Bee Lab Manual

[email protected] Exp. No. 1 Date:

SERIES AND PARALLEL RESONANCE

AIM: To find the resonant frequency, quality factor, and band width of a series and parallel resonant circuit. Apparatus: S. No. 1 2 3 4 5

Apparatus Function generator Decade resistance box Decade inductance box Decade capacitance box Ammeter

Circuit Diagram: Series resonance:

Parallel resonance:

Range

Type

Quantity

Procedure: 1. Connect the circuit as shown in fig.1 for series resonant circuit & fig.2 for parallel resonant circuit. 2. Set the voltage of the signal from function generator to 5V. 3. Vary the frequency of the signal from 100 Hz to 1KHz in steps and note down the corresponding ammeter readings. 4. Observe that the current first increases & then decreases in case of series resonant circuit & the value of frequency corresponding to maximum current is equal to resonant frequency. 5. Observe that the current first decreases & then increases in case of parallel resonant circuit & the value of frequency corresponding to minimum current is equal to resonant frequency. 6. Draw a graph between frequency and current & calculate the values of bandwidth & quality factor. MODEL GRAPHs:

f1= lower cutoff frequency f2 = upper cutoff frequency fr=Resonating Frequency

Observation Table:Series Resonance S. No.

Frequency (Hz)

Current (mA)

1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. Observation Table:Parallel Resonance S. No. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18.

Frequency (Hz)

Current (mA)

19. 20.

Result:

Comments:

TIME RESPONSE OF FIRST ORDER RL/RC NETWORK

Exp. No. 2 Date:

Aim: To design and analyze RL/RC first order network circuit with short, medium and long time constants. Apparatus: S. No. 1. 2. 3. 4. 5.

Apparatus

Quantity

Circuit Board CRO BNC Adaptors Function Generator Patch Cards

Circuit Diagrams: R-L Network:

R =10KΩ 10 P-P 1KHz

Output L

Fig (a)

R-C Network:

1

C

10 P-P 1KHz

Fig (b)

Output

Procedure: 1. Connect the circuit as shown in the fig. (a) 2. Apply the square wave input of 10V P-P at 1KHz 3. Observe the output at short, medium and long time constants by choosing appropriate inductance 4. Repeat the same procedure for RC network shown in fig. (b) by choosing appropriate capacitance. 5. Plot the wave forms for both RL and RC for all cases

Wave forms:

Result:

Comments:

Circuit Diagram :

1 Port – 1 11

2 Network Network

Port - 2 21

Exp. No. 3 Date:

TWO PORT NETWORK PARAMETERS Aim: To find the Z & Y parameters of a two port network. Apparatus: S.No. 1 2 3 4

Apparatus Circuit board RPS Ammeter Voltmeter

Range

Type

Quantity

Procedure:Z – Parameters 1. Connect the circuit as shown in fig.

2. Open circuit port-2 (i.e I2 = 0 ) and measure V1,I2 and V2 and calculate Z11 & Z21 using the formulae

Z11 =

V1 I2 =0 I1

Z 21 =

V2 I2 =0 I1

3. To Measure Z12 and Z22, open circuit port-1 (i.e. I1=0) and measure V1, V2 and I2 and calculate Z12 & Z21 using the formulae

Z12 =

V1 I1 = 0 I2

Z 22 =

V2 I1 = 0 I2

Y – Parameters 1. Connect the circuit as shown in fig.

2. Short circuit port-2 (i.e V2 = 0 ) and measure V1, I1 & I2 and calculate Y11 & Y21 using the formulae

Y11 =

I1 V2 = 0 V1

Y21 =

I2 V2 = 0 V1

3. To Measure Y12 and Y22, short circuit port-1 (i.e. V1=0) and measure V2, I1 and I2 and calculate Y12 & Y22 using the formulae

Y12 =

Tabulation

I1 V1 = 0 V2

Y22 =

I2 V1 = 0 V2

S. No. 1. 2. 3. 4. 5. 6. 7. 8.

Parameter Z11 Z12 Z21 Z22 Y11 Y12 Y21 Y22

Theoretical Value

Practical Value

Result:

Comments:

Circuit Diagram:

Fig. 1

Fig. 2

Fig. 3

Tabulation: Parameters I1 I2 I

Theoretical Values

Practical Values

SUPERPOSITION THEOREM & RECIPROCITY THEOREM

Exp. No. 4 Date:

