of multiplier.

4. Get the null point of galvanometer by pressing the push key only and by adjusting the

main dial and slide wire.

5. Get the value of resistance from the readings of multiplier, slide wire and ohms dials

TABULAR COLUMN:-

S.No.

Ratio dial

R(Ω)

Main dial

m(Ω)

Slide wire

s(Ω)

X = (s+m)R

(Ω)

FORMULA:- X = (s + m) R

PRECAUTIONS:-

1. The sensitivity knob of the galvanometer should be in shorted position when bridge is

unbalanced. it should be brought back to shorted position from direct position

immediately after obtaining balance.

2. Resistance R should be in maximum position to start with and adjusted later if necessary

to get large deflection.

RESULT: - The resistance of the given wire has been found using Kelvin’s double

bridge.


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EXPERIMENT NO. 7

MEASUREMENT OF ACTIVE, REACTIVE POWER

MEASUREMENTS BY USING TWO WATTMETER METHOD

Aim:

To measure the 3-phase active and reactive power by 2 – wattmeter method for resistance load.

Apparatus Required:

S.No. Apparatus Range Quantity

1 Voltmeter (0-600V) MI 1

2 Ammeter (0-20A) MI 1

3 Wattmeter 600V, 10A, UPF 2

4 Wattmeter 600V, 10A, LPF 2

Precautions:

•

•

THE TPST switch must be kept open

initially.

Load must not be applied while starting.

Procedure:


2. Give the supply by closing TPST switch.

3. Vary the resistance load and note down the corresponding readings.

Circuit Diagram:

Fig.1


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Tabular Column:

Result:

Thus Active and Reactive power was measured using Two wattmeter method.


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EXPERIMENT NO. 8

CALIBRATION OF SINGLE PHASE ENERGY METER BY

PHANTOM LOADING AND MEASUREMENT OF POWER BY

DIRECT LOADING

PART A:

AIM: - To determine the meter constant for a single phase energy meter by phantom loading

method

and also to find the creep time.

APPARATUS REQUIRED:-


1 Single phase Energy meter - 5A,220V 1

2 Wattmeter LPF 300V,10A A.C 1

3 Voltmeter MI 0-300 V 1

4 Ammeter MI 0-10 A 1

5 Variac - 0-270V 1

6 Phase shifting transformer - 220/240V,30A 1

7 Rheostat - 4.5Ω, 3A 2

8 Stop watch Analog - 1


THEORY:-

When the capacity of the meter to be tested is high, considerable power will be

wasted if ordinary loading arrangement is made. For testing of meter of higher capacities,

phantom or fictitious loading arrangement is employed in order to avoid wastage of power.

In phantom loading arrangement, the pressure circuit of the meter under test is energized

from a circuit of the required (normal) voltage and current circuit of the meter under test is

connected across a low voltage supply. Thus in this arrangement of load only a

comparatively small amount of power is required being equal to the sum of power supply

to the small pressure coil current at normal voltage and that due to load current at a low

voltage.

In case of testing of meter of high capacity while in service, the pressure circuit of

the meter is supplied from the line in the normal way while the current circuit of the meter

is removed from the consumer load circuit and supplied from the source of low voltage.


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CIRCUIT DIAGRAM: -

PROCEDURE:-

1. Make the connections as per circuit diagram.

2. Set the current coil such that rated current flows through it using the variac.

3. Adjust the phase shifting transformer till maximum reading on the watt meter is obtained.

This corresponds to unity power factor.

4. Find the time taken for 20 revolution of the disc using stop watch. Also note down the

values of wattmeter.

5. Repeat the procedure for a) Full load 0.5 P.F. b) Half load U.P.F c) Half load 0.5 P.F etc.

6. Also determine the creep time for energy meter (creep time is the time taken, if any, to

revolution on no load.


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TABULAR COLUMN:-

CALCULATIONS:-

Meter Constant K= (N*3600*1000)/ (w*t) Revolutions/Kwh

Creep time= _________________ Seconds for one revolution.

RESULT: - The meter constant for a single phase energy meter by phantom loading method

and also the creep time has been found.

PART B:

Aim: Measurement of power By Direct Loading

Apparatus Required:

S.No. Apparatus Specification Quality

1 Voltmeter

2 Ammeter

3 Wattmeter

4 Lamp Load

5 Energy Meter

Theory:

The Process of comparing of an Instrument with Standard or absolute instrument is called

calibration. The energy meter records the energy consumed in KWH. Let Rx be the number of

revolutions of the disc. Kx is the revolution per KWH(meter constant).

