Maximum Power Transfer Theorem: Statement: Maximum Power Transfer Theorem states that “maximum...

17
Maximum Power Transfer Theorem: Statement: Maximum Power Transfer Theorem states that “maximum power is transferred from the source to the load when the load resistance is equal to the Thevenin’s equivalent resistance”. i.e, R L = R TH

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Transcript of Maximum Power Transfer Theorem: Statement: Maximum Power Transfer Theorem states that “maximum...

Page 1: Maximum Power Transfer Theorem: Statement: Maximum Power Transfer Theorem states that “maximum power is transferred from the source to the load when the.

Maximum Power Transfer Theorem:

Statement: Maximum Power Transfer Theorem states that “maximum power is transferred from the source to the load when the load resistance is equal to the Thevenin’s equivalent resistance”.

i.e, RL = RTH

Page 2: Maximum Power Transfer Theorem: Statement: Maximum Power Transfer Theorem states that “maximum power is transferred from the source to the load when the.

Proof:

1...............

,

LTH

TH

RR

VI

Here

and

2.................2LRIP

Substitute the value of I,

2

22

)( LTH

LTHL

LTH

TH

RR

RVR

RR

VP

Page 3: Maximum Power Transfer Theorem: Statement: Maximum Power Transfer Theorem states that “maximum power is transferred from the source to the load when the.

For max power,

4

222

)(

)(2)(0

LTH

LTHLTHTHLTH

L RR

RRRVVRR

dR

dP

0)(

)(2)(

4

222

LTH

LTHLTHTHLTH

L RR

RRRVVRR

dR

dPor

THL

LLTH

LTHLTHTHLTH

RRor

RRR

RRRVVRRor

2)(

)(2)( 222

Page 4: Maximum Power Transfer Theorem: Statement: Maximum Power Transfer Theorem states that “maximum power is transferred from the source to the load when the.

Now, maximum power transfer is given by

)(max

2

2

22

LL

LTHL

LTH

TH

RR

RVR

RR

VP

inputting

L

TH

R

V

4

2

Page 5: Maximum Power Transfer Theorem: Statement: Maximum Power Transfer Theorem states that “maximum power is transferred from the source to the load when the.
Page 6: Maximum Power Transfer Theorem: Statement: Maximum Power Transfer Theorem states that “maximum power is transferred from the source to the load when the.

Output power=I2RL

Input power= I2RTh

η = o/p power / (o/p power+i/p power)

=I2RL / I2(RL+RTh)

For max efficiency RL=RTh

Hence efficiency η = RL/(2RL)*100= 50%

Page 7: Maximum Power Transfer Theorem: Statement: Maximum Power Transfer Theorem states that “maximum power is transferred from the source to the load when the.

Example

3Ω

2Ω

10V

10Ω

RL

2Ω

Evaluate RL for maximum power transfer and find the power

Note: To solve a question for maximum power transfer, the thevenin equivalent needs to be calculated.

Page 8: Maximum Power Transfer Theorem: Statement: Maximum Power Transfer Theorem states that “maximum power is transferred from the source to the load when the.

Vth = VA - VB = 6V

Rth=(2 3׀׀ )+ 10+2=13.2 Ω

Rth

2

3

2

10

Calculation of Vth and Rth:

Page 9: Maximum Power Transfer Theorem: Statement: Maximum Power Transfer Theorem states that “maximum power is transferred from the source to the load when the.

13.2

6V RL

Thevenin’s equivalent circuit

RL should be set to 13.2Ω to get max. power transfer

Max. power is WRth

Vth68.0

2.13*4

)6(

4

22

Page 10: Maximum Power Transfer Theorem: Statement: Maximum Power Transfer Theorem states that “maximum power is transferred from the source to the load when the.
Page 11: Maximum Power Transfer Theorem: Statement: Maximum Power Transfer Theorem states that “maximum power is transferred from the source to the load when the.
Page 12: Maximum Power Transfer Theorem: Statement: Maximum Power Transfer Theorem states that “maximum power is transferred from the source to the load when the.
Page 13: Maximum Power Transfer Theorem: Statement: Maximum Power Transfer Theorem states that “maximum power is transferred from the source to the load when the.

Example: Evaluate RL for maximum power transfer and find the power

Page 14: Maximum Power Transfer Theorem: Statement: Maximum Power Transfer Theorem states that “maximum power is transferred from the source to the load when the.

Calculation of RTH :

RL = RTH =6Ω

Page 15: Maximum Power Transfer Theorem: Statement: Maximum Power Transfer Theorem states that “maximum power is transferred from the source to the load when the.

Calculation of VTH :

Page 16: Maximum Power Transfer Theorem: Statement: Maximum Power Transfer Theorem states that “maximum power is transferred from the source to the load when the.
Page 17: Maximum Power Transfer Theorem: Statement: Maximum Power Transfer Theorem states that “maximum power is transferred from the source to the load when the.

• RL must equal to RTh = 6 ohms• The maximum power transferred=

6*4

8.64

4

22

L

Th

R

V


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