Aim: To verify the Superposition theorem and Reciprocity theorem. Apparatus: S. No. 1 2 3

Apparatus Circuit board RPS Ammeter

Range

Type

Quantity

SUPERPOSITION THEOREM: Statement: Superposition theorem states that "In any linear bilateral network containing two or more sources, the response in any element is equal to the algebraic sum of the responses caused by individual sources acting alone, while the other sources are non-operative i.e., while considering the effect of individual sources, other ideal voltage sources and ideal current sources in the network are replaced by short circuit and open circuit across their terminals”. Procedure: 1. Make the connections as shown in fig.1 and measure the current 'I'.

2. Short circuit E2 (assuming the internal resistance of E2 source to be zero) as shown in fig.2 and note down the current I1 when only E1 is acting.

3. Short circuit E1 (assuming the internal resistance of E1 source to be zero) as shown in fig. 3 and note down the current I2 when only E2 is acting.

4. By superposition theorem I = I1+I2.

Tabular column Circuit Diagram:

RECIPROCITY THEOREM Statement: Reciprocity theorem states that “In any linear, bilateral, single source network the ratio of excitation to response is constant even when their positions are interchanged”. Procedure: 1. Connect the circuit as shown in fig. 1. 2. Measure the current 'I’ in the branch CD. 3. Interchange voltage source and response as shown in fig.2 and note down

the

current in the branch AB. 4. Observe that the current is same in both the branches AB in Fig. 2 and CD in Fig. 1.

Tabular column: Parameters Before interchange After Interchange

V I V/I V I1 V/I1

Theoretical Values

Practical Values

Result:

Comments:

Given Circuit:

A Given Circuit B

Practical Circuit: A

Given Circuit

Fig. 1 Model Graphs: For DC Circuit:

‘P’ in Watts

For AC Circuit:

VRL

Exp. No. 5 Date:

MAXIMUM POWER TRANSFER THEOREM

Aim:- To verify the maximum power transfer theorem for DC & AC circuits. Apparatus: S. No. 1 2 3 4

Apparatus Ammeter Voltmeter Variable Resistor R.P.S

Range

Type

Quantity

Statement: DC Circuit: The maximum power transfer theorem states that “maximum power is delivered from a source resistance to a load resistance when the load resistance is equal to source resistance.” Rs = RL is the condition required for maximum power transfer. AC Circuit: a. The maximum power transfer theorem states that maximum power is delivered from a source impedance to load impedance when the load impedance is equal to the complex conjugate of the source impedance. b. The maximum power transfer theorem states that maximum power is delivered from a source impedance to load resistance when the load resistance is equal to the magnitude of the source impedance. Procedure: 1. Connect the circuit as per the practical circuit shown in fig.1 2. Vary the load resistance in steps and note down voltage across the load and current flowing through the circuit. 3. Calculate power delivered to the load by using formula P=V X l 4. Draw the graph between resistance and power (resistance on X- axis and power on Yaxis).

5. Verify the maximum power is delivered to the load when RL = Rs for DC * and RL = Zs for AC.

Tabular Column: (DC Circuit) R

VL

IL

P=VLIL

VL

IL

P=VLIL

Tabular Column: (AC Circuit) R

Theoretical Calculations Maximum Power = PMax = V2 / 4RL

Parameters D.C. Circuit A.C. Circuit

Theoretical Value (PMax)

Practical Value (PMax)

Result:

Comments:

Given Circuit Diagram:

A

Given Network B

Practical Circuit Diagram for Vth:

A V

B Fig. (1)

Practical Circuit Diagram for Rth:

A

Voltage & current sources are to be replaced by open ckt and short ckt respectively Fig (2)

A

V B

THEVENIN'S AND NORTON'S THEOREMS

Exp. No. 6 Date:

Aim: - To Verify Thevenin's and Norton's theorems. Apparatus:

S.No. 1 2 3

Apparatus Ammeter Voltmeter Circuit board

Range

Type

Quantity

Thevenin's theorem. Statement: - Thevenin's theorem states that “in any two terminal, linear, bilateral network having a number of voltage, current sources and resistances can be replaced by a simple equivalent circuit consisting of a single voltage source in series with a resistance, where the value of the voltage source is equal to the open circuit voltage across the two terminals of the network, and the resistance is the equivalent resistance measured between the terminals with all energy sources replaced by their internal resistances.” PROCEDURE: (a)

To find Vth

1. Connect the circuit as per the practical circuit. (Fig. 1) 2. Measure Voc between A and B terminals. (b) To find Rth 1. Connect the circuit as per the practical circuit (Fig. 2) 2. Replace the voltage and current sources by open circuit and short circuit respectively and connect a voltage source and series with an ammeter between the terminals A&B 3. Note down the ammeter readings for different voltages.

