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
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
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
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
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%
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.
Vth = VA - VB = 6V
Rth=(2 3׀׀ )+ 10+2=13.2 Ω
Rth
2
3
2
10
Calculation of Vth and Rth:
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
Example: Evaluate RL for maximum power transfer and find the power
Calculation of RTH :
RL = RTH =6Ω
Calculation of VTH :
• 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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