The Maximum Power Transfer Theorem states that maximum power is transferred to a load when the load resistance equals the Thevenin equivalent resistance of the circuit. The document outlines the theorem's proof, steps for application, efficiency calculations, and real-world applications such as in audio systems and automobile engines, while also noting its limitations in efficiency, typically capping at 50%. It emphasizes that the theorem is not suitable for applications where higher efficiency is critical.

1. Topic – Maximum Power
Transfer Theorem
PowerPoint Presentation by:- Mohit

2. Content
• Maximum power transfer theorem for DC circuit
• Proof
• Steps for solving network using maximum power
transfer theorem
• Example
• Efficiency
• Applications
• Limitations

3. Maximum Power Transfer
Theorem for DC Circuit
• Maximum power transfer theorem states that the
maximum power will be transferred to the load
when the value of load resistance is equal to
thevenin’s equivalent resistance of the circuit.
• Now, thevenin’s equivalent resistance is nothing
but the equivalent of the circuit, seen through
load by turning off all the independent sources in
the electrical circuit.

4. • Lets consider a DC circuit in which load resistance is
connected.
• Now, for the above circuit maximum power transfer
to the load RL when the value of load resistance RL =
Rth ( Thevenins’s equivalent resisatnce )

5. Proof :-
• Let consider a circuit with load resistance RL and
current I is flowing.
• Current through the load,
IL = Vth / RL + Rth
• P will be,
P = I2 RL = ( Vth / RL + Rth )2 . RL …………(1)

6. • Power will be maximum if dP/dRL = 0
d/dRL ( Vth / RL + Rth )2 . RL = 0
Vth
2 [( RL + Rth )2 - 2RL ( RL + Rth ) / (RL + Rth )4 ] = 0
( RL + Rth )2 - 2RL ( RL + Rth ) = 0
( RL + Rth )2 = 2RL ( RL + Rth )
RL + Rth = 2RL
Rth = RL ………….(2)
Equivalent resistance = load resistance
• We conclude that for maximum power transfer
theorem, the load resistance RL must be equal to
the internal resistance of source i.e. Rth .
• From above proof, if we put RL = Rth in eqn 1
• We get, Pmax = Vth
2 / 4Rth

7. Steps for solving network using
maximum power transfer theorem :-
• Remove the load resistance of the circuit.
• Find the thevenin’s resistance ( Rth ) by applying
thevenin theorem.
• As per the maximum power transfer theorem,
this Rth is the load resistance of the network, i.e.
RL = Rth that allow the maximum power to
transfer .
• Maximum power is calculate by,
Pmax = Vth
2 / 4Rth

8. Example : Find the value of R for
maximum power transfer in network.

9. • Let’s remove the load from the network and find the
eqn .
• Resistance of the network by turning off all the
independent sources i.e. V source will get short
circuited and I source will get open circuited.
• Hence, the circuit
• Rth = ( 5 II 20 ) + 4
= 4 + 4
= 8 Ω
• According to maximum power transfer theorem
Rth = RL
So, RL = 8 Ω

10. Efficiency :
• η(efficiency) as the fraction of power dissolved through the
load R to power extended with source Vth , then
η = Pmax / P * 100
where
Pmax = Vth
2 / 4Rth
(P) Power supplied is
P = 2 Vth
2 / 4Rth = Vth
2 / 2Rth
η = ½ * 100 = 50 %

11. Application of Maximum power
transfer theorem :-
• Audio System Speaker : In audio system we
require that maximum amount of power from the
audio amplifier should get transfer to the
speaker.

12. • Automobile engine : In automobile engines, the
power transmitted to the motor stator of
automobile will depend on the effective
resistance of the motor and the batteries inner
resistance. When the two resistance are
equivalent, then the highest power will be
transmitted to the motor to activate the engine.
• Radio transmission system : In radio transmission
also we want that maximum amount of power
from power amplifier should get transfer to
antenna.

13. LIMITATIONS :
• Maximum power transfer theorem gets efficiency
of only 50%. So, it is not well in application
where efficiency is more corcern.
• Like in use of power system , there efficiency is
more concerned than output power.