4. Calculate Rth = V/I 5. Draw the thevenins equivalent circuit

Tabular Column S. No.

V (volts)

I (mA)

R=V/I kΩ

Theoretical calculations

Given Circuit Diagram: A

Given Network B

Theoretical Calculations

A

Given Network

A

B

Practical Circuit Diagram for Rth:

A

Voltage & current sources are to be replaced by open ckt and short ckt respectively

A

V B

Norton's theorem:

Statement: Norton's theorem States that “in any two terminal, linear, bilateral network with current sources, voltage sources and resistances can be replaced by an equivalent circuit consisting of a current source in parallel with a resistance. The value of the current source is the short circuit current between the two terminals of the network and the resistance is the equivalent resistance measured between the terminals of the network with all the energy sources replaced by their internal resistances.” Procedure: (a) To find IN

1. Connect the circuit as per the practical circuit. (Fig. 1) 2. Measure the current Isc (or) IN through 'AB' by short-circuiting the resistance between A and B. (b) To find Rth

1. Connect the circuit as per the practical circuit (Fig.2) 2. Replace the voltage and current sources by open circuit and short circuit respectively and connect a voltage source and series with an ammeter between the terminals A&B

3. Note down the ammeter readings for different voltages. 4. Calculate Rth = V/I 5. Draw Norton's equivalent circuit.

Tabulation S. No.

V (volts)

I (mA)

Parameters Voc Isc RTH RN

Theoretical Values

R=V/I kΩ

Practical Values

Result:

Comments:

Circuit Diagram:

MOTOR

GENERATOR

Voltage : 230v

Voltage : Current :

Current :

Speed

Speed

Field Current :

:

Field Current :

Model Graph:

Circuit

:

MAGNETIZATION CHARACTERISTIC OF A DC GENERATOR

Exp. No. 7 Date:

Aim: To find critical field resistance of a separately excited DC generator from its open circuit characteristic. Apparatus Required: S.

Name of the Equipment

Range

Type

Quantity

No. 1.

Voltmeter

2.

Ammeter

3.

Rheostat

4.

Tachometer Potential Divider

5. Precautions:

a) Motor field rheostat must be kept in minimum resistance position. b) Potential divider must be kept in minimum potential position. c) Starter arm must be in OFF position. Procedure: 1) Connect the circuit as shown in the circuit diagram. 2) Observing the precautions close the DPST Switch and switch ON 220V DC supply. 3) Start the Motor-Generator set with the help of starter. 4) Adjust the speed of motor to a fixed value by adjusting field rheostat and maintain the speed constant throughout the experiment. 5) Increase the excitation of the generator in steps by adjusting the potential divider and note down the corresponding voltmeter readings. 6) Take the readings up to a value little higher than the rated voltage of the generator. 7) Again decrease the excitation in the same steps till field current is zero by adjusting the potential divider noting down the corresponding voltmeter readings. 8) Observing the precautions switch OFF the supply.

Tabulation: Speed of the Generator: S. No.

r.p.m.

If

Eg

Eg

(A)

(V)

(V)

(Increasing)

(Decreasing)

From Graph Critical field resistance, Rcf=

Result:

Circuit Diagram: Swinburne’s Test:

fig. (a) To find Armature Resistance:

fig. (b) Name Plate Details: Voltage : Current : Speed

:

Field Current : Model Graph:

Exp. No. 8

SWINBURNE’S TEST

Date:

Aim: To pre-determine the efficiency of a DC shunt machine when run both as generator and motor. Apparatus Required: S. No.

Name of the Equipment

1.

Voltmeter

2.

Ammeter

3.

Rheostat

4.

