COMPENSATION THEOREM

Aim: To verify Compensation theorem.

Apparatus:

S.No Equipment Type Range Quantity

1. RESISTORS WW

2. MULTIMETER 0-20A

3. RPS 0-30V

4. BREADBOARD

5. Fuse TCC

6. CONNECTING WIRES

AS REQUIRED

Circuit Diagram:

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Theory: The compensation theorem states that any element in the network either linear or non linear may be replaced by a voltage source of magnitude

equal to the current passing through the element multiplied by the value of element provide the currents and voltages in other parts of the circuit remain unaltered.

Procedure:

1. Connections are made as per the circuit diagram. 2. Calculate valus of I, I1,∆I. 3. Current values are taken from the fig.

4. Compare theoretical and practical values. Observations:

parameter theoretical practical

I

I1

∆I

Model calculations:

From the fig:

I = V/R I1 = V/(∆R+R)

∆I = I- I1

Precautions:

1. All connections should be tight.

2. All reading should be taken with out parallax error. 3. Before giving are removing the connections, supply should be switched

off.

Result:

Thus the Compensation theorem is verified.

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MAXIMUM POWER TRANSFER THEOREM

Aim: To verify Maximum power transfer theorem.

Apparatus:

S.No Equipment Type Range Quantity

1. Voltmeter MI

2. Ammeter MI

3. Rheostats WW

4. Variacs 1-ф

5. Knife switches DPDT

6. Fuse TCC

Circuit diagram for Maximum Power Tranfer Theorem:

Theory:

In any linear network containing an independent voltage source in series with the resistance Rs or an independent current source in parallel with

a resistance rs, delivers maximum power to that load resistance RL for which RL = RS.

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Procedure for Maximum Power Transfer theorem: 1. Connections are made as per the circuit diagram.

2. 20V of input voltage is applied to the given circuit

3. By varying RL note down the corresponding VL , IL

4. Calculate the power in each case 5. Draw the graph between maximum power verses load resistance and

indicate the maximum.

Observations for Maximum Power Transfer Theorem:

S.No RL VL(V) IL(A) PL = VLIL(W)

1. 2. 3.

4. . .

.

.

.

.

Theoretical calculations:

Pmax =Vth

2/4Rth

Model Graph:

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Precautions: 4. All connections should be tight.

5. All reading should be taken with out parallax error. 6. Before giving are removing the connections, supply should be switched

off.

Result:

1. Maximum power was transferred when RL = _________(ohms) 2. Actual Source resistance RS = ________(ohms)

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RECIPROCITY & MILLIMAN’S THEOREMS

Aim:

a) To verify Reciprocity theorem. b) To verify Milliman’s theorem.

Apparatus:

S.No Equipment Type Range Quantity

1. Voltmeter MI

2. Ammeter MI

3. Rheostats WW

4. Variacs 1-ф

5. Knife switches DPDT

6. Fuse TCC

Circuit Diagram for Reciprocity Theorem:

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Circuit Diagram for Milliman’s Theorem:

Theory:

Reciprocity theorem: It states that in any linear network containing two or more sources, if we

apply some input to the circuit, the ratio of the response in any element to input is constant even when the position of the input and outputs are interchanged.

Milliman’s Theorem: This theorem states that when a number of voltage sources(V1, V2…..Vn)

are in parallel having internal resistances (R1, R2, R3…… Rn) respectively, the arrangement can be replaced by a single equivalent voltage source V in series with an equivalent series resistance R.

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Procedure for Reciprocity Theorem:

1. Connections are made as per the circuit diagram. 2. Keep the varic is in mnimum output position, supply is taken.

3. Keep the switch S1 is in position A and switch S2 is in position X, all meter readings are noted.

4. Keep the switch S1 is in position A and switch S2 is in position Y, all meter

readings are noted. 5. Keep the switch S1 is in position B and switch S2 is in position X, all

meter readings are noted.

Procedure for Milliman’s Theorem:

1. Connections are made as per the circuit diagram. 2. Keep the variacs in minimum output position and switch is in postion-2,

supply is taken. 3. Adjust the variac such that desired voltage is obtained. 4. Note down the meter readings.

5. Keep the switch is in open position, note down the meter readings. 6. Again keep the switch is in position-1, note down the meter readings.

Observations for Reciprocity Theorem:

S.No V1(V) I1(A) V2(V) I2(A) Test condition

1. Both sources are

active

2. Source 1 only active

3. Source 2 only active

Model Calculations:

V1 / I2

1 = ____________

V2 / I111 = _____________

Observations for Milliman’s theorem:

S.No V(V) I(A) Test condition

1. Switch is in position 2

2. Switch is in open position

3. Switch is in position 1

Model calculations:

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V = (± V1G1 ± V2G2 ±……..) / ( G1 + G2+….) R = 1 / ( G1 + G2 +……)

REQ = VOC / ISC Precautions:

7. All connections should be tight. 8. All reading should be taken with out parallax error.

9. Before giving are removing the connections, supply should be switched off.

Result: Thus Reciprocity Theorem and Milliman’s Theorem is verified .

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THEVENIN’S, NORTON’S AND MAXIMUM POWER TRANSFER THEOREM

Aim:

a) To verify Thevenin’s theorem.

b) To verify Norton’s theorem c) To verify Maximum power transfer theorem.

Apparatus:

S.No Equipment Type Range Quantity

1. Voltmeter MI

2. Ammeter MI

3. Rheostats WW

4. Variacs 1-ф

5. Knife switches DPDT

6. Fuse TCC

Circuit diagram for Thevenin’s & Norton’s Theorem:

Theory: Thevenin’s theorem:

Thevenin’s theorem states that any linear network with terminals could be replaced by a single voltage source Vth in series with a single

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resistance Rth. The Thevenin’s equivalent voltage Vth is the open circuit voltage measured at the terminals. The resistance Rth is the driving point

resistance of the network at the terminals when all the internal sources are set equal to zero.

Norton’s theorem: Norton’s theorem states that any linear active network with output

terminals can be replaced by a single current source in parallel with a single resistance. The Norton’s equivalent current source In is the current through a short circuit applied to terminals. The shunt resistance RN is the driving point

resistance of the network seen through the points when all the internal sources are set to zero.

Procedure fro Thevenin’s& Norton’s Theorems:

1. Connections are made as per the circuit diagram. 2. Keep the variac is in minimum output position and supply is taken. 3. Keeping the SPDT switch in position-1, supply is taken. Voltmeter and

Ammeter readings are noted. 4. Keeping the SPDT switch is in open position, Voltmeter readings are

noted. 5. Keeping the SPDT switch is in position-2, Ammeter readings are noted.

Observations for Thevenin’s & Norton’s theorems:

At Vs =

S.No I(A) V(V) Test condition

Load present

Load removed

Load is replaced by short

Rth = Voc / Isc = _____________ ohms

IL (From thevenin’s theorem) = Voc / ( Rth + RL) = ____________ Amps.

IL( From Norton’s theorem) = INRN / ( RN+ RL) = ____________ Amps.

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10. All connections should be tight. 11. All reading should be taken with out parallax error. 12. Before giving are removing the connections, supply should be switched

off. Result:

3. IL from Thevenin’s Theorem = _______________ (amps) 4. IL from Norton’s theorem = ___________(amps)

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