S.No.

P.F

V

(Volts)

I

(Amps)

W

(Watts)

Time for

5

revolution

Meter Constant

K= N*3600*1000 (rev/kwh)

( W*t)

1.

2.

3.

4.

5.


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Recorded Energy= Rx/ Kx KWH

The true energy= w/m reating * Time

% error=((recorded energy-true energy)/true energy) x100.

PROCEDURE

1. Connections are made as per the circuit diagram

2. Keep the autotransformer at minimum position and switch on the supply

3. Adjust the autotransformer to the rated voltage of the energy meter

4. Adjust the load to a suitable value and note the corresponding w/m reading and time taken for

5 revolution of energy meter disc

5. Repeat the step no 4 after increasing the load

6. Tabulate the readings and calculate the %error RESULT Sl No Apparatus Specification

Quantity 1 2 3 4 5 Voltmeter Ammeter Wattmeter Lamp load Energy meter Calibrated the given

single phase energy meter by direct loading at UPF and plotted the error curve.


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RESULT

Calibrated the given single phase energy meter by direct loading at UPF and plotted the error curve and the power has been measured by direct loading using single phase energy meter.


36 | P a g e

EXPERIMENT NO. 9

(a) MEASUREMENT OF INDUCTANCE BY MAXWELL’S AND

ANDERSON’S BRIDGE

(b) MEASUREMENT OF CAPACITANCE BY DE SUATY’S BRIDGE

Part (a)

(i) MAXWELL’S BRIDGE

AIM: - To determine the unknown inductance using Maxwell’s bridge.

APPARATUS:-


1 Maxwell Inductance capacitance

bridge

- - 1

2 Unknown Inductance - - 1

3 Head phones - - 1

4 Oscillator - 1Khz 1


THEORY:-

In this bridge, Self Inductance is measured in terms of standard variable capacitance.

The Bridge is suitable for low Q values less than 10. The connections and phasor diagrams

are shown below.

In the diagram

L1 = Unknown Inductance, R1 = Effective resistance of L1, R4 = Known non

inductive.

Resistance in the form of 3 decades of 10x 10, 10x100 & 10x 1k ohms.

C4 is a standard accurately calibrated 3-decade capacitance. Balance is obtained by varying

R4 & C4 alternately. At balance

L1 = R2R3 C4 Henrys; If R2 = R3 = 1 K ohm each.

L1 = C4 Henries if C4 is in micro farads.


37 | P a g e

CIRCUIT DIAGRAM& PHASOR DIAGRAM:-

Separating the real and imaginary terms, we have

R1 = R2R3 and L1 = R2 R3 C4

R4

Thus we have two variables R4 and C4, which appear, in one of the two balance equations

and hence the two equations are independent and balance is obtained by varying R4 & C4

alternately.

The expression for Q factor Q= ωL1 /R1 + ωC4 R4

PROCEDURE:-

1. Make the connections for oscillator, Head phones and unknown inductance.

2. By varying R4 and C4 get minimum sound in the headphone.

3. Get the value of unknown inductance by using the formula

L = R2.R3.C4 and dial readings of R4& C4.


38 | P a g e

TABULAR COLUMN: -

S.No R2 (Ω) R3 (Ω) C4 (μF) L1 (H)

RESULT: - By using Maxwell’s bridge the value of unknown inductance has been found.

(ii) ANDERSON’S BRIDGE FOR SELF – INDUCTANCE

AIM:- To determine the value of self – inductance using Anderson’s bridge.

APPARATUS:-


1 Anderson bridge kit - - 1

2 Unknown Inductance - - 1

3 Head phones - - 1



THEORY:-

This bridge is very common for measurement of self-inductance in term of standard

capacitance and non-inductive resistance. An audio frequency oscillator of say 1000 CPS

and a variable output of 10 Volts is used as a source as a sources of supply.

A pair of headphone of good sensitivity is used as a detector in the bridge network.


39 | P a g e

CIRCUIT DIAGRAM& PHASOR DIAGRAM:-

P = 1000Ω, Q = 1000Ω, R = 1000Ω.

BRIDGE ARMS:

P = Non –Inductive resistance of 1000 ohms

Q = Non Inductive resistance of 1000 ohms

R =Non Inductive resistance of 1000 ohms

S = A variable non- inductive resistance in the form of 3 decades of 10x1, 10x 10, 10x100

ohms.

This resistance also includes the resistance of Self – inductance L which is also connected

in the same arm.

m = A non – inductive variable resistance of 3 decades of 10x10, 10x100,10x 1000 ohm.