Tachometer

Range

Type

Quantity

Precautions: d) Field rheostat must be kept in minimum resistance position. e) Armature rheostat must be kept in maximum resistance position. Procedure: 1) Connect the circuit as shown in the circuit diagram. 2) Observing the precautions close the DPST Switch and switch ON 220V DC supply. 3) Start the Motor with the help of starter keeping the switch ‘S’ connected across the ammeter closed. 4) Adjust the speed of motor to it’s rated value by adjusting field and/or armature rheostats. 5) Now open the switch ‘S’ and note all the meter readings. 6) Observing the precautions switch OFF the supply. To find the armature and series field resistance: 1) Connect the circuit as shown in circuit diagram (fig.(b)) 2) Keeping the rheostat in its maximum resistance position close the DPST Switch and switch ON 220V DC supply. 3) By adjusting the rheostat for different values of current note down the meter readings. 4) Observing the precautions switch OFF the supply.

Tabulation: For Swinburne’s Test: Speed of the motor: S. NO.

r.p.m.

Supply voltage

Line current IL

Shunt current

(Volts)

(amps)

If (amps)

To find Armature resistance: S. No.

Va

Ia

Ra

(V)

(A)

(Ohms)

Average Ra Machine when run as Motor: S. No.

Voltage

IL

If

Ia

I.P

Wcu

WT

O.P

η=

(V)

(A)

(A)

(A)

(W)

(W)

(W)

(W)

0.P / I.P (%)

Machine when run as Generator: S. No.

Voltage

IL

If

Ia

O.P

Wcu

WT

I.P

η=

(V)

(A)

(A)

(A)

(W)

(W)

(W)

(W)

0.P / I.P (%)

Model Calculation: IL =

; If =

Ia = IL - If

;V=

= 2

Constant Loss, WC = V Х IL - Ia Х Ra

Reading No. Machine When run as Motor

IL =

; If =

Ia = IL - If

;V= =

Input = V Х IL = 2

CU Loss, WCU = Ia Х Ra = Total Loss, WT = WC + WCU = Output = Input - WT = Efficiency, η = 0.P / I.P = Machine When run as Motor

V=

; IL =

Ia = IL + If

; If = =

Output = V Х IL = 2

CU Loss, WCU = Ia Х Ra = Total Loss, WT = WC + WCU = Input = Output + WT = Efficiency, η = 0.P / I.P = Result:

Circuit Diagram:

Name Plate Details: Voltage : Current : Speed

:

Power

:

Field Current :

Model Graph:

BRAKE TEST ON DC SHUNT MOTOR

Exp. No. 9 Date:

Aim: To obtain the performance characteristics of DC shunt motor by direct loading. Apparatus Required: S. No. 1. 2. 3. 4.

Name of the Equipment

Range

Type

Quantity

Voltmeter Ammeter Rheostat Tachometer

Precautions: f)

Motor field rheostat must be kept in minimum resistance position.

g) Starter arm must be in OFF position.

Procedure: To conduct Load Test: 1) Connect the circuit as shown in circuit diagram. 2) Observing the precautions close the DPST Switch and switch ON 220V DC supply. 3) Start the motor with the help of starter. 4) Now load the motor in steps to its full-load and note down all the meter readings. 5) Observing the precautions switch OFF the supply.

Tabulation: For Load Test: Radius of Brake Drum: S.

VL

IL

Speed

Spring Balance

Torque

I.P

O.P

η

No.

(V)

(A)

(r.p.m.

readings

(N-m)

(KW)

(KW)

0.P / I.P

)

(Kgs) S1

S2

S1∼S2

(%)

Model Calculations: Reading No. V=

; IL =

;N=

;R=

Torque, T =

Input = V Х I = Output = (2 Х ∏ Х N Х T) / 60

Efficiency, η = 0.P / I.P =

Result:

; S1 =

; S2 =

Circuit Diagram: (a) OC Test

Name Plate Details 1Φ T/F: (b) SC Test

KVA

=

LV Voltage = HV Voltage = Frequency

MODEL GRAPHS:

=

Exp. No. 9 Date:

OC & SC TESTS ON SINGLE PHASE TRANSFORMER

Aim: (a) To predetermine the efficiency and regulation of Single Phase Transformer by conducting no-load test and short circuit test. (b) To draw the equivalent circuit of single phase transformer referred to LV side as well as HV side. Apparatus Required: S. No.

Name of the Equipment

1.

Single Phase Variac

2.

Ammeter

3.

Voltmeter

4.

Wattmeter

Range

Type

Quantity

Precautions: a) There should not be loose and wrong connections in the circuit b) Single phase auto transformer should be in minimum output voltage position c) Before making or breaking the circuit, supply must be switched OFF Procedure: 1)

Connect the circuit for O.C. test as per the circuit diagram.

2)

Keep the variac in minimum output voltage position and switch ON the supply.

3)

Apply the rated voltage to the transformer by properly adjusting the variac.

4)

Note down the readings of various meters and switch OFF the supply.

5)

Connect the circuit for SC test as per the circuit diagram, with appropriate ranges of meters.

6)

Keep the variac in minimum output voltage position and switch on the supply.

7)

Apply proper voltage (low voltage) to the transformer by adjusting the variac such that rated current flows through the transformer.

8)

Note down the readings of various meters and switch OFF the supply.

OC Test Observations S.No.

Vo (V)

Io (A)

Where M. F. = Multiplication factor =

Wo = W x M.F (w)

VI cos φ FSD

FSD  Full scale divisions SC Test Observations S.No.

VSC (V)

ISC (A)

WSC = W x M.F (w)

Equivalent Circuit of the Transformer:

(i)

(ii)

Referred to L.V. side

Referred to H.V. side

Calculations:

(a)Calculation of Equivalent circuit parameters: Let the transformer be the step-up transformer Primary is L. V. side.(V1) , Secondary is H. V. side (V2) (i) Parameters calculation from OC test

Wo = Vo I o

cos φ0 =

Iw = I0 cos φ0

I w1 = I w / K

=

=

V1 Iw

=

R01 = R0

Iμ = I0 sin φ0

=

I µ1 = I µ / K

=

X 01 = X 0

K2 =

R0 =

X0 =

K=

V1 Iµ

=

V2 V1

=

(ii) Parameters calculation from SC test

R02 =

Z 02 =

WSC I sc

=

2

VSC I SC

=

2

X 02 = Z 02 − R02

2

=

X 01 = X 02 / K 2

=

R01 = R02 / K 2

=

Z 01 = Z 02 / K 2

=

K2 =

Tabulation: (a) Efficiency at different loads and P.fs cos φ1 = ___________ S.No.

Load

Cu.loss (W)

cos φ2 = ___________

Output Input (W)

(W)

η

Xx

S.No.

Load

(%)

1.

¼F.L.

1.

¼F.L.

2.

½F.L.

2.

½F.L.

3.

¾F.L.

3.

¾F.L.

4.

F.L.

4.

F.L.

Cu.loss

Output

Input

η

(W)

(W)

(W)

(%)

(b) Regulation at full load

Lagging Pf S. No. 1. 2. 3. 4. 5. 6. 7.

P.F. 0.3 0.4 0.5 0.6 0.7 0.8 Unity

% Reg.

Leading Pf S. No. 1. 2. 3. 4. 5. 6. 7.

P. F. 0.3 0.4 0.5 0.6 0.7 0.8 Unity

% Reg.

(b) Calculations to find efficiency: For ½ full load Cupper losses = Wsc x (1/2)2 watts = where Wsc = full – load copper losses Constant losses = W0 watts = Output = ½ KVA x cos φ

=

Input = output + Cu. Loss + constant loss =

%

efficiency =

Output x 100 = Input

(c) Calculation of Regulation at full load:

I2 = Load (KVA) X 103 / V2 =

% Re gulation =

I 2 R02 cos φ ± I 2 X 02 sin φ x 100 = V2

‘+’ for lagging power factors ‘-‘ for leading power factors

Result:

Comments:

[cos φ may be assumed]

Circuit Diagram:

W1

3Φ IM Spring Balance V

I

W2

Name Plate Details: Power

=

Voltage

=

Current

=

Speed

=

Conn.

=

Type

=

Frequency =

MODEL GRAPH:

Brake Drum

BRAKE TEST ON THREE PHASE INDUCTION MOTOR

Exp. No. 11 Date:

AIM: To conduct brake test on the given 3 phase induction motor and to plot its performance characteristics. Apparatus Required: S. No.

Equipment

1.

3 Phase Variac

2.

Ammeter

3.

Voltmeter

4.

Wattmeter

5.