C = A standard capacitance in the form of 5 values of 0.002, 0.005, 0.01, 0.02,0.05 mf

selected by a selector switch.

PROCEDURE:-

1. Connect an audio oscillator and head phone to proper terminals.

2. Select a certain value of C say equal to .01 mfd.

3. Vary s & m values to get minimum in the headphones.

4. Calculate the value of L using the formula.

5. Repeat the above two steps for value of inductance.

FORMULA: - L = C [RQ + (R + S ) m]


40 | P a g e

PRECAUTIONS:-

1. The value of capacity C should be small so as to allow sufficient variation of m.

2. In all calculations, the value of S should include the resistance of self-inductance

3. There cannot be perfect silence in the headphone; only minimum of sound should be

tried for.

4. The experiment should be performed at silent place.

5. Numerical value of L should be greater than CRQ if m is to be positive.

TABULAR COLUMN:

S.NO P(Ω) Q(Ω) R(Ω) S(Ω) m(Ω) C(mF) L(H)

RESULT: - By using Anderson’s bridge the value of self-inductance has been found.

PART (b):

DE SAUTY’S BRIDGE

AIM: - To determine the unknown capacitance using De Sauty’s bridge.

APPARATUS: -


1 Desauty’s bridge - - 1

2 Unknown Capacitance - - 1

3 Head phones - - 1



THEORY:-

This bridge is used to determine the unknown capacitance by comparing it with

known standard capacitor. The circuit shown below has


41 | P a g e

C1= Capacitor under test

C2= Standard Capacitor

R1& R2 = known inductive resistances.

The bridge is balanced by adjustment of either R1 or R2. At balanced condition

I1R1= I2R2-----------------(1) &−𝑗

𝜔𝐶1I1=

−𝑗

𝜔𝐶2I2------- (2)

Dividing (1) by (2) we get C2 = R1 / R2 * C1

CIRCUIT DIAGRAM:-

PROCEDURE:-

1. Make the connections for Oscillator, Head phones, unknown capacitance.

2. Adjust the voltage to 5v, 1 kHz on audio oscillator.

3. Adjust C1, to some value.

4. Now vary R3 & R4 alternately to get minimum sound on head phone.

5. Get the value of unknown capacitance using the formula R3 / R4 & dial reading or R3,

R4 & C1.

TABULAR COLUMN:-


42 | P a g e

S.No R3(Ω) R4(Ω) C2 (μf) C1 (μf)

FORMULA: - C1 = (R4 / R3) * C2

RESULT: - By using De Sauty’s bridge the value of unknown capacitance has been found.


43 | P a g e

EXPERIMENT NO. 10

USE OF DC POTENTIOMETER FOR MEASUREMENT FOR

MEASUREMENT OF UNKNOWN VOLTAGE AND IMPEDANCE

AIM: - To calibrate the given voltmeter by DC Potentiometer

APPARATUS:-


1 DC Potentiometer - - 1

2 Galvanometer - - 1

3 DC power supply - 2 Volts 1

4 Standard Cell - - 1

5 Rheostat - 4.5Ω 1


THEORY:-

For calibration of voltmeter a potential divider of a high resistance is connected

across high voltage dc supply main as shown in fig. 1. The voltmeter under calibration is

connected across this potential divider in such a way that the potential difference across

the voltmeter can be varied. The volt-ratio box is connected in parallel with voltmeter under

calibration to reduce the voltage across them to a value, which is within the range of

potentiometer. Now this reduced potential difference is measured on the potentiometer.

The potential difference measured on the potentiometer multiplied by the ratio of volt-ratio

box gives the actual potential difference across the voltmeter under calibration, to which

the instrument reading can be compared.

CIRCUIT DIAGRAM:-

Fig.1


44 | P a g e

Fig. 2

PROCEDURE:-

1. Connect the circuit diagram as shown in fig.

2. Switch on the power supply and adjust it to 2 V by keeping the potentiometer in zero

position.

3. Switch on the standard cell. Adjust the potentiometer to the standard cell voltage.

4. Standardized the potentiometer as follows

Press standardized switch and obtain null deflection in the galvanometer by

Varying fine, coarse controls in the potentiometer circuit.

5. Without disturbing the above adjustment, the unknown voltage is connected to test

terminals.

TABULAR COLUMN:-

RESULT: - Hence the calibration of Voltmeter by DC Potentiometer has been performed.

S.No Voltmeter reading

( Volts)

D.CVoltageReading

(from Potentiometer)

(Volts)

Error = Voltmeter reading-

potentiometer reading

(Volts)

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