Tachometer

Range

Type

Quantity

Precautions: d) There should not be loose and wrong connections in the circuit e) Three phase auto transformer should be in minimum output voltage position f) Initially there should be no load on the motor g) Apply water into brake drum during operation to control the heat of the brake drum. h) Before making or breaking the circuit, supply must be switched OFF. Procedure: 1. Connect the circuit as per the circuit diagram. 2. Observing precautions, close the TPST switch. 3. Apply the rated voltage to the stator windings of 3 φ induction motor with the help of 3-phase auto transformer. 4. Note down the readings of all meters on no-load. 5. Load the induction motor in steps using the brake-drum arrangement. At each step note down the readings of all meters up to full load of the motor. 6. Gradually release the load and switch OFF the supply. 7. Using thread, measure the circumference of the brake-drum when motor is at rest.

Tabulation:

S. No.

Voltage V (volts)

Current I (Amps)

Wattmeter reading (W) MF = MF = W1

W2

Spring balance reading Speed N (rpm)

S1 Kg

S2 Kg

%Slip

Power factor

Torque N-m

Output Watts

η %

Model calculations: S. No.: Input power drawn by the motor W = (W1 + W2) watts = R  Radius of drum in meters = (Circumference of brake drum in mtrs) / 2 π = Shaft Torque, Tsh = 9.81 (S1 ~ S2) R N-m =

Output power in watts =

2 π N Tsh watts 60

=

% efficiency =

output power in watts x 100 Input power in watts

=

Ns =

120 x f p

% slip =

=

Ns − N x 100 Ns

= power factor of the induction motor

Result:

Comments:

cos φ =

W 3 VL I L

=

Circuit Diagram: (a) OC & SC Test

(b) Armature Resistance

Name Plate Details: Parameter Power Voltage Current Speed type Excitation Voltage Excitation Current P.F.

DC Motor

Alternator

REGULATION OF ALTERNATOR USING SYNCHRONOUS IMPEDANCE METHOD

Exp. No. 12 Date:

AIM: To pre-determine the regulation of a given three-phase alternator by conducting O. C. and S. C. tests by synchronous Impedance method (EMF method) Apparatus Required: S.No.

Equipment

1.

Tachometer

2.

Ammeter

3.

Voltmeter

4.

Rectifier

5.

Rheostat

Range

Type

Quantity

PROCEDURE: 1.

OC test: (i)

Connections are made as shown in the circuit diagram for OC & SC test.

(ii)

With the rectifier in the zero voltage position, TPST switch open and the rheostats in their proper positions, the d.c. supply to the motor is switched ON.

(iii)

The dc motor is brought to rated speed of the alternator by properly varying the field rheostat of motor.

(iv)

Now, the alternator field is excited by applying the dc voltage through the rectifier in steps. At each step, note down the field current and the corresponding generated voltage. This procedure is repeated till the voltage generated is much beyond rated value.

(v)

Reduce the alternator field excitation to zero level.

MODEL GRAPHS

Tabulation: a) OC & SC Test:

O. C. Test

S. C. Test

Speed = S.No.

xxxx

Field current

Phase voltage

(A)

(V)

Speed = S.No.

Field

Short circuit

current,

current (ISC), (A)

(If) (A)

2.

SC test (i)

with the rectifier in the minimum voltage position, the TPST switch is closed.

(ii)

Increase field excitation gradually till the S.C. current of the alternator reaches the rated current of alternator.

(iii)

Note down all the meter readings.

b) Armature Resistance: S.No.

I (A)

V (volts)

Rdc = V/I Ω

Percentage regulation at _______ load at different power factors Power factor (Cosφ)

E0 (V) Lagging

Leading

% Reg Lagging

Leading

Model Calculations: From Graph

ZS =

VOC for the same If and speed: = I SC

Ra = (1.6) RdC =

XS =

Z S2 − Ra2

=

Assume p.f. (CosΦ) = Assume armature current (Ia) = Generated emf of alternator on no load is

E0 =

( v cos φ

+ I a Ra )

2

+ ( v sin φ ± I a X S )

2

=

+ for lagging p.f. - for leading p.f. The percentage regulation of alternator for a given p.f. is

% Re g =

E0 −V x 100 = V

where E0 – Generated emf of alternator per phase voltage V – Full load, rated terminal voltage per phase.

Result:

